Sensors and actuators used in active control of smart structures have to be located appropriately in order to ensure maximum control and measurement effectiveness. Many placement techniques are based on the structure itself and overlook the effects of the applied control law. The optimal locations determined from open-loop system can not guarantee the best performance of the closed-loop system because the performance is closely related with the design requirements and applied controller. In this paper, we presented a method of obtaining the optimal locations of actuators/sensors by combining the open-loop and closed-loop optimal criterions. First, for open-loop system, location indices of the controlled modes are calculated on the basis of modal controllability and observability. The controlled modes are weighted based on the controller design requirements. To reduce the spill-over effect of uncontrolled modes, the location index values of uncontrolled modes are added as penalty terms. Locations with high index values are chosen as candidate locations of actuator/sensor for the next determining step on the closed-loop system. Three control techniques, optimal H₂, H_(infinity ) norms and optimal pole-placement, are utilized for two different control objectives, disturbance rejection and damping property enhancement. Linear matrix inequality (LMI) techniques are utilized to formulate the control problems and synthesize the controllers. For each candidate location of actuator/sensor, a controller is designed and the obtained performance is taken as location index. By solving the location problem in two steps, we reduced the computational burden and ensured good control performance of the closed-loop system. The proposed method is tested on a clamped plate with piezoelectric actuators and sensors.

This paper focuses on the dynamic analysis, simultaneous precision positioning and vibration suppression, and experiments of Active Composite Panels (ACPs). First, the dynamics of a panel with two surface-mounted PZT patches is analyzed and measured by the finite element method and experiments. A hybrid adaptive control scheme is then proposed to achieve precision positioning and vibration suppression simultaneously. The control scheme takes advantage of two adaptive feed forward controllers and an adaptive feedback controller. The simulation results of the hybrid adaptive controller are compared with those of a PID controller, showing that it can provide better precision position and faster vibration suppression. The experimental results demonstrate that the relative precision can reach 98.5% of the required position in large vibration level, verifying that the hybrid adaptive control scheme is reliable and efficient.

Increased control demands in applications including high speed milling and hybrid motor design have led to the utilization of magnetostrictive transducers operating in hysteretic and nonlinear regimes. To achieve the high performance capabilities of these transducers, models and control laws must accommodate the nonlinear dynamics in a manner which is robust and facilitates real-time implementation. This necessitates the development of models and control algorithms which utilize known physics to the degree possible, are low order, and are easily updated to accommodate changing operating conditions such as temperature. We consider here the development of nonlinear adaptive identification for low order, energy-based models. We illustrate the techniques in the context of magnetostrictive transducers but they are sufficiently general to be employed for a number of commonly used smart materials. The performance of the identification algorithm is illustrated through numerical examples.

In this paper, a novel hybrid Rayleigh-Ritz/Boundary Element (RR/BE) solution method is proposed to model acoustic domains with flexible walls with piezoelectric patches. The RR approach is a simple, computationally inexpensive approach when compared to the finite element method for flexible walls with surface mounted piezoelectric patches. The RR method is then combined with the boundary element model of the interior acoustic domain and the coupled fluid-structure model is used for designing an active noise control system. This model also allows a designer to incorporate a passive absorber at the fluid-structure interface. The predicted sound pressure attenuation for three different thicknesses of passive absorber in the frequency range of 200 to 1200 Hz is calculated and an optimal thickness value of for the absorber for the smart panel is calculated. The attenuation in sound pressure levels due to an active control system in the presence of passive absorber is also computed. The system matrices resulting from this method are very smaller in size when compared to the FE models, which makes this approach most suitable for optimization studies. This new approach can be further extended to model the more complicated acoustic enclosures with complex interface.

Payload protection against noise induced vibrations in rocket fairings is an important issue. In the work presented here, active structural acoustic control using an Hinf-controller together with piezoceramic sensors and actuators attached to the structure and interior microphones is investigated as an approach to this problem. For this a generic experiment has been set up. One objective of the work is to find and validate a method for getting accurate low-order parametric models for controller design based on finite element calculations. Therefore parameter estimation methods are applied to measured data as well as to numerical simulation data. A comparison of both yields information about the accuracy of the numerically calculated frequency responses. Due to uncertainties in the finite element model and time varying parameters, the robustness of the closed-loop system is an important design criterion. The most critical perturbations are variations of natural frequencies due to temperature-induced prestresses. The perturbations and uncertainties can be modeled by using linear fractional transformations. Robust stability and performance properties of the closed loop are investigated, both analytically and experimentally. These analyses allow a statement about the necessary accuracy of the numerical model and about the achievable performance.

This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controller design. The reduced structural model is combined with an acoustic model which uses the radiation mode concept. For a test case consisting of a rectangular plate with one piezo patch the model reduction technique is validated. The results show that the an accurate prediction of both the structural and acoustic response is predicted by the reduced model. The model is compact requiring small simulation times, which makes it attractive for control system design. Finally the control performances for both structural and acoustic error criteria are presented.

Two different methods are introduced for the determination of optimal active control inputs and passive shunting parameters in the PZT-based smart structure vibration and sound pressure control problems. The first method makes use of the dynamic vibration absorber principle; the second method uses the receptance of the open circuit structure-PZT system for determination of active control laws and parameters of optimal passive shunting. The advantages of each method are discussed. Using both methods, optimal passive electrical shunting parameters and active control input voltage values are determined for minimization of the vibration level and near field sound pressure at a particular point located above the plate. Additionally, at moderate to higher forcing levels the hysteretic non-linearity inherent in the PZT affects the dynamic response of the system. Calculated optimal passive shunting values under the linear system assumption become less than optimal. For high forcing levels, nonlinearity effects are accounted for in calculation of optimal values for passive shunting by using a discretized Ishlinskii-type hysteresis model of the PZT dielectric behavior.

It is well known that adding viscoelastic materials (VEM) in a vibrating structure reduces its resonance amplitudes through dissipation of a part of its vibration energy into heat. This is the basement of many passives damping treatments, such as constrained viscoelastic layers. They have been widely implemented in the automotive industry and have proven to be effective. Nevertheless, in order to design smart passive damping systems, there is still a need for finite element models capable of predicting the frequency response of structures containing VEM. We address in this paper the problem of local frequency-dependent VEM treatment in the finite element vibration analysis of large automotive structures. For reducing the prohibitive direct response's computing time, we propose to use Component Mode Synthesis where the elastic and viscoelastic components are reduced using a modified MacNeal method. The components are then coupled using an approach that eliminates the junction degrees of freedom. The small size of the complex reduced system allows to compute quickly the frequency responses of the damped structure.

Piezoceramic wafer (patch) actuators have been used for the excitation and control of vibrations of beam and plate-like structures. Accurate constitutive modeling of the beam or plate with a piezo-patch actuator adhered to it is an important aspect to understanding this problem. In this paper, a multi-layered beam model is presented that predicts natural frequencies of the open-circuited beam-patch system. Both the beam and the patch actuator are modeled as Timoshenko beams. Constraints are introduced to ensure continuity of the axial and transverse displacements at the interface of the two Timoshenko beams. The cross section of each layer is allowed to take different values, which adds an additional degree of freedom to the system. The displacement equation of each Timoshenko beam is represented in a factored matrix form. This factored matrix form is utilized to develop a procedure for derivation of element mass and stiffness matrices using a symbolic manipulation program (MAPLE). MAPLE is used to form the global mass and stiffness matrices. An eigenvalue analysis is conducted and natural frequencies of the layered beam are calculated. To verify the model, experimental studies are performed to determine cantilevered beam-patch system natural frequencies. Better agreement between the theoretical and experimental results is observed than could be obtained using Euler's (thin) beam theory.

An analytical method is given for the determination of the eigenfunctions and eigenfrequencies for two-dimensional structural vibration problems in the presence of patch sensors and patch actuators. The method is based on converting the differential equation formulation of the problem to an integral equation. The conversion is accomplished by introducing an explicit non-symmetric kernel. The kernel consists of two parts, one taking account of the stiffness and the other taking account of the control moments induced by the distributed actuators. The control moments involve piezoelectric constants and feedback voltages made up of gains times the sensor signals. Eigenfrequencies are obtained for a representative example. The results presented in the study can be used for benchmarking solutions based on numerical or approximation approaches.

Much of the recent and past work in the area of smart materials and structures has focused on analysis of actuators and actively controlled systems. Although many sophisticated analysis models have been developed, they are often coupled with ad-hoc design methods or informal optimization procedures. A subset of the work done by the smart structures community has focused on development of formal design methodologies and optimization methods specifically for smart actuators and structures. The objective of this paper is to review the current work in development of design methodologies and application of formal optimization methods to the design of smart structures and actuators. In a related paper, optimization strategies for sensor and actuator placement were reviewed by a researcher at NASA Langley in 1999. The current paper reviews the recent work done in this area since 1999, in addition to optimization strategies for topology design of actuators, actively controlled structures, and drive electronics design. The main focus is on piezoelectric ceramic actuators, but relevant work in shape memory alloys and magnetostrictive actuation are included as well. Future directions for research in optimization are also recommended.

Compliant mechanical amplifiers are often used to amplify small motions such as those of PZT actuators, since they do not incur displacement losses that frequently occur in pin-jointed mechanisms. Their optimal design is key to maximizing actuator performance. Our previous work was focused on developing a topology optimization methodology wherein the size of the design domain and the location of the PZT actuator were pre-defined. The resultant solution was one that maximized stroke amplification. In this paper we study the effects of stack and structural properties on resultant topology and output stroke with focus on quantitative performance for practical application. The motivating example is an actuator-design problem where +/- 400micrometers stroke and 45 N force is required. The problem is solved using topology design methodology and the results obtained are verified using finite element analysis. We demonstrate that magnitude of output displacement is extremely sensitive to preload on the compliant mechanical amplifier, amplifier and actuator material, topology interpretation while converting it into a solid model, and magnitude of applied voltage. We discuss effects of asymmetric placement of the PZT stack, multiple stacks, and increased stack length on resultant displacement.

A system dynamic model has been developed for assessing the performance of a piezoelectric hydraulic pump. The pump system comprises a stack actuator driven pump, four-way valve, hydraulic accumulator, and hydraulic actuator. A system of differential equations was developed that governs the electrical / mechanical / fluid coupled behavior. The system of equations was simultaneously solved using MATLAB. The results were compared to pump data for a stack actuator input of 2 MV/m at operating frequencies between 2.5 Hz and 100 Hz. Previous work comparing the model to experimental results was recently accepted for publication in a future article . The work presented below presents a review of the model and discusses additional experimental results of the pump's flow rate response under hydraulic actuator loads. The model achieved reasonable agreement with flow rate measurements when the hydraulic actuator was loaded with 62 N and 142 N of constant force. Rate effects were observed to limit the high frequency performance. These effects were attributed to fluid compressibility, check valve resistance, and self heating of the stack actuator. The model provides a design tool for evaluating bandwidth limitations and increasing pressure and flow rate.

This paper presents a numerical modeling technique of piezoelectric transducers by taking into account wave radiation and scattering. It is based on the finite element modeling. Coupling problems between piezoelectric and elastic materials as well as fluid and structure systems associated with the modeling of piezoelectric underwater acoustic sensors are formulated. In the finite element modeling of unbounded acoustic fluid, IWEE (Infinite Wave Envelop Element) is adopted to take into account the infinite domain. The IWEE code is added to an in-house finite element program, and commercial pre and post-processor are used for mesh generation and to see the output. The validation of the numerical modeling is proved through an example, and scattering and radiation analysis of Tonpilz transducer is performed. The scattered wave on the sensor is calculated, and the sensor response, so called RVS (Receiving Voltage Sensitivity) is predicted.

Preisach models formulated in terms of density or measure-based expansions have proven highly successful for characterizing hysteresis and constitutive nonlinearities in materials where the underlying physics is difficult to quantify. This provides a rich mathematical framework for characterizing nonlinear material behavior as well as a framework which facilitates either full or approximate inversion for linear control design. However, the lack of an energy basis for Preisach representations yields models which often have a large number of parameters and are difficult to update to accommodate changing operating conditions (e.g., temperature) since the model parameters are not correlated with physical quantities. Moreover, it is difficult in general to incorporate the frequency-dependence exhibited by essentially all smart materials without resorting to vector-valued parameters or measures which much be identified throughout the range of operation for the system. In this paper, we develop an energy formulation for Preisach models through consideration of appropriate Gibbs and Helmholtz free energy representations. This permits the incorporation of frequency and temperature-dependence in the underlying basis, rather than in parameters identified for a specific system which expands significantly the flexibility of the technique.

This paper addresses the development of a free energy model for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic materials. In the first step of the development, free energy relations for a single crystal with uniform lattice are considered and used to construct evolution equations which quantify the polarization as a function of the applied field. The effects of nonuniform lattice structures, nonhomogeneous effective fields and polycrystalline materials are then incorporated through the use of appropriate distributions in the free energy formulation. The resulting model, which is an extension of the Muller-Achenbach-Seelecke theory for shape memory alloys, is low-order and hence highly efficient to implement. Attributes of the model are illustrated through comparison with experimental data.

Piezoelectric actuators usually are analyzed using finite element programs. These programs are often restricted to linear constitutive equations. Furthermore, the coupling with electrical element types is very problematical. Experiments showed, that even at weak electric fields the piezoceramics show nonlinear behavior, if the structure is excited near a resonance frequency. In many applications actuators are excited in resonance, for instance in ultrasonic motors and therefore these nonlinearities are important in practice. In this paper a nonlinear model for piezoelectric materials is presented. Nonlinear constitutive equations are derived from Hamiltons principle to calculate the longitudinal oscillations of a piezoceramic slender rod. The oscillations are excited by a harmonic electric potential at the electrodes of the rod, which is polarized in longitudinal direction. The resulting nonlinear partial differential equation is approximated using a Rayleigh Ritz ansatz. This leads to a set of ordinary nonlinear differential equations. In the present analysis, the displacement-functions used for the approximation are the eigenfunctions of the linearized system. The resulting nonlinear differential equation is solved by the harmonic balance method. This leads to a set of equations, that can be solved numerically to calculate the amplitude of the oscillations. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model. In future investigations the focus will be on the identification of the parameters of the nonlinear model.

Piezoelectric plates have been widely used for the vibration reduction and noise control of structures. Due to power forces considerations, electrostrictive patches present a growing interest. It is thus the purpose of the present research to contribute to modeling aspects of thin structures integrating such actuators. Several three-dimensional finite elements have been elaborated to simulate these structures behavior. Using the constitutive relationships analyzed by the first author in a previous paper, an original two-dimensional plate theory have been presented at SPIE'01 with a focus on modeling aspects and corresponding appropriate variational formulations. Let us recall that the element here developed has the particular property of reducing the initial electromechanical problem to a purely mechanical problem based on a modified elastic constitutive law. The electrical unknowns are then explicitly derived from the mechanical displacements. This theory thus proved that there is no need to develop new plate finite elements but that one could use classical elements for laminated plates. The previous paper, moreover underlined that using current as actuators driving input leads in simplifications of the behavior modeling. The purpose of this presentation is then to validate the current driven and voltage driven plate models, previously established, through numerical finite element results and experimental correlations.

In an ultrasonic transducer, the cross talk between array elements is an important performance degrading factor, and there is strong need to identify the sources of the problem and to find the means to reduce its level. This paper considers two most representative ultrasonic transducers, capacitive micromachined ultrasonic transducer (cMUT) and piezoelectric transducer. Both are linear array immersion transducers. Two-dimensional finite element models of the transducers are constructed using the commercial code ANSYS. We analyze the origin and level of the cross talk between array elements, with evidence of coupling through certain waves such as the Stoneley wave propagating at the transducer-water interface and the Lamb wave propagating in the substrate or the impedance matching layer. For reduction of the cross talk level, the effects of various structural schemes are investigated. They are the change of wafer thickness, the installation of etched trenches of various dimension and sound absorbing materials inside, and installation of polymer walls between array elements for a cMUT as well as the change of the dimension and material of kerfs for a piezoelectric transducer. Results for the two transducers are discussed to describe the general method to reduce the cross talk level in ultrasonic transducers.

Most aircraft wings are optimized to produce minimum drag under one particular flying speed, while the flying speed actually varies continuously throughout flight. Although conventional hinged mechanisms can change the wing shape in response to the change in flying speed, the connecting hinges create discontinuities over the wing surface, leading to earlier airflow separation. In this paper, we propose a systematic approach to synthesize compliant mechanisms that can deform an initial curve into a target shape with a smooth boundary. As opposed to the two-step synthesis that separates the interrelated topology and dimensional aspects of a compliant mechanism, we propose an optimization model using a mixed-variable formulation that addresses both aspects simultaneously. The effectiveness of the shape change is evaluated using Fourier Descriptors (FDs), which capture the pure 'shape' differences between curves. Due to the discrete nature in the design variables, a Genetic Algorithm (GA) is employed to find the optimal solution. The preliminary results demonstrate the feasibility of simultaneously addressing the topology and dimensional aspects. They also indicate that the reference shape used for curve description can significantly affect the optimal solutions. This suggests that a more refined objective function is necessary to improve the effectiveness of the results.

In this paper, the problem of modeling and output feedback control design for smart structural system using piezoelectric as sensor/actuator is addressed. The model for a smart cantilever beam is developed by Finite Element Method (FEM). State space models for a smart cantilever beam with single sensor/actuator for three different sensor/actuator locations are obtained. The fast output sampling feedback control is designed to control the first two vibration modes for each sensor/actuator location and its performance is evaluated.

An algorithm is presented which uses adaptive Q-parameterized compensators for control of stable or unstable systems. Internal stability is maintained by forming the compensator out of plant-stabilizing coprime factors, and an on-line gradient descent method adapts the free parameter to minimize the mean squared error between the desired and actual output. The adaptation algorithm is derived for a compensator in the form of a finite impulse response (FIR) filter and a lattice infinite impulse response (IIR) filter. Simulations predict good performance for both tonal and broadband disturbances, and a duct noise control experiment results in a 37 dB tonal reduction.

This research is concerned with the adaptive positive position feedback (PPF) controller design for the vibration suppression of smart structures. The main advantage of the PPF controller is that it can tackle the target mode without disturbing other modes. However, its major drawback is that we should tune the PPF filter frequency to the natural frequency of the target mode. In this study, we developed a new algorithm, which can adaptively trace the optimal PPF filter frequency in real time. To this end, we applied the gradient descent method to the digital PPF controller and derived the adaptive PPF control algorithm in digital form, which can be implemented in real time. The proposed adaptive PPF controller was tested using the simple beam structure. The experimental results show that the adaptive PPF controller is capable of tuning the PPF filter frequency to the optimal one in real time thus achieving vibration suppression in changing environments.

The application of robust control theory, H₂ and H_(infinity ) controls, on the active control of smart structural systems results in higher order controllers. The implementations of these controllers need complex hardware and more power and is difficult to embed in the structure. In this paper, we present two lower-order controller design methods, indirect and direct methods. For indirect method, using linear matrix inequalities (LMIs), the full order strictly proper controller with output limitations is first synthesized for given control objectives, bounded H_(infinity ) or H₂ system norm. The full order controller is then reduced to a lower-order controller by a LMI based model reduction method for minimal H_(infinity ) norm reduction error. For direct method, the fixed-order controller synthesis conditions are represented by LMIs with an additional nonconvex rank constraint. To utilize efficient computational tool for numerical solutions of convex LMIs, we relax the rank condition to a convex optimization. Although this relaxation can not fully solve the rank condition, in most cases, it gives a controller with lower-order. The proposed methods are tested on an experimental three-mass structure with PZT sensors and actuators. These two methods are compared based on the simulation and experimental results.

Application of the wavelet transforms on the measured vibration data provides a new tool for the damage detection analysis of the two-dimensional structural systems. In this paper, a novel two-dimensional wavelet mapping technique for damage detection based on the wavelet transforms and residual mode shapes are proposed. After vibration data was collected, wavelet de-noising shrinkage was performed in order to reduce measurement noise. By performing wavelet decomposition of the residuals of mode shapes and by taking only detail coefficients, wavelet energy maps are constructed for all decomposition levels. The orthogonal property of the wavelet transforms has bee utilized to correlate energy at decomposition levels with the measured vibrational energy. After wavelet maps of interest are determined, they are mapped on top of each other to figure out damaged areas of the two-dimensional structural systems. The energy segmentation procedure is performed by using minimum homogeneity and uncertainty based thresholding methods. It has been shown that the proposed method can clearly locate the multiple damage locations on the two- dimensional structures. This method requires few sampling points, robust and independent of the type of damage or the material damaged. The proposed method is applied to detect multiple damage locations on a two-dimensional plate. The results are very satisfactory.

Damage detection in metallic structures has been the subject of many investigations. Recent developments have shown applications of acousto-ultrasonic and Lamb wave testing. Lamb wave inspection is based on theory of longitudinal waves propagating in plates. In general, the principles of acousto-ultrasonic and Lamb wave inspection techniques are similar. Damage in a structure is identified by a change in the output signal. Previous studies show that even simple input signals can lead to complex output waves, which are difficult to interpret. It is clear that knowledge and understanding of wave propagation in analyzed structures can ease the interpretation of damage detection results. The paper reports an application of local interaction modeling of acousto-ultrasonic waves in metallic structures. The focus of the analysis is on one-dimensional interactions between different material boundaries. This includes modeling of acousto-ultrasonic waves in piezoceramic, adhesive glue and copper in an actuator/sensor configuration. The study also involves experimental validation of the simulation results. The method shows the potential for modeling of acousto-ultrasonic waves in complex media for damage detection applications.

The first and most important objective of any damage identification algorithms is to ascertain with confidence if damage is present or not. Many methods have been proposed for damage detection based on ideas of novelty detection founded in pattern recognition and multivariate statistics. The philosophy of novelty detection is simple. Features are first extracted from a baseline system to be monitored, and subsequent data are then compared to see if the new features are outliers, which significantly depart from the rest of population. In damage diagnosis problems, the assumption is that outliers are generated from a damaged condition of the monitored system. This damage classification necessitates the establishment of a decision boundary. Choosing this threshold value is often based on the assumption that the parent distribution of data is Gaussian in nature. While the problem of novelty detection focuses attention on the outlier or extreme values of the data i.e. those points in the tails of the distribution, the threshold selection using the normality assumption weighs the central population of data. Therefore, this normality assumption might impose potentially misleading behavior on damage classification, and is likely to lead the damage diagnosis astray. In this paper, extreme value statistics is integrated with the novelty detection to specifically model the tails of the distribution of interest. Finally, the proposed technique is demonstrated on simulated numerical data and time series data measured from an eight degree-of-freedom spring-mass system.

Health monitoring of aerospace structures can be done passively by listening for acoustic waves generated by cracks, impact damage and delaminations, or actively by propagating diagnostic stress waves and interpreting the parameters that characterize the wave travel. This paper investigates modeling of flexural wave propagation in a plate and the design of sensors to detect damage in plates based on stress wave parameters. To increase understanding of the actual physical process of wave propagation, a simple model is developed to simulate wave propagation in a plate with boundaries. The waves can be simulated by applied forces and moments in the model either to represent passive damage growth or active wave generation using piezoceramic actuators. For active wave generation, the model considers a piezoceramic patch bonded perfectly to a quasi-isotropic glass-epoxy composite plate. Distributed sensors are used on the plate and are modeled as being constructed using active fiber composite and piezoceramic materials. For active wave generation, a moment impulse is generated by the actuation of a piezoceramic patch. The waves generated from the patch are detected by the distributed sensor. For passive sensing of acoustic waves, a step function is used to simulate an acoustic emission from a propagating damage. The resulting acoustic wave is measured by the distributed sensor and produces micro-strains in the sensor nodes. The strains produce a single voltage signal output from the distributed sensor. Computational simulations and animations of acoustic wave propagation in a plate are discussed in the paper. A new method to locate the source of an acoustic emission using the time history of the dominant lower frequency components of the flexural wave mode detected by continuous sensors is also presented.

An intensity modulated sensor, based on the microbending concept, has been incorporated in laminates produced from a C/epoxy prepreg. Pencil lead break tests (Hsu-Neilsen sources) and tensile tests have been performed on this material. In this research study, fibre optic sensors will be proven to offer an alternative for the robust piezoelectric transducers used for Acoustic Emission (AE) monitoring. The main emphasis has been put on the use of advanced signal processing techniques based on time-frequency analysis. The signal Short Time Fourier Transform (STFT) has been computed and several robust noise reduction algorithms, such as Wiener adaptive filtering, improved spectral subtraction filtering, and Singular Value Decomposition (SVD) -based filtering, have been applied. An energy and frequency -based detection criterion is put forward to detect transient signals that can be correlated with Modal Acoustic Emission (MAE) results and thus damage in the composite material. There is a strong indication that time-frequency analysis and the Hankel Total Least Squares (HTLS) method can also be used for damage characterization. This study shows that the signal from a quite simple microbend optical sensor contains information on the elastic energy released whenever damage is being introduced in the host material by mechanical loading. Robust algorithms can be used to retrieve and analyze this information.

We develop a model that quantifies constitutive nonlinearities and hysteresis inherent to ferroelastic compounds, with emphasis placed on shape memory alloys. We formulate the model in two steps. First, we use the Landau theory of phase transitions to characterize the effective Gibbs free energy for both single-crystal and polycrystalline ferroelastics. The resulting nonlinear equations model ideal material behavior in the absence of impurities. Second, we incorporate pinning losses to account for the energy required to move domain walls across material inclusions. We illustrate aspects of the model through comparison with experimental stress-strain data.

Advances in active materials and smart structures, especially in applications of Shape Memory Alloys (SMA) as vibration isolation devices requires modeling of the pseudoelastic hysteresis found in SMAs. In general SMA hysteresis has been modeled either through constitutive models based on mechanics and material parameters or through system identification based models that depend only on input-output relationships, most popular being the Preisach Model. In this work, a basis is set forth for studying the effect of SMA pseudoelasticity on the behavior of vibrating systems. A Preisach Model is implemented to predict the component level pseudoelastic response of SMA spring elements. The model is integrated into a numerical solution of the non-linear dynamic system that results from the inclusion of Shape Memory Alloy components in a dynamic structural system. The effect of pseudoelasticity on a dynamic system is investigated for various loading levels and system configurations and the importance of large amplitude motion is discussed. Promising results are obtained from these investigations and the application of these studies to experimental work in progress by the authors is briefly discussed.

Shape memory alloy (SMA)s, in particular the nickel-titanium alloy (or Nitinol), have been used as actuators in some astronautic, aeronautic and industrial applications. Future will see more SMA application if less energy is required for actuation. This paper presents the design and experimental results of control of an SMA actuator using Pulse Width (PW) Modulation to reduce the energy consumption by the SMA actuator. An SMA wire test stand is used in this research. Open-loop testing of the SMA wire actuator is conducted to study the effect of the PWM parameters. Based on results of testing results and parameter analysis of the PW modulator, a PW modulator is designed to modulate a Proportional plus Derivative (PD) controller. Experiments demonstrate that control of the SMA actuator using PW modulation effectively save actuation energy whiling maintaining same control accuracy as compared to continuous PD control. PW modulator also demonstrates robustness to external disturbances. A comparison with pulse width pulse frequency (PWPF) modulator is also presented.

A direct hybrid adaptive control method based on the Lyapunov-like stability theorem is proposed for performing active vibration control of a gear pair system being subjected to multiple harmonic disturbances. The analysis uses a reduced single-degree-of-freedom definite gear pair representation of the elastic mesh mode, which includes the effect of time-varying tooth stiffness. It is assumed that the resultant actuation force can be directly applied to the gear body along the tooth contact line-of-action employing specially configured inertial actuators for suppressing rotational vibration. The proposed controller simultaneously adapts both the feed-back and feed-forward gains, and only requires knowledge of the instantaneous gear rotational speed and number of gear teeth or equivalently the fundamental gear mesh frequency. The numerical results of this study show that the proposed controller is somewhat insensitive to estimation error at the fundamental gear mesh frequency and the resulting vibration control is better than those provided by the well-known adaptive notch filter and Filtered-X LMS algorithms. Furthermore, the dynamic optimization normalization enhancement is incorporated into the basic controller to optimize performance and improve robustness.

Four actuation concepts for the active suppression of gearbox housing mesh frequency vibrations caused by transmission error excitation from the gear pair system are modeled and compared by computing the required actuation force and amplifier power spectra. The proposed designs studied consist of (i) active inertial actuators positioned tangentially on the gear body to produce a pair of reactive force and moment, (ii) semi-active gear-shaft torsional coupling to provide tuned vibration isolation and suppression, (iii) active bearing vibration control to reduce vibration transmissibility, and (iv) active shaft transverse vibration control to suppress/tune gearbox casing or shaft response. Numerical simulations that incorporate a transmission error term as the primary excitation are performed using a finite element model of the geared rotor system (dynamic plant) constructed from beam and lumped mass/stiffness elements. Several key comparison criteria, including the required actuation effort, control robustness and implementation cost, are examined, and the advantages and disadvantages of each concept are discussed. Based on the simulated data, the active shaft transverse vibration scheme is identified as the most suitable approach for this application.

Shape Memory Alloys have been used in a wide variety of actuation applications. A bundled shape memory alloy cable actuator, capable of providing large force and displacement has been developed by United Technologies Corporation (patents pending) for actuating a Variable Area fan Nozzle (VAN). The ability to control fan nozzle exit area is an enabling technology for the next generation turbofan engines. Performance benefits for VAN engines are estimated to be up to 9% in Thrust Specific Fuel Consumption (TSFC) compared to traditional fixed geometry designs. The advantage of SMA actuated VAN design is light weight and low complexity compared to conventionally actuated designs. To achieve the maximum efficiency from a VAN engine, the nozzle exit area has to be continuously varied for a certain period of time during climb, since the optimum nozzle exit area is a function of several flight variables (flight Mach number, altitude etc). Hence, the actuator had to be controlled to provide the time varying desired nozzle area. A new control algorithm was developed for this purpose, which produced the desired flap area by metering the resistive heating of the SMA actuator. Since no active cooling was used, reducing overshoot was a significant challenge of the controller. A full scale, 2 flap model of the VAN system was built, which was capable of simulating a 20% nozzle area variation, and tested under full scale aerodynamic load in NASA Langley Jet Exit Test facility. The controller met all the requirements of the actuation system and was able to drive the flap position to the desired position with less than 2% overshoot in step input tests. The controller is based on a adaptive algorithm formulation with logical switches that reduces its overshoot error. Although the effectiveness of the controller was demonstrated in full scale model tests, no theoretical results as to its stability and robustness has been derived. Stability of the controller will have to be investigated for the next stage of technology readiness.

In this paper, analytical and experimental investigations conducted into the design and use of fiber-tip based Fabry-Perot sensors for control of structural acoustics are presented. Noise is transmitted into the enclosure through a flexible boundary, and the fiber-tip sensors are designed for acoustic pressure and air particle velocity measurements inside and outside the enclosure as well as panel acceleration measurements. The benefits of these sensors for realizing zero spillover control schemes and other schemes are discussed.

The behavior of smart localized structural elements for nonlinear vibration control of a taut string is investigated in this manuscript. A nonlinear lumped mass dynamical system is derived and analyzed numerically to reveal conditions for possible forced vibration reduction. The strategy employed consists of an open loop excitation approach enabled via actuation of a smart element by a slight harmonic change of its length. Results of a bifurcation analysis reveal possible vibration reduction via two distinct mechanisms: i) parametric excitation that enables reduction of external forcing and ii) energy transfer from the directly excited vertical response to both rotation and horizontal motions.

This paper focuses on various vibration suppression schemes for Active Composite Struts (ACS) and Active Composite Panels (ACP). Dynamic responses of struts and panels using piezoelectric sensors and actuators were analyzed and evaluated by the finite element method. Four different vibration suppression schemes for ACS and ACP have been studied. Objectives were to first investigate various schemes for active vibration suppression that can be determined directly without trial and error, and Second to determine a scheme that can completely suppress the vibration and is easy to use. Four schemes were considered, namely, 1) constant voltage (CV), 2) optimum voltage (OV), 3) corresponding voltage (COV) and 4) truncated corresponding voltage (TCOV) schemes. This paper also discusses the pros and cons of each and provides guidelines for active vibration suppression of intelligent structures.

The objective of the paper is to present an overall design methodology based on the finite element method (FEM), where the focus is on the relation between the controller design and the multi-physics structure, consisting of the passive base structure, the actuators, the sensors and also the control electronics. First, it is shown how such an overall virtual computer model can be generated and applied to design smart structures and to study the behavior of the structures under different operating conditions taking into account also disturbances, model uncertainties, etc. As a reference example a smart plate structure is used to discuss different design versions and controller approaches in detail. Then two industrial applications are briefly mentioned, where our approach was used to design the structures based on an overall virtual computer model.

Hybrid active/passive control systems present unique, energy-efficient solutions to noise and vibration problems. In many applications, active systems offer the only feasible control of low-frequency, high intensity vibrations, while passive materials offer superior attenuation at higher frequencies. These two systems can be optimally coordinated for broad-band control. An energy balancing metric forms the basis of an optimization routine designed to minimize both the broad-band vibratory energy of the structure and the weight, volume, and energy use of the control system. The optimization routine also investigates placement, size, and orientation of the active and passive control system elements. Initial experimentation on two-dimensional panels confirms the advancements provided by the optimization scheme. Here, active piezoceramic patches partner with passive constrained layer damping treatment to present the notable achievement of a coordinated control system no longer confined to a particular frequency range.

A rotating composite blade, modeled as a box-beam that incorporates a number of non-classical effects such as transverse shear traction free boundaries and restrained warping, is considered. The blade consists of host orthotropic (graphite-epoxy laminate) with surface embedded and spanwise distributed transversely isotropic (PZT-4) sensors and actuators. The total current output from all sensors is distributed to the actuators after suitable weighting. A modified Galerkin method that uses only admissible functions is considered, and the optimal control problem is studied via the classical and instantaneous LQR methods. The effect of transverse shear, ply angle, fulfilment of traction free boundary conditions, piezopatch location and size, and weighting matrices in the performance index on the controlled blade-tip response is obtained for various excitations, and pertinent conclusions are outlined.

In the design procedure of surface acoustic wave (SAW) devices simple models like equivalent circuit models or the Coupling of Modes (COM) model are used to achieve short calculation times. Therefore, these models can be used for iterative component optimization. However, they are subject to many simplifications and restrictions. In order to improve the parameters required for the simpler models and to achieve better insight ot the physics of SAW devices analysis tools solving the constitutional partial differential equations are needed. We have developed an efficient calculation scheme based on the finite element method. It makes use of newly established periodic boundary conditions (PBCs) allowing the simulation of an infinitely extended SAW device. This is a good approximation of many SAW devices which show a large number of periodically arranged electrodes. We have developed two different formulations for the PBCs: One leads to a small quadratic eigenvalue problem operating on a larger matrix. These formulations allow the calculation of the complete dispersion relation. Bulk acoustic waves (BAWs) which are generated due to mode conversion at electrode edges are allowed to leave the calculation area nearly without reflection. Therefore, the calculation scheme also considers damping coefficients caused by the conversion of surface waves into bulk waves. This behavior coincides well with real SAW devices in which the substrate thickness is large compared to the used wavelengths and, additionally, the bulk waves are scattered in all directions at the rough substrate bottom. In the paper, a short introduction to the basic theory of the numerical calculation scheme will be given first. The applicability of the calculation scheme will be demonstrated by comparing analytical, measured and simulated results.

Due to the coupled mechanical and electrical properties, piezoelectric materials are widely adopted for sensing purpose. In order to predict the device behavior in the design phase, many finite element tools were developed. However, most of the elements did not concern about the equipotential nature of sensor electrodes and the equipotential constraint has to be imposed in the structure level. This paper develops a composite plate element that the equipotential condition of electrode is ensured automatically. The element is displacement-electric potential type that can model elastic plates bonded with piezoelectric sensing layer. The formulations of displacement and electric potential fields are based on Mindlin plate model and the element is deduced from Hamilton's principle. In order to model physical behavior reasonably, different power series are assigned to displacements and electric potential respectively. Employing penalty function method imposes the equipotential condition on element electrode. Thus the element has the capability to analyze deformation, natural frequencies, and electrical signal efficiently. Patch tests are carried on different problems whose analytic solutions are available. In static constant stress situations, these tests show that the element correctly finds out the displacements, stresses, and electric potential. The excellent convergent rate of the natural frequencies demonstrates it is also good for dynamic analysis.

Atomic force microscopes employ stacked or cylindrical piezoceramic actuators to achieve sub-angstrom resolution. While these devices produce excellent set-point accuracy, they exhibit hysteresis and constitutive nonlinearities even at low drive levels. Feedback mechanisms can mitigate the deleterious effects of these nonlinearities for low frequency operation but such techniques fail at higher frequencies due to increased noise to signal ratios. In this paper, we quantify the hysteresis and constitutive nonlinearities through a Preisach model. As illustrated through a comparison with experimental data, this provides a characterization which is sufficiently accurate for inclusion as an inverse compensator in various control designs.

An analytical model for free vibration analysis of piezoelectric coupled thick circular plate is presented based on Mindlin's plate theory. The distribution of electric potential along the thickness direction is simulated by a sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. Numerical investigations are performed for plates sandwiched in between two surface-bonded piezoelectric layers for various diameter-thickness ratios and the results agree well with those from three-dimensional finite element analyses.

This paper addresses the development of distributed models for unimorphs comprised of an active PVDF layer bonded to an inactive polyimide layer. Thin beam theory is employed to quantify displacements along the unimorph length as a function of input voltages. The theory is based on the assumption of linear piezoelectric relations but is posed in a format which can be directly extended to incorporate dielectric hysteresis and nonlinearities if the application warrants. A variety of structural damping models are considered and it is illustrated that in low drive regimes, the assumption of Kelvin-Voigt damping produces a unimorph model which accurately predicts the elliptic losses measured in experimental data.

Comprehensive micromechanical models for smart composite materials with a periodic structure are derived and effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients pertaining to these structures are obtained. The actuation coefficients characterize the intrinsic nature of adaptive structures that can be used to induce strains and stresses in a controlled manner. The effective coefficients replace the rapidly oscillating coefficients inherent to the differential equations that govern the behavior of smart anisotropic materials with a regular array of reinforcements and actuators. The mathematical framework employed is that of asymptotic homogenization that permits the determination of the effective coefficients through solution of unit cell problems. The unit cell problems are shown to be independent of the global boundary value problem. It is implicit of course that the physical model based on these coefficients should give predictions differing as little as possible from those of the original problem. Once determined, the effective coefficients can be utilized in studying different types of boundary value problems associated with a given structure. The effectiveness of the derived models and the use of the effective coefficients is illustrated by means of various two- and three-dimensional examples associated with periodic laminates.

Over the past years, piezoelectric ultrasonic motors have received considerable attention. Significant research has been done towards modeling disc and shell type ultrasonic traveling wave motors. In this paper, a simple mathematical model of a different kind of ultrasonic motor, the bar-type or wobbling-disc motor is attempted, giving reliable results in the torque-speed characteristics including stick as well as slip conditions.

Ultrasonic motors often use a combination of structural modes to generate the desired elliptical vibration field that ultimately results in the linear or rotary motion of an object. Designing an ultrasonic device that combines structural modes of vibration represents a non-trivial exercise, especially when it is desired to maximize the electromechanical coupling coefficient of the piezoelectric elements, the amplitude of vibration, and the force factor of the device. Other parameters may also be combined and render the exercise even more difficult: targeting a specific frequency, constraining dimensions, electrical constraints, etc. To help designing such ultrasonic structures, we propose to use the genetic optimization method in combination to the finite element method. Although evolutionary methods are not new and have been successfully applied to a variety of problems (including smart devices), they have never been applied, to the best of our knowledge, to the design of ultrasonic motors. In this paper, we review the general aspects of the method utilized, and provide several examples, including experimental verification.

We consider the integrated optimization of electrically driven Recurve actuators. The drive circuit is based on a half-bridge switching amplifier topology. Both actuator and circuit physical design variables are considered in the optimization formulation. The objective is to minimize the weight of the system while satisfying performance and stability constraints. The interactions and trade offs between the actuator and the drive circuit are investigated. Optimization results show clear interrelations between the design of the electric circuit and the actuator. The optimization is based on an integrated model of the electronics with the Recurve actuator. A finite element model for Euler-Bernoulli beams is developed with appropriate coupling interface to the drive circuit. The proposed finite element model correctly considers charge variation over the actuator and leads to an energy conservative formulation. The structural model is coupled to the electric circuit model via charge-voltage transfer function.

Piezoelectric shunt damping systems reduce structural vibration by shunting an attached piezoelectric transducer with an electrical impedance. Current impedance designs result in a coupled electrical resonance at the target modal frequencies. In practical situations, variation in structural load or environmental conditions can result in significant changes in the structural resonance frequencies. This variation can severely reduce shunt damping performance as the electrical impedance remains tuned to the nominal resonance frequencies. This paper introduces a method for online adaption of the shunting impedance. A reconstructed estimate of the RMS\ strain is minimized by varying the component values of a synthetic shunt damping circuit. The presented techniques are applied in real time, to tune the component values of a randomly excited beam.

This paper present a methodology for impact identification on smart composites. The methodology is composed of four major parts: smart structures for detecting impact to composite; the cross correlation process; feature extraction and adaptive neuro fuzzy inference system (ANFIS) for identifying impacts. The smart structure comprises two piezoelectric transducers embedded in a composite specimen. These are used to measure impact signals caused by foreign object impacts. The impact signals are processed with a cross correlation algorithm and show very clean and meaningful variations in amplitude and shape with differing impact events. Signal features are extracted from the cross correlation results and are processed by methods of mean, standard deviation, kurosis and skewness. The ANFISs are trained, checked, and tested with the feature data to identify abscissas of impact location, ordinates of impact location, and impact magnitude. There are two new aspects to have been developed in this study. The results of implementing the system are discussed and conclusions drawn.

A control scheme which attempts to address the performance improvement of a system subject to spatiotemporally varying disturbances is proposed within the context of vibration suppression in flexible structures. This is achieved by switching to different actuators at different time intervals. Specifically, the flexible structure under study is assumed to have multiple piezoceramic actuators available with only one being active over a time interval of fixed length while the remaining ones remain dormant. By viewing the system as a Linear Parameter Varying one, a global controller is found that is a stabilizing one for all combinations of active/dormant actuators. The computation of the parameter varying compensator employs convex optimization methods and via LMIs, the desired controller having a certain performance level is found. This actuator switching mimics the case of a moving actuator capable of residing in predetermined positions within the spatial domain of the flexible structure. In the proposed algorithm, a control logic is incorporated that only selects the next actuator to be activated from the set of the remaining actuators using a performance-based measure. Numerical studies for a flexible beam are presented to support the analytical findings of this work.

Engineers are often required to design mechanical structures to meet specific loading conditions. Topological optimization automates the process of finding an optimal structural design, allowing for size, shape and topological variations. For a given set of boundary conditions and design specifications (constraints), a structure, optimal in terms of a formulated cost function, is computed. As the cost function, static properties such as the mean compliance, as well as dynamic properties such as the eigenfrequencies of the structure can be chosen. In this paper, the optimization considers not only the placement of conventional material, but also, simultaneously, the placement of smart PZT material. In the formulation of the topology optimization problem, a microstructure consisting of smart as well as conventional material is used. Instances of the microstructure occur in a rectangular grid and cover the design domain. Since the microstructure is defined parametrically, the density of each material can be controlled independently at each point. This enables one to formulate the problem of finding an optimal material distribution as a parameter optimization problem. A homogenization approach is used to find and use effective material properties for the limiting case of an infinitely small microstructure. Several numerical examples demonstrate the use of this method.

In this work, the mechanical design and optimization of high-sensitivity piezoresistive cantilevers used for detecting changes in surface stresses due to binding and hybridization of biomolecules on the surface of the cantilever is investigated. The silicon-based cantilevers are typically of a micron order thickness doped with boron to introduce piezoresistivity. Microcantilever beams can be built as micro-mechanical arrays which could provide a basis for developing devices capable of performing multi-plexed, low-cost genomic and proteomic analyses. This paper provides several design solutions in optimizing the cantilever mechanical design to address the sensitivity required when approaching recognition of single base pairing of DNA molecules. The sensitivity of such piezoresistive cantilevers to the chemo-mechanical stress induced currents depends not only on the cantilever geometric properties, such as depth and width but also on the depth of the piezo layer (dopant) and its doping characteristics. It is often an expensive exercise to determine the optimum design parameters for increased sensitivity, particularly the dopant characteristics for such MEMS devices. A managed solution or parametric solution algorithm based on a finite element simulation is used to help determine optimum location and depth of this piezoresistive layer in the cantilever that maximizes the piezoresistor signals. Further, novel approaches for increasing the sensitivity of piezoresistive cantilevers through selected structural discontinuities are discussed.

The optimal placement of piezoelectric sensor/actuator (S/A) pairs to maximize the damping effect of a composite plate under a classical control framework using the finite element approach is investigated. Due to the discretization of the spatial domain, the problem falls under the class of discrete optimization. Two optimization performance indices based on modal and system controllability are adopted. The classical direct pattern search method is employed to obtain local optima. It is proposed that the starting point for the pattern search be selected based on the maxima of integrated principal strains consistent with the size of piezoelectric patches used, which would maximize the virtual work done by the equivalent actuation forces along the corresponding mechanical displacements. In this way, the global optimal placement can be efficiently deduced. Numerical simulation using a cantilever composite plate under free vibration shows that the proposed strategy to locate the optimal placement is practical and efficient, with results very close to the global optimal layout from exhaustive search. The speed of convergence is rapid compared to an initial blind discrete pattern search approach. For the specific example used, the S/A pairs positioned close to the support are most effective whereas those near the free end are the least effective, for the first two modes. S/A pairs placed furthest from the center line of the cantilever plate are most effective for torsional vibration control. These findings are in good agreement with the published results.