This paper develops a macroscopic polarization switching model which characterizes the ferroelastic switching mechanisms inherent to lead zirconate-titanate (PZT) in a manner suitable for subsequent transducer and control design. We construct Helmholtz and Gibbs energy relations at the lattice level which quantify the internal and electrostatic energy associated with 90 and 180 degree dipole orientations. Equilibrium relations appropriate for homogeneous materials in the presence of thermal relaxation are determined by balancing the Gibbs and relative thermal energies using Boltzmann principles. Macroscopic models suitable for nonhomogeneous, polycrystalline compounds are constructed through stochastic homogenization techniques. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.

A computational multi-field mechanics model of composite micromechanical systems (MEMS) with piezoelectric actuation and sensing has been developed as a design tool for micro-resonators. These devices are to be used for filters and other signal processing applications. The developed dynamic model of MEMS resonators accounts for structural properties and the electromechanical coupling effect through finite element analysis. It is assumed that the deflection is large and that the geometric nonlinearity must be included. The mechanical strain is assumed to be small so that the linear constitutive relations are valid. The dynamic admittance model is derived by combining the linear piezoelectric constitutive equations with the modal transfer function of the micro-resonator structure. The resonator receptance matrix is constructed through modal summation by considering only a limited number of dominant modes. The electromechanical coupling determination at the input and output ports makes use of the converse and direct piezoelectric effects. In the development of the finite-element models, boundary conditions, electrodes shaping, and factors such as varying elastic modulus across the length of the beam for the multilayered structure are taken into account. The coupled model can be used to carry out sensitivity studies with respect to the following: i) resonator thickness and length; ii) influence of constant axial forces on the transverse vibrations of clamped-clamped micro-resonators; geometry of the drive and sense electrodes; and iii) imperfect boundary conditions due to mask imperfections and fabrication procedure. The developed model has been validated by comparing the predictions with results available in the literature for clamped-clamped resonators.

Forced oscillations of piezoelectric, micro-electromechanical (MEMS) resonators fabricated as clamped-clamped composite structures are studied in this effort. Piezoelectric actuation is used to excite these structures on the input side and piezoelectric sensing is carried out on the output side. Each resonator structure is modeled as an Euler-Bernoulli beam with axially varying properties across the length and distributed actuation. A nonlinear integro-partial differential system is derived to describe the micro-resonator. For weak damping and weak forcing, the method of multiple scales is used to obtain an approximate solution of the system about a post-buckling position. The different modeling assumptions are presented and discussed, and the analytical prediction is compared with experimental observation.

In this paper, the dynamic analysis of an Adaptive Circular Composite Plate (ACCP) with asymmetric constraints with respect to the angular coordinate system is investigated. Due to the asymmetric constrains, the shape functions of the circular plate could not be simply obtained from the partial differential equation by ignoring the angular dependency. Using the method of separation of variables, the mode shapes are expanded in Bessel series. The comparison of the developed analytical mode shapes with the Finite Element Method (FEM) mode shapes confirmed the validation of the analytical model. A modeling strategy using Rayleigh-Ritz method is presented to build the system model. Taking the effects of piezoelectric actuators on the dynamics of the ACCP into account, the optimal placement of the actuators is investigated. Also, employing the developed model, the simulation of the vibration control is implemented on the ACCP with one central simply support and three edge simply supports using LQR controller. The simulation results verify the best performance of the LQR controller with the optimal configuration for vibration suppression of the ACCP.

The objective of this investigation is to present a computational scheme for the optimal placement of actuating devices in flexible plates that utilize piezoceramic patches as actuators. In addition to controllability criteria, the candidate locations are required to also exhibit robustness with respect to the spatial distribution of disturbances. These PZT actuators are bonded at optimal locations that are determined by statically minimizing the optimal value of a disturbance-to-output transfer function with respect to the worst distribution of disturbances. Once the optimal actuator locations are determined, that in addition to performance specifications also satisfy a spatial robustness criterion, a suitable LQR-based controller is designed. At a given interval of time, only one PZT is activated and the remaining ones are kept dormant. The rationale of actuator/controller switching is to demonstrate the better vibration alleviation characteristics of switching between actuators over the use of a single actuator that is always in continuous use. The optimality of switching is made with respect to a cost-to-go performance index that corresponds to each actuating device. Extensive computer simulations with repeatable spatiotemporally varying disturbance profiles, reveal that this algorithm offers better performance over the non-switched case.

