This PDF file contains the front matter associated with SPIE Proceedings Volume 9064, including the Title Page, Copyright information, Table of Contents, and Conference Committee listing.

Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

Characterization of dolomitic limestone rock is presented using linear and nonlinear ultrasonic approaches. The linear approach is based upon the concept of complex moduli, which is estimated using ultrasonic dilatational and shear phase velocity measurements and the corresponding attenuations. The nonlinear approach is based upon noncollinear wave mixing, involving mixing of two dilatational waves. Criteria were used to assure that the detected scattered wave originated via wave interaction in the limestone and not from nonlinearities in the testing equipment. These criteria included frequency and propagating direction of the resultant scattered wave, and the time-of-flight separation between the two primary waves and the resulting scattered wave. Three cases of non-collinear interaction of two longitudinal waves are presented and discussed including one that requires only access to a plane surface of the stone test sample.

Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.

Fatigue crack is one of the main culprits for the failure of metallic structures. Recently, it has been shown that nonlinear wave modulation spectroscopy (NWMS) is effective in detecting nonlinear mechanisms produced by fatigue crack. In this study, an active wireless sensor node for fatigue crack detection is developed based on NWMS. Using PZT transducers attached to a target structure, ultrasonic waves at two distinctive frequencies are generated, and their modulation due to fatigue crack formation is detected using another PZT transducer. Furthermore, a reference-free NWMS algorithm is developed so that fatigue crack can be detected without relying on history data of the structure with minimal parameter adjustment by the end users. The algorithm is embedded into FPGA, and the diagnosis is transmitted to a base station using a commercial wireless communication system. The whole design of the sensor node is fulfilled in a low power working strategy. Finally, an experimental verification has been performed using aluminum plate specimens to show the feasibility of the developed active wireless NWMS sensor node.

In Lamb wave based techniques for damage detection, Piezoelectric Wafer (PW) transducers are often used for actuating Lamb wave. They offer advantages such as portability and, cost effectiveness. However, because of prolonged use, excessive voltage supply, or improper bonding onto the host structure, these PW actuators may get partially debonded from the host structure. In this paper, the nonlinear effect of this debonding on the behavior of Lamb wave manifested in the form of higher harmonics, is studied both experimentally and through Finite Element (FE) simulation. Augmented Lagrangian algorithm is used in FE simulation to solve the contact problem at the breathing debond. Three higher harmonics are observed in the experiments and also in the FE simulation. Morlet wavelet transform is implemented in the study for time-frequency analysis and the results are reported in the paper. Nonlinearity parameter β obtained from fundamental and second harmonics in the experiments and the simulation, is found to be increasing with increase in the debonding area. This shows that actuator debonding produces contact nonlinearity and thereby induces higher harmonics in the Lamb wave. Therefore, in damage detection using Lamb wave based nonlinear techniques, the higher harmonics produced may get influenced by the false higher harmonics produced by actuator debonding, leading to incorrect results. Also these false higher harmonics resulting from actuator debonding may show illusory presence of defect in a pristine material, if bonding of the actuator is not taken care of properly.

Streicker Bridge is a pedestrian bridge on the Princeton University campus. It consists of a main span and four curved continuous girders (legs). The main span and the southeast leg of the bridge are equipped with fiber optic strain and temperature sensors, allowing the bridge to also function as an on-campus laboratory for the Structural Health Monitoring research group. Parallel sensors were embedded at critical cross-sections in the deck prior to the pouring of concrete. The deck of the southeast leg experienced early age cracking within a few days of concrete pouring, which was detected by the strain sensors. Post-tensioning was then performed and it is assumed that it closed off the cracks. Evaluation of post-tensioning forces is complex due to the existence of the cracks, and this paper researches a procedure to estimate the post-tensioning forces at cracked and uncracked locations. The obtained post-tensioning forces were compared to design forces and conclusions regarding the status of post-tensioning were made. This is important as it gives information on the actual health condition and performance of the structure. It also provides information on the safety of the structure. The objective of this paper is to present a methodology for the evaluation of the post-tensioning force along the deck based on strain measurements. The monitoring system, results, data analysis method, and conclusions regarding the bridge health condition and performance are presented in this paper.

Structural Health Monitoring (SHM) systems help to monitor critical infrastructures (bridges, tunnels, etc.) remotely and provide up-to-date information about their physical condition. In addition, it helps to predict the structure’s life and required maintenance in a cost-efficient way. Typically, inspection data gives insight in the structural health. The global structural behavior, and predominantly the structural loading, is generally measured with vibration and strain sensors. Acoustic emission sensors are more and more used for measuring global crack activity near critical locations. In this paper, we present a procedure for local structural health monitoring by applying Anomaly Detection (AD) on strain sensor data for sensors that are applied in expected crack path. Sensor data is analyzed by automatic anomaly detection in order to find crack activity at an early stage. This approach targets the monitoring of critical structural locations, such as welds, near which strain sensors can be applied during construction and/or locations with limited inspection possibilities during structural operation. We investigate several anomaly detection techniques to detect changes in statistical properties, indicating structural degradation. The most effective one is a novel polynomial fitting technique, which tracks slow changes in sensor data. Our approach has been tested on a representative test structure (bridge deck) in a lab environment, under constant and variable amplitude fatigue loading. In both cases, the evolving cracks at the monitored locations were successfully detected, autonomously, by our AD monitoring tool.

We propose dynamic response based condition assessment of prestressed box beam (PSBB) bridges that will be more realistic and cost-efficient. The hypothesis includes that the dynamic response is a sensitive indicator of the physical integrity and condition of a structure. We deployed two wireless sensor networks for collecting the real-time dynamic response of a 25-year old PSBB bridge under trucks with variable loads and speeds. The dynamic response of the bridge at its newest condition was collected from FE simulations of its 3-D FE models mimicking field conditions. The FE model was validated using experimental and theoretical methods. We used Fast Fourier Transform and peak-picking method to determine peak amplitudes and their corresponding fundamental frequencies at its newest and current condition. The analyses interestingly indicate a 37% reduction in its fundamental frequency over a 25-year service life. This reduction has been correlated to its current visual inspection to develop application software for quick and efficient condition assessment of PSBB bridges. The research outcome will provide an efficient and cost-effective solution for bridge inspection and maintenance.

We propose a method for load rating of prestressed box beam (PSBB) bridges based on their dynamic response collected using wireless sensor networks (WSNs). The hypothesis includes that the health of a bridge is associated with its vibration signatures. We deployed two WSNs on a 25-year old PSBB bridge, and ran trucks with variable loads and speeds for collecting its real-time dynamic response at current condition. We also performed FE simulations of 3-D bridge models under vehicular loads to acquire the representative dynamic response at its newest condition. We validated the bridge model by field testing and numerical analysis. We used Fast Fourier Transform and peak-picking algorithms to find maximum peak amplitudes and their corresponding frequencies. We calculated the in-service stiffness of the bridge to determine its load rating, which resembles the actual load rating of the bridge. The application software developed from this research can instantly determine the load rating of a PSBB bridge by collecting its real-time dynamic response. The research outcome will help reduce bridge maintenance costs and increase public safety.

Guided wavefield detection is at the basis of a number of promising techniques for the identification and the characterization of damage in plate structures. Among the processing techniques proposed, the estimation of instantaneous and local wavenumbers can lead to effective metrics that quantify the extent of delaminations in composite plates. This paper illustrates the application of instantaneous and local wavenumber damage quantification techniques for high frequency guided wave interrogation. The proposed methodologies can be considered as first steps towards a hybrid structural health monitoring/ nondestructive evaluation approach for damage assessment in composites.

The application of Carbon Fibre Reinforced Polymers (CFRP) in aeronautics has been increasing. The CFRP elements are joint using rivets and adhesive bonding. The reliability of the bonding limits the use of adhesive bonding for primary aircraft structures, therefore it is important to assess the bond quality. The performance of adhesive bonds depends on the physico-chemical properties of the adhered surfaces. This research is focused on characterization of surfaces before bonding. In-situ examination of large surface materials, determine the group of methods that are preferred. The analytical methods should be non-destructive, enabling large surface analysis in relatively short time. In this work a spectroscopic method was tested that can be potentially applied for surface analysis. Four cases of surface condition were investigated that can be encountered either in the manufacturing process or during aircraft service. The first case is related to contamination of CFRP surface with hydraulic fluid. This fluid reacts with water forming a phosphoric acid that can etch the CFRP. Second considered case was related to silicone-based release agent contamination. These agents are used during the moulding process of composite panels. Third case involved moisture content in CFRP. Moisture content lowers the adhesion quality and leads to reduced performance of CFRP resulting in reduced performance of the adhesive bond. The last case concentrated on heat damage of CFRP. It was shown that laser induced fluorescence method can be useful for non-destructive evaluation of CFRP surface and some of the investigated contaminants can be easily detected.

The work deals with the reduction of numerical dispersion in simulations of wave propagation in solids. The phenomenon of numerical dispersion naturally results from time and spatial discretization present in a numerical model of mechanical continuum. Although discretization itself makes possible to model wave propagation in structures with complicated geometries and made of different materials, it inevitably causes simulation errors when improper time and length scales are chosen for the simulations domains. Therefore, by definition, any characteristic parameter for spatial and time resolution must create limitations on maximal wavenumber and frequency for a numerical model. It should be however noted that expected increase of the model quality and its functionality in terms of affordable wavenumbers, frequencies and speeds should not be achieved merely by denser mesh and reduced time integration step. The computational cost would be simply unacceptable. The authors present a nonlocal finite difference scheme with the coefficients calculated applying a Fourier series, which allows for considerable reduction of numerical dispersion. There are presented the results of analyses for 2D models, with isotropic and anisotropic materials, fulfilling the planar stress state. Reduced numerical dispersion is shown in the dispersion surfaces for longitudinal and shear waves propagating for different directions with respect to the mesh orientation and without dramatic increase of required number of nonlocal interactions. A case with the propagation of longitudinal wave in composite material is studied with given referential solution of the initial value problem for verification of the time-domain outcomes. The work gives a perspective of modeling of any type of real material dispersion according to measurements and with assumed accuracy.

The achievement and the maintenance of dental implant stability are prerequisites for the long-term success of the osseointegration process. Since implant stability occurs at different stages, it is clinically required to monitor an implant over time, i.e. between the surgery and the placement of the artificial tooth. In this framework, non-invasive tests able to assess the degree of osseointegration are necessary. In this paper, the electromechanical impedance (EMI) method is proposed to monitor the stability of dental implants. A 3D finite element model of a piezoceramic transducer (PZT) bonded to a dental implant placed into the bone was created, considering the presence of a bone-implant interface subjected to Young’s modulus change. The numerical model was validated experimentally by testing bovine bone samples. The EMI response of a PZT, bonded to the abutment screwed to implants inserted to the bone, was measured. To simulate the osseointegration process a pulp canal sealer was used to secure the implant to the bone. It was found that the PZT’s admittance is sensitive to the stiffness variation of the bone-implant interface. The results show that EMIbased method is able (i) to evaluate the material properties around the implant, and (ii) to promote a novel non-invasive monitoring of dental implant surgical procedure.

This paper describes the development of an optical three-dimensional controller. A typical 3D controller consists of a two dimensional controller with a superfluous secondary controller for its third dimension. These 3D controllers have a severely limited operating range and do not allow the user to move simultaneously in three dimensions. In the past, controllers commonly used potentiometers to detect movement; this component limits the operating range as the sensors must be fixed to a point. The proposed optical controller incorporates all three dimensions into a single controller allowing for further utility while decreasing complexity for its user. The use of an optical controller would be advantageous in terms of its size and weight as many mechanical and electrical components in traditional controllers would be eliminated. The optical controller could be used for precision controlling in many circumstances because of its direct mapping to 3D systems.

Structural health monitoring (SHM) systems provide real-time damage and performance information for civil, aerospace, and mechanical infrastructure through analysis of structural response measurements. The supervised learning methodology for data-driven SHM involves computation of low-dimensional, damage-sensitive features from raw measurement data that are then used in conjunction with machine learning algorithms to detect, classify, and quantify damage states. However, these systems often suffer from performance degradation in real-world applications due to varying operational and environmental conditions. Probabilistic approaches to robust SHM system design suffer from incomplete knowledge of all conditions a system will experience over its lifetime. Info-gap decision theory enables nonprobabilistic evaluation of the robustness of competing models and systems in a variety of decision making applications. Previous work employed info-gap models to handle feature uncertainty when selecting various components of a supervised learning system, namely features from a pre-selected family and classifiers. In this work, the info-gap framework is extended to robust feature design and classifier selection for general time series classification through an efficient, interval arithmetic implementation of an info-gap data model. Experimental results are presented for a damage type classification problem on a ball bearing in a rotating machine. The info-gap framework in conjunction with an evolutionary feature design system allows for fully automated design of a time series classifier to meet performance requirements under maximum allowable uncertainty.

The blades are crucial components of a wind turbine, and its steady and reliable operation is directly related to the power output. Thus, condition monitoring and fault diagnosis of the wind turbine blades is highly beneficial to the operational cost. This paper presents a study of small horizontal axis wind turbine blade rotational speed measurement by laser Doppler velocimeter based on dual-core photonic crystal fiber (DC-PCF). The theory on the DC-PCF Doppler velocimeter is presented, and the measurement system is designed and tested. Experimental results show that the DC-PCF Doppler velocimeter has been proved to work successfully. The uncertainty of the rotational speed is about 0 ~ 4 rpm. The accuracy can meet the requirements for monitoring the rotational operation of the wind turbine.

X-ray radiography is an important and frequently used NDE method of testing metal structures, such as tube welding quality, cracks and voids in cast iron or other metals. It gives fast and visible answer for structural defects. The Varian high energy portal imagers on Clinacs used in cancer treatment were tested for this purpose. We compared the traditional Gadox (LANEX) screen with and without a 1mm Cu buildup plate as used clinically. We also tested different hybrid scintillators, which consisted of different phosphor layers deposited onto fiberoptic plates. The last screen tested was a 2cm thick fiberoptic plate which contained scintillating fibers. The sensitivity (ADU = number of digital counts per a given X-ray dose), the resolution (MTF – modulation transfer function) and the DQE (detective quantum efficiency) were compared, with a 1 MV source, for these X-ray conversion screens. We found that the additional 1mm Cu plate, which improves the absorption and the contrast at 6 or higher energy MeV imaging, does not improve the image quality at 1MV. Rather it attenuates the X-rays, resulting in lower sensitivity and a lower DQE(0) of 2.2% with the additional Cu plate compared to DQE(0) of ~4% without the Cu plate. The hybrid scintillators with evaporated phosphors on fiberoptic plates tested were too thin resulting in low sensitivity. The best results were obtained from the thick scintillating fiberoptic screens, which provided the best DQE and high resolution with the 1MV X-ray beam. Further optimization is planned by changing the thickness of the scintillating fiber optic plate.

This work investigates the problem of anomaly detection by means of an agnostic inference strategy based on the concepts of spatial saliency and data sparsity. Specifically, it addresses the implementation and experimental validation aspects of a salient feature extraction methodology that was recently proposed for laser-based diagnostics and leverages the wavefield spatial reconstruction capability offered by scanning laser vibrometers. The methodology consists of two steps. The first is a spatiotemporal windowing strategy designed to partition the structural domain in small sub-domains and replicate impinging wave conditions at each location. The second is the construction of a low-rank-plus-outlier model of the regional data set using principal component analysis. Regions are labeled salient when their behavior does not belong to a common low-dimensional subspace that successfully describes the typical behavior of the anomaly-free portion of the surrounding medium. The most at­ tractive feature of this method is that it requires virtually no knowledge of the structural and material properties of the medium. This property makes it a powerful diagnostic tool for the inspection of media with pronounced heterogeneity or with unknown or unreliable material property distributions, e.g., as a result of severe material degradation over large portions of their domain.

Curvature mode shape is an effective feature for damage detection in beams. However, it is susceptible to measurement noise, easily impairing its advantage of sensitivity to damage. To deal with this deficiency, this study formulates an improved curvature mode shape for multiple damage detection in beams based on integrating a wavelet transform (WT) and a Teager energy operator (TEO). The improved curvature mode shape, termed the WT - TEO curvature mode shape, has inherent capabilities of immunity to noise and sensitivity to damage. The proposed method is experimentally validated by identifying multiple cracks in cantilever steel beams with the mode shapes acquired using a scanning laser vibrometer. The results demonstrate that the improved curvature mode shape can identify multiple damage accurately and reliably, and it is fairly robust to measurement noise.

This paper develops a new vibration based damage detection method to identify the location and severity of structural damage of periodically time-varying systems. The frequency response function (FRF) shifts induced by cracks are utilized to detect the location, depth and orientation angle of open transverse cracks on a shaft-disk system. The dynamical model of system is built based on the Lagrange principle and the assumed mode method while the crack model for periodically time-varying systems is based on the fracture mechanics. This method provides the advantages of arbitrary interrogation frequency and multiple inputs/outputs which greatly enriches the dataset for damage identification. The method is synthesized via harmonic balance and numerical examples for a shaft/disk system to demonstrate the effectiveness in detecting both location and severity of the structural damage.

Fatigue assessment includes estimation of the expected damage accumulation and the remaining life-time of the structure. This work is based on output-only vibration measurements at a limited number of locations provided by a sensor network installed on the structure. For the fatigue damage assessment, the stress time responses are obtained by using the vibration sensor data and a modal expansion approach enabling predictions of stresses at positions where sensor installation is not possible. A methodology for the prediction of stresses based on the combination of a finite element numerical model and the accelerations recorded at measurement locations is presented in this paper.

It is well known that the dynamic properties of a structure such as natural frequencies depend not only on damage but also on environmental condition (e.g., temperature). The variation in dynamic characteristics of a structure due to environmental condition may mask damage of the structure. Without taking the change of environmental condition into account, false-positive or false-negative damage diagnosis may occur so that structural health monitoring becomes unreliable. In order to address this problem, an approach to construct a regression model based on structural responses considering environmental factors has been usually used by many researchers. The key to success of this approach is the formulation between the input and output variables of the regression model to take into account the environmental variations. However, it is quite challenging to determine proper environmental variables and measurement locations in advance for fully representing the relationship between the structural responses and the environmental variations. One alternative (i.e., novelty detection) is to remove the variations caused by environmental factors from the structural responses by using multivariate statistical analysis (e.g., principal component analysis (PCA), factor analysis, etc.). The success of this method is deeply depending on the accuracy of the description of normal condition. Generally, there is no prior information on normal condition during data acquisition, so that the normal condition is determined by subjective perspective with human-intervention. The proposed method is a novel adaptive multivariate statistical analysis for monitoring of structural damage detection under environmental change. One advantage of this method is the ability of a generative learning to capture the intrinsic characteristics of the normal condition. The proposed method is tested on numerically simulated data for a range of noise in measurement under environmental variation. A comparative study with conventional methods (i.e., fixed reference scheme) demonstrates the superior performance of the proposed method for structural damage detection.

In this paper, a vibration testing and health monitoring system based on an impulse response excited by laser-induced breakdown is proposed to detect damage on membrane structure. A health monitoring apparatus is developed with this vibration testing system and damage detecting algorithm which only requires the vibration mode shape of the damaged membrane. The vibration mode shapes of the membrane structure are analyzed by using 2-D continuous wavelet transform, and applying boundary treatment and the concept of iso-surface. The effectiveness of the present approach is verified by finite element analysis and experimental results, demonstrating the ability of the method to detect and identify the location of damages.

The University of California at San Diego (UCSD), under a Federal Railroad Administration (FRA) Office of Research and Development (R&D) grant, is developing a system for high-speed and non-contact rail integrity evaluation. A prototype using an ultrasonic air-coupled guided wave signal generation and air-coupled signal detection, in pair with a real-time statistical analysis algorithm, is under development. Experimental tests results, carried out at the UCSD Rail Defect Farm, indicate that the prototype is able to detect internal rail defects with high reliability. Extensions of the system are planned to add rail surface characterization to the internal rail defect detection.

We present a non-destructive inspection method for the structural health monitoring of underwater structures. A laser operating at 532 nm is used to excite leaky guided waves on an aluminum plate immersed in water. The plate has a few artificial defects namely vertical notch, horizontal notch, corrosion, and small hole. An array of five immersion transducers arranged in half-circle is used to detect the propagating waves. A signal processing technique is implemented to assess the presence of damage; the method is based on continuous wavelet transform to extract a few damagesensitive features fed to an artificial neural network for damage classification. The experimental results show that the proposed system can be employed for the inspection of underwater plates.

Electromechanical impedance is a popular diagnostic method for assessing structural conditions at high frequencies. It has been utilized, and shown utility, in aeronautic, space, naval, civil, mechanical, and other types of structures. By contrast, fiber optic sensing initially found its niche in static strain measurement and low frequency structural dynamic testing. Any low frequency limitations of the fiber optic sensing, however, are mainly governed by its hardware elements. As hardware improves, so does the bandwidth (frequency range * number of sensors) provided by the appropriate enabling fiber optic sensor interrogation system. In this contribution we demonstrate simultaneous high frequency measurements using fiber optic and electromechanical impedance structural health monitoring technologies. A laboratory specimen imitating an aircraft wing structure, incorporating surfaces with adjustable boundary conditions, was instrumented with piezoelectric and fiber optic sensors. Experiments were conducted at different structural boundary conditions associated with deterioration of structural health. High frequency dynamic responses were collected at multiple locations on a laboratory wing specimen and conclusions were drawn about correspondence between structural damage and dynamic signatures as well as correlation between electromechanical impedance and fiber optic sensors spectra. Theoretical investigation of the effect of boundary conditions on electromechanical impedance spectra is presented and connection to low frequency structural dynamics is suggested. It is envisioned that acquisition of high frequency structural dynamic responses with multiple fiber optic sensors may open new diagnostic capabilities for fiber optic sensing technologies.

The paper focuses on the further development of the model of the electromechanical impedance (EMI) of the piezoceramics transducer (PZT) and its application for aircraft structural health monitoring (SHM). There was obtained an expression of the electromechanical impedance common to any dimension of models (1D, 2D, 3D), and directly independent from imposed constraints. Determination of the dynamic response of the system "host structure - PZT", which is crucial for the practical application supposes the use of modal analysis. This allows to get a general tool to determine EMI regardless of the specific features of a particular application. Earlier there was considered the technology of separate determination of the dynamic response for the PZT and the structural element”. Here another version that involves the joint modal analysis of the entire system "host structure - PZT" is presented. As a result, the dynamic response is obtained in the form of modal decomposition of transducer mechanical strains. The use of models for the free and constrained transducer, analysis of the impact of the adhesive layer to the EMI is demonstrated. In all cases there was analyzed the influence of the dimension of the model (2D and 3D). The validity of the model is confirmed by experimental studies. Correlation between the fatigue crack length in a thin-walled Al plate and EMI of embedded PZT was simulated and compared with test result.

The local interaction simulation approach (LISA), a finite difference based numerical method, has been proven to be efficient in modeling guided wave (GW) propagation in isotropic and composite laminated structures. Recently, the LISA framework has been augmented to incorporate the piezoelectric material directly in the formulation so to more accurately model the transducer effects in the GW generation. This paper presents a study to assess the importance of the actuation modeling from surface-mounted piezoelectric actuators in LISA. Actuation modeling includes the prescribed displacements (either in plane or out of plane) that are commonly found in the literature, as well as the direct modeling of the piezoelectric material of the actuator with prescribed electric potentials. The study is carried out both for isotropic and composite laminated substrates. Numerical and experimental results are used to characterize the quality of the actuator modeling options.

This paper discusses combined transfer matrix method (TMM) with stiffness matrix method (SMM) for obtaining a stable solution for dispersion curves of Lamb wave propagation in non-isotropic layers. TMM developed by Thomson and Haskell experiences numerical deficiency at high frequency thickness simulations. SMM was proposed by different researchers to solve the instability issue of TMM. This study shows that stable SMM is good at high frequencies, and TMM needs to be combined with SMM to obtain stable and robust behavior over the frequency range. Numerical simulations of dispersion curves are presented for wave propagation in orthotropic unidirectional fiber composites and cross ply composites. The paper ends with conclusions and future work.

This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.

This paper illustrates a Human-Machine Interface based on Augmented Reality (AR) conceived to provide to maintenance operators the results of an impact detection methodology. In particular, the implemented tool dynamically interacts with a head portable visualization device allowing the inspector to see the estimated impact position on the structure. The impact detection methodology combines the signals collected by a network of piezosensors bonded on the structure to be monitored. Then a signal processing algorithm is applied to compensate for dispersion the acquired guided waves. The compensated waveforms yield to a robust estimation of guided waves difference in distance of propagation (DDOP), used to feed hyperbolic algorithms for impact location determination. The output of the impact methodology is passed to an AR visualization technology that is meant to support the inspector during the on-field inspection/diagnosis as well as the maintenance operations. The inspector, in fact, can see interactively in real time the impact data directly on the surface of the structure. Here the proposed approach is tested on the engine cowling of a Cessna 150 general aviation airplane. Preliminary results confirm the feasibility of the method and its exploitability in maintenance practice.

Vibroacoustic three-dimensional finite element simulations are performed to validate a novel formulation that model leaky guided waves properties for waveguides surrounded by fluids. The above formulation couples a mesh of semi-analytical finite elements (SAFE), to discretize the waveguide cross-section, with a mesh of boundary elements (BEM) to model the unbounded outer fluid domain. The resulting dispersion curves are validated through dedicated finite element simulations where the extracted time-transient waveforms are analyzed via a modified Matrix Pencil Method in time and space. Wave simulations are achieved using ABAQUS/Explicit for an elastic steel bar of square cross section immersed in water and the results obtained are compared with those given by the SAFE-BEM method.

In this study, a correlation-based imaging technique called "Excitelet" is used to monitor an aerospace grade aluminum plate, representative of an aircraft component. The principle is based on ultrasonic guided wave generation and sensing using three piezoceramic (PZT) transducers, and measurement of reflections induced by potential defects. The method uses a propagation model to correlate measured signals with a bank of signals and imaging is performed using a roundrobin procedure (Full-Matrix Capture). The formulation compares two models for the complex transducer dynamics: one where the shear stress at the tip of the PZT is considered to vary as a function of the frequency generated, and one where the PZT is discretized in order to consider the shear distribution under the PZT. This method allows taking into account the transducer dynamics and finite dimensions, multi-modal and dispersive characteristics of the material and complex interactions between guided wave and damages. Experimental validation has been conducted on an aerospace grade aluminum joint instrumented with three circular PZTs of 10 mm diameter. A magnet, acting as a reflector, is used in order to simulate a local reflection in the structure. It is demonstrated that the defect can be accurately detected and localized. The two models proposed are compared to the classical pin-force model, using narrow and broad-band excitations. The results demonstrate the potential of the proposed imaging techniques for damage monitoring of aerospace structures considering improved models for guided wave generation and propagation.

In aircraft industry the Carbon Fiber Reinforced Polymer (CFRP) elements are joint using rivets and adhesive bonding. The reliability of the bonding limits the use of adhesive bonding for primary aircraft structures, therefore it is important to assess the bond quality. The performance of adhesive bonds depends on the physico-chemical properties of the adhered surfaces. The contamination leading to weak bonds may have various origin and be caused by moisture, release agent, hydraulic fluid, fuel, poor curing of adhesive and so on. In this research three different causes of possible weak bonds were selected for the investigation: 1. Weak bond due to release agent contamination, 2. Weak bond due to moisture contamination, 3. Weak bond due to poor curing of the adhesive. In order to assess the bond quality electromechanical impedance (EMI) technique was selected and investigation was focused on the influence of bond quality on electrical impedance of piezoelectric transducer. The piezoelectric transducer was mounted at the middle of each sample surface. Measurements were conducted using HIOKI Impedance Analyzer IM3570. Using the impedance analyzer the electrical parameters were measured for wide frequency band. Due to piezoelectric effect the electrical response of a piezoelectric transducer is related to mechanical response of the sample to which the transducers is attached. The impedance spectra were investigated in order to find indication of the weak bonds. These spectra were compared with measurements for reference sample using indexes proposed in order to assess the bond quality.

A sensor diagnostic and validation process that performs in-situ monitoring of the operational status of piezoelectric (PZT) active-sensors in structural health monitoring (SHM) applications is presented. The basis of this process is to track the changes in the capacitive value of piezoelectric materials, which shows up in measured admittance. Both degradation of the mechanical/electrical properties of a PZT transducer and the bonding defects between a PZT patch and a host structure could be identified by the proposed process. Due to the temperature dependent nature of piezoelectric materials, we investigated the effects of temperature on sensor diagnostic process. The effect of temperature found to be remarkable, modifying the measured capacitive values significantly. This results indicates that there is need for developing a rigorous signal processing technique to normalizing the temperature effects. It has been also found that, as the temperature changes, the sensor diagnostic process was influenced not only by a sensor and a structure, but by a bonding materials that was used for attaching a piezoelectric transducers to a structure, which would be an important characteristic when designing an SHM system. This paper summarizes considerations needed to develop such sensor diagnostic processes, experimental procedures and results, and additional issues that can be used as guidelines for future investigations.

Acoustic emission (AE) is a well-known technique for monitoring onset and propagation of material damage. The technique has demonstrated utility in assessment of metallic and composite materials in applications ranging from civil structures to aerospace vehicles. While over the course of few decades AE hardware has changed dramatically with the sensors experiencing little changes. A traditional acoustic emission sensor solution utilizes a thickness resonance of the internal piezoelectric element which, coupled with internal amplification circuit, results in relatively large sensor footprint. Thin wafer piezoelectric sensors are small and unobtrusive, but they have seen limited AE applications due to low signal-to-noise ratio and other operation difficulties. In this contribution, issues and possible solutions pertaining to the utility of thin wafer piezoelectrics as AE sensors are discussed. Results of AE monitoring of fatigue damage using thin wafer piezoelectric and conventional AE sensors are presented.

Carbon fiber laminate composites, consisting of layers of polymer matrix reinforced with high strength carbon fibers, are increasingly employed for aerospace structures. They offer advantages for aerospace applications, e.g., good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, fiber and matrix breakage or delaminations can occur, reducing the load carrying capacity of the structure. Efficient structural health monitoring of composite panels can be achieved using guided ultrasonic waves propagating along the structure. Impact damage was induced in the composite panels using standard drop weight procedures. The guided wave scattering at the impact damage was measured using a noncontact laser interferometer, quantified, and compared to baseline measurements on undamaged composite panels. Significant scattering of the first anti-symmetrical (A₀) guided wave mode was observed, allowing for the detection of barely visible impact damage. The guided wave scattering was modeled using full three-dimensional Finite Element (FE) simulations, and the influence of the different damage mechanisms investigated. Good agreement between experiments and predictions was found. The sensitivity of guided waves for the detection of barely visible impact damage in composite panels has been verified.

Physics-based wave propagation computational models play a key role in structural health monitoring (SHM) and the development of improved damage quantification methodologies. Guided waves (GWs), such as Lamb waves, provide the capability to monitor large plate-like aerospace structures with limited actuators and sensors and are sensitive to small scale damage; however due to the complex nature of GWs, accurate and efficient computation tools are necessary to investigate the mechanisms responsible for dispersion, coupling, and interaction with damage. In this paper, the local interaction simulation approach (LISA) coupled with the sharp interface model (SIM) solution methodology is used to solve the fully coupled electro-magneto-mechanical elastodynamic equations for the piezoelectric and piezomagnetic actuation and sensing of GWs in fiber reinforced composite material systems. The final framework provides the full three-dimensional displacement as well as electrical and magnetic potential fields for arbitrary plate and transducer geometries and excitation waveform and frequency. The model is validated experimentally and proven computationally efficient for a laminated composite plate. Studies are performed with surface bonded piezoelectric and embedded piezomagnetic sensors to gain insight into the physics of experimental techniques used for SHM. The symmetric collocation of piezoelectric actuators is modeled to demonstrate mode suppression in laminated composites for the purpose of damage detection. The effect of delamination and damage (i.e., matrix cracking) on the GW propagation is demonstrated and quantified. The developed model provides a valuable tool for the improvement of SHM techniques due to its proven accuracy and computational efficiency.

A layered Timoshenko beam (TB) model of a high-rise building is presented and applied to system identification of a full-scale building from recorded seismic response. This model is a new development in a wave method for earthquake damage detection and structural health monitoring being developed by the authors’ research group. The method is based on monitoring changes in the wave properties of the structure, such as the velocity of wave propagation vertically through the structure. This model is an improvement over the previously used layered shear beam (SB) model because it accounts for wave dispersion caused by flexural deformation present in addition to shear. It also accounts for the rotatory inertia and the variation of the building properties with height. The case study is a 54-story steel frame building located in downtown Los Angeles. Recorded accelerations during the Northridge earthquake of 1994 are used for system identification of the NS response. The model parameters are identified by matching, in the least squares sense, the model and observed impulse response functions at all levels where motion was recorded. The model is then used to compute the building vertical phase and group velocities. Impulse responses computed by deconvolution of the recorded motions with the roof response are used, which represent the building response to a virtual source at the roof. The better match of transfer-function amplitudes of the fitted TB model than of previously fitted SB model indicates that the layered TB model is a better physical model for this building.

A stochastic multi-scale based approach is presented in this work to detect signatures of micro-anomalies from macrolevel response variables. By micro-anomalies, we primarily refer to micro-cracks of size 10–100 μm (depending on the material), while macro-level response variables imply, e.g., strains, strain energy density of macro-level structures (typical size often varying in the order of 10–100 m). The micro-anomalies referred above are not discernible to the naked eyes. Nevertheless, they can cause catastrophic failures of structural systems due to fatigue cyclic loading that results in initiation of fatigue cracks. Analysis of such precursory state of internal damage evolution, before amacro-crack visibly appears (say, size of a few cms), is beyond the scope of the conventional crack propagation analysis, e.g., classical fracture mechanics. The present work addresses this issue in a certain sense by incorporating the effects of micro-cracks into the macro-scale constitutive material properties (e.g., constitutive elasticity tensors) within a probabilistic formalism based on random matrix theory, maximum entropy principle, and principles of minimum complementary energy and minimum potential energy. Distinct differences are observed in the macro-level response characteristics depending on the presence or absence of micro-cracks. This particular feature can now be used to reliably detect micro-cracks from experimental measurements of macro-observables. The present work, therefore, further proposes an efficient and robust optimization scheme: (1) to identify locations of micro-cracks in macroscopic structural systems, say, in an aircraft wing which is of the size of 10– 100 m, and (2) to determine the weakened (due to the presence of micro-cracks) macroscopic material properties which will be useful in predicting the remaining useful life of structural systems. The proposed optimization scheme achieves better convergence rate and accuracy by exploiting positive-definite structure of the macroscopic constitutive matrices.

This paper investigates the nonlinear cross-modulation vibro-acoustic technique for fatigue crack detection in metallic structures. The method is used in an aluminium plate instrumented with low-profile piezoceramic transducers that are used for excitation. Laser vibrometry is used to acquire vibro-acoustic responses. The results demonstrate the modulation transfer from one excitation signal to the other excitation signal in the presence of crack in the plate. The work presented focuses on the analysis of modulation intensities. The paper demonstrates that the method can be used for fatigue crack detection in metallic structures.

Frost resistance of concrete is a major concern in cold regions. RILEM (International union of laboratories and experts in construction materials, systems and structures) recommendations provide two alternatives for evaluating frost damage by nondestructive evaluation methods for concrete like materials. The first method is based on the ultrasonic pulse velocity measurement, while the second alternative technique is based on the resonant vibration test. In this study, we monitor the frost damage in Portland cement mortar samples with water to cement ratio of 0.5 and aggregate to cement ratio of 3. The samples are completely saturated by water and are frozen for 24 hours at -25°C. The frost damage is monitored after 0, 5, 10, 15 and 20 freezing-thawing cycles by nonlinear impact resonance acoustic spectroscopy (NIRAS). The results obtained are compared with those obtained by resonant vibration tests, the second alternative technique recommended by RILEM. The obtained results show that NIRAS is more sensitive to early stages of damage than the standard resonant vibration tests.

The increasing demand for renewable and clean power generation has resulted in increasing sizes of rotor blades in wind turbine systems. The demanding and variable operational environments have introduced the need for structural health monitoring systems in the blades in order to prevent unexpected downtime events in the operation of the power plant. Many non-destructive evaluation methods used for structural health monitoring purposes need external excitation sources. However, several systems already accepted in the wind turbine industry are passive. Here we present a new approach to health monitoring of a wind turbine blade using only passive sensors and the existing noise created on the blade during operation. This is achieved using a known method to reconstruct the causal and anticausal time-domain Green’s function between any two points in an array of passive sensors placed in a diffuse field. Damage is indicated when the similarity between the causal and anticausal signals decrease due to nonlinearities introduced from structural damage. This method was studied experimentally using a CX-100 wind turbine test blade located at the UCSD’s Powell Structural Laboratories where a diffuse field was approximated by exciting the skin of the blade with a random signal at several locations.

Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990’s versus late 2000’s), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA’s rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed solutions are discussed and recommendations are made for a follow-on hybrid implementation.

Because this paper was not presented at the conference, it has been withdrawn by the publisher.

Damage detection of pipeline systems is a tedious and time consuming job due to digging requirement, accessibility, interference with other facilities, and being extremely wide spread in metropolitans. Therefore, a real-time and automated monitoring system can pervasively reduce labor work, time, and expenditures. This paper presents the results of an experimental study aimed at monitoring the performance of full scale pipe lining systems, subjected to static and dynamic (seismic) loading, using Acoustic Emission (AE) technique and Guided Ultrasonic Waves (GUWs). Particularly, two damage mechanisms are investigated: 1) delamination between pipeline and liner as the early indicator of damage, and 2) onset of nonlinearity and incipient failure of the liner as critical damage state.

Structural health monitoring (SHM) has attracted much interest in the last two decades to handle the aging infrastructure systems all over the world. As one of the potential solutions, Electro-mechanical impedance (EMI) method was introduced in the early 1990s for SHM of civil, mechanical and aerospace structures. This paper presents the current investigation at UCSD on the feasibility of using an impedance-based Structural Health Monitoring (SHM) technique to monitor the Continuous Welded Rail (CWR). The objective of this research is to investigate the temperature and axial loading effect on theoretical models of the Electro-Mechanical Impedance (EMI) technique based on structural dynamics, integrated with experimental studies. Signatures and features from analytical models and experimental results are compared. The final results illustrate that the proposed models would be promising to characterize the temperature and axial stress effects.

This paper presents a subspace system identification for estimating the stiffness matrix and flexural rigidities of a shear building under earthquake. Subspace SI is a kind of inverse problem and suffers from inherent instabilities caused by modeling error and measurement noise. The size of Hankel matrix (k(m+p)×T_w/Δt), which represents the amount of selected dynamic data among measured responses, is closely related to the accuracy and numerical instability of estimated system matrices. The numerical instability and accuracy of subspace SI is investigated through the estimation error curve of stiffness matrix. The estimation error curve is obtained with respect to the number of block row(k) and sampling rate (Δt) for various time window size (Tw) using a prior finite element model of a shear building. k, Δt and T_w resulting in a target accuracy level, are determined through this curve considering the computational cost of subspace identification. The validity of the proposed method is demonstrated through the numerical example of a five-story shear building model with and without damage.

Asphalt concrete mixtures with different levels of oxidative aging, prepared by oven-aging the mixture at 135 °C for different amounts of time, were used to study the effects of oxidative aging upon the ultrasonic phase velocities and attenuation measurements. It was a observed that both the dilatational and shear velocities increase up to approximately 24 hours of aging after which they significantly decease with aging. Also, both the dilatational and shear attenuation decrease up to around 24 hours of aging, after which both attenuations strongly increase. These results are consistent with results obtained using the mechanical Disk-shaped Compact Tension (DC[T]) fracture tests. Based upon these velocity and attenuation measurements, the dynamic moduli were calculated. It was observed that the dynamic moduli increase from 0 hours to 24 hours and decrease from 24 to 36 hours of oven-aging. The modulus obtained using ultrasonic measurements is also compared with the modulus obtained using the AASHTO recommended mechanical testing. The differences are due to scattering effects, which are present in ultrasonic testing. It was also observed that to avoid the uncertainty associated with assuming a suitable value for the Poisson’s ratio, both the dilatational and shear velocities and corresponding attenuation measurements must be carried out. Furthermore, to eliminate the need for traditional mechanical testing during estimation of complex moduli, frequency-dependent ultrasonic measurements must also be carried out.

Nondestructive measurement of the concrete strength is an important topic of research. Among different nondestructive testing (NDT) methods the ultrasonic pulse velocity (UPV) technique is the most popular method for concrete strength estimation. While measuring concrete strength by this method almost all researchers have neglected the effect of applied stress or load on the concrete member. In this investigation attempts were made to properly incorporate the effect of the applied load on the strength prediction of concrete specimens from UPV value. To achieve this goal, 4 groups of concrete specimens with different values of final strength were made. Materials used for making cylindrical specimens of 3 inch diameter and 6 inch height included regular Portland cement, water and two types of aggregate - fine and coarse. After applying the load on the specimen in multiple steps – up to 70% of its failure strength f_c'- the time of flight (TOF) value was measured for every loading step. The recorded results showed that applied load on the member has significant effect on the measured UPV value on concrete specimens. Therefore, to find the strength of the concrete from the UPV value, the applied load on the sample should be considered as an important factor that cannot be neglected.

Railway turnouts (railroad switches) are the weakest components of a rail track system. Cracks may occur in the railway turnouts due to cyclic loadings and impact loadings imposed by passing trains. It is of great significance to continuously monitor the health condition of the railway turnouts and promptly detect crack once it initiates. It is well-known that acoustic emission (AE) signals are generated when a crack initiates and propagates. Detecting the high-frequency AE signals by piezoelectric sensors can help identify the crack and its location. This paper reports the design and implementation of a PZT-based system for crack monitoring of railway turnouts. This online monitoring system is activated for signal collection by a trigger system when a train is arriving to pass through the instrumented railway turnout. It mainly detects the AE signals generated when a crack initiates during the train passage or when the initiated crack expands during the passage of a heavy haul wagon. This system has been installed on a railroad line for over one year and has successfully detected the damage occurring at a railroad switch during its service period. This paper also briefs a guided-wave-based system for monitoring of micro-cracks in rail tracks by integrating FBG and PZT sensors.

A class of active acoustic metamaterial (AAM) is presented. The proposed AAM consists of an acoustic transmission line connected in parallel to an array of Helmholtz resonators that are provided with actively controlled boundaries. In this manner, the AAM is in effect an assembly of periodic cells, each of which consists of a Helmholtz resonator connected in parallel to two sections of the transmission line. The two sections meet the Helmholtz resonator at its neck. The local control action at each Helmholtz resonator of a unit cell is generated by using a Fractional Derivative (FD) controller that relies in its operation on the measurement of the flow resulting from the deflection of the resonator boundary and the flow rates inside the two transmission line sections before and after the resonator. Such a single local control action is shown to be capable of controlling the local effective density and elasticity of each unit cell. A lumped-parameter model is developed to model the dynamics and control characteristics of the AAM under different gains and exponents of the FD controller. The model is exercised to demonstrate the ability of the FD controller in generating metamaterials with double negative effective density and elasticity over broad frequency ranges as compared to conventional Proportional and Derivative (PD) controllers. With such capabilities, the development of AAM with FD control action may provide viable means for generating desirable spatial distributions of density and elasticity over broad frequency band using a small number of control actuators.

The paper discusses the wave propagation characteristics of two-dimensional (2D) magneto-elastic kagome lattices, periodic lattices governed by a combination of elastic and magnetic forces. These structures demonstrate the ability to undergo large topological and stiffness changes, which allows for dramatic changes in wave propagation characteristics. The analysis is conducted using a lumped mass system of magnetic particles with both translational and rotational degrees of freedom. Particles within the lattice interact through axial and torsional elastic forces as well as magnetic forces. Instabilities caused by the highly nonlinear distance-dependent characteristics of magnetic interactions are exploited in combination with particle contact to bring about the desired changes in the topology and stiffness of the lattices. The result is multiple stable lattice configurations with very different properties. The propagation of plane waves is predicted by applying Bloch theorem to lattice unit cells with linearized interactions. The propagation of plane waves in these lattices before and after topological changes is compared, and large differences are evident.

This paper presents a new metamaterial beam based on multi-frequency vibration absorbers for broadband vibration absorption. The proposed metamaterial beam consists of a uniform isotropic beam and small two-mass spring-mass- damper subsystems at many locations along the beam to act as multi-frequency vibration absorbers. For an infinite metamaterial beam, governing equations of a unit cell are derived using the extended Hamilton principle. The existence of two stopbands is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. For a finite metamaterial beam, because these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths, a finite-element method is used for detailed modeling and analysis. The concepts of negative effective mass and effective stiffness and how the spring-mass-damper subsystem creates two stopbands are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. For an incoming wave with a frequency in one of the two stopbands, the absorbers are excited to vibrate in their optical modes to create shear forces to straighten the beam and stop the wave propagation. For an incoming wave with a frequency outside of but between the two stopbands, it can be efficiently damped out by the damper with the second mass of each absorber. Hence, the two stopbands are connected into a wide stopband. Numerical examples validate the concept and show that the structure’s boundary conditions do not have significant influence on the absorption of high-frequency waves. However, for absorption of low-frequency waves, the structure’s boundary conditions and resonance frequencies and the location and spatial distribution of absorbers need to be considered in design, and it is better to use heavier masses for absorbers.