Use of piezoelectric patches as sensors and actuators for the vibration control of beams is a well established technology. Various techniques developed to analyze these problems range from analytical to computational ones, each with a different level of complexity and accuracy. In the present paper three techniques, namely, Laplace Transform, integral equation and assumed modes are applied to the vibration control problem involving a cantilever beam with piezoelectric patches attached to the top and bottom surfaces. These patches act as sensors and actuators providing a feedback control mechanism for the damping of vibrations. The Laplace Transform involves the transform of the space part of the partial differential equation governing the motion of the beam and inverse transform to find the exact solution. The integral equation approach transforms the differential equation formulation to an integral equation formulation which, in turn, is replaced by an infinite system of equations. As such this method provides an approximate solution, the accuracy of which depends on the size of the system of linear equations involved. The assumed modes method is quite widely used because of its ease of application, and its accuracy depends on the number of terms in the series approximation used to express the solution. The above solution methods are summarized and difficulties, drawbacks and advantages associated with each method are discussed. The accuracy of each technique is compared and assessed in the context of a vibrating cantilever beam with patches. The results are given in a comparative manner which also includes the exact solutions.

The constitutive behavior of magnetostrictive materials exhibits many nonlinearities. One of the dominate nonlinearities is the quadratic dependence between the drive current and the transducer displacement. While the transducer can be operated at low drive levels with little distortion, at high drive levels the square law distortion is evident. In this paper we propose a nonlinear feedback loop for the drive amplifier such that the amplifier provides a compensation for this transducer nonlinearity. Thus the combination of the amplifier and the magnetostrictive transducer presents a linear input output relationship to the user. The effectiveness of this nonlinear control is demonstrated in simulation.

Electrostrictor transducers are attractive because of their (relatively) large displacements. However, they exhibit a quadratic nonlinearity between the charge and displacement as well as a nonlinear relationship between charge and voltage. These nonlinearities limit the useful range for linear output. For example, in acoustic applications, these nonlinearities limit the range of displacements that do not generate higher order harmonics. In this paper we describe a nonlinear electronic controller to mitigate the effects of the material nonlinearity. We also provide a stability proof for the nonlinear controller. This proof is based on a Lyapunov stability proof for a nonlinear capacitor with modifications.

We consider a three layer Rao-Nakra sandwich beam with damping proportional to shear included in the core layer. We prove that eigenvectors of the beam form a Riesz basis for the natural energy space. In the damped case, we are able to give precise conditions under which solutions decay at a uniform exponential rate. We also consider the problem of boundary control using bending moment and lateral force control at one end. We prove that the space of exact controllability has finite co-dimension and provide sufficient conditions (related to small damping) for exact controllability to a zero energy state.

A one-dimensional, axisymmetric, linear finite element model describing a fluid interacting with a piezoelectric actuator is developed. This system is used to generate finite amplitude standing waves in an acoustic cavity with rigid walls. The model includes the effects of viscous and thermal damping of the fluid at the boundary of the cavity, and material damping in the piezoelectric actuator. Two types of piezoelectric actuators are considered, a stacked layer actuator, and a bending bimorph actuator. The resulting finite element equations are used to determine the optimum shape for the acoustic cavity that results in the highest pressure for the least input power. Optimal chambers were found that could generate 19 psi at 1700 Hz for 50 watts of power using air as a working fluid and 70 psi at 950 Hz for 42 watts of power using R-134A as a working fluid. The optimization results were verified against the commercial finite element code ANSYS and published experimental data. The potential of the transition of the developed technology to other fields is viable and is only limited by our imagination as it includes numerous applications such as the inflation of inflatable structures, inflation of tires and refrigeration and air-conditioning.

The idea of a morphing aircraft wing has generated considerable interest in recent years. Such a structure has inherent advantages of possessing high maneuverability and efficiency under different flight conditions such as take off, cruise and loiter. The current focus is on achieving continuous wing shape change, as opposed to discrete, in order to help reduce drag. This research aims to achieve continuous wing morphing by employing a wing structure comprising of an optimized internal layout of cables and struts. Cables are employed as actuators while struts provide rigidity to the wing. In addition to achieving continuous morphing by changing cable length, this structure has the advantage of being light in weight. The focus of this paper is on obtaining an optimized cable and strut layout in the body of the wing. Non-linear Finite Element Analysis (FEA) has been performed to account for the large deflection requirements. An objective function that considers deflection under actuation and air loads has been incorporated. Results comparing linear and non-linear FEA are presented for a particular wing design. The nonlinear finite element is found to be effective when using large actuation forces.

This paper concerns optimization of prestress of a tensegrity structure to achieve the optimal mixed dynamic and control performance. A linearized dynamic model of the structure is derived. The force density variables that parameterize prestress of the structure appear linearly in the model. The feasible region of these parameters is defined in terms of the extreme directions of the prestress cone. Several properties of the problem are established inside the feasible region of the parameters. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.

The objective of this research is to determine the optimal topology of a piezoelectric actuator on an elastic base beam undergoing harmonic excitation. The piezoelectric actuator is modeled using finite elements. This preliminary research provides insight into the potential of optimized piezoelectric actuators. Results from topology optimization show that significant improvements in vibration amplitude reduction are possible by optimizing the actuator damping layer topology.

Reconfigurable and morphing structures have attracted attention for potentially providing a range of new functionalities including system optimization over broad operational conditions and multi-mission capability. One promising approach for creating large deformation morphing structures uses variable stiffness components to provide large deformation without large energy input to the system. In this paper, we present an automated approach to design shape morphing strategies for reconfigurable surfaces composed of variable stiffness components. Variable stiffness components create an ill-posed control problem and generally have multiple solutions for any given morphing task. We formulate this problem as an optimization search using genetic algorithms (GA) to efficiently search the design space and rapidly arrive at a family of plausible solutions. Our novel approach can simultaneously satisfy a broad range of design constraints including structural properties, mechanical loading, boundary conditions and shape. Critical to GA searching is an accurate and computationally efficient variable stiffness surface model. Computer simulation of the reconfigurable surface was performed using a physics based model of the variable stiffness surface. The surface is modeled as a thin elastic plate in which the stretching and bending elastic moduli are treated separately and as arbitrary functions defined over the surface. This allows for large deformations including complete foldings. The resulting non-linear difference equations are solved using various preconditioned global search based relaxation algorithms. The results of our simulations show that our approach not only allows us to verify the feasibility of morphing tasks of variable stiffness surfaces, but also enables us to efficiently explore much larger design spaces resulting in unique and non-obvious morphing strategies.

Piezoresistive materials, materials whose resistivity properties change when subjected to a mechanical stresses, currently have wide industry application for building MEMS, such as, pressure sensors, accelerometers, inclinometers, and load cells. A basic piezoresistive sensor consists of piezoresistive material bonded to a flexible structure, such as a cantilever, membrane, or compliant mechanism, where the flexible structure transfers pressure, force, or inertial force (due to acceleration), thereby causing a stress that changes the resistivity of the piezoresistive material. By applying a voltage to the material, its resistivity can be measured and correlated with the degree of applied pressure or force. The performance of the piezoresistive sensor is closely related to the design of its flexible structure which can be achieved by applying systematic design methods, such as topology optimization. Thus, in this work, a topology optimization formulation has been applied to the design of piezoresistive sensors. As an initial problem, a piezoresistive force sensor design is considered. The optimization problem is posed as the design of a flexible structure that bonded to the piezoresistive material generates the maximum response in terms of resistivity change (or output voltage) when a force is applied.

This paper presents a new class of compliant surfaces, dubbed tensegrity fabrics, for the problem of reducing the drag induced by near-wall turbulent flows. The substructure upon which this compliant surface is built is based on the "tensegrity" structural paradigm, and is formed as a stable pretensioned network of compressive members ("bars") interconnected by tensile members ("tendons"). Compared with existing compliant surface studies, most of which are based on spring-supported plates or membranes, tensegrity fabrics appear to be better configured to respond to the shear stress fluctuations (in addition to the pressure fluctuations) generated by near-wall turbulence. As a result, once the several parameters affecting the compliance characteristics of the structure are tuned appropriately, the tensegrity fabric might exhibit an improved capacity for dampening the fluctuations of near-wall turbulence, thereby reducing drag. This paper improves our previous work (SPIE Paper 5049-57) and uses a 3D time-dependent coordinate transformation in the flow simulations to account for the motion of the channel walls, and the Cartesian components of the velocity are used as the flow variables. For the spatial discretization, a dealiased pseudospectral scheme is used in the homogeneous directions and a second-order finite difference scheme is used in the wall-normal direction. The code is first validated with several benchmark results that are available in the published literature for flows past both stationary and nonstationary walls. Direct numerical simulations of turbulent flows at Re_tau=150 over the compliant tensegrity fabric are then presented. It is found that, when the stiffness, mass, damping, and orientation of the members of the the unit cell defining the tensegrity fabric are selected appropriately, the near-wall statistics of the turbulence are altered significantly. The flow/structure interface is found to form streamwise-travelling waves reminiscent of those found at air-water interfaces, but traveling at a faster phase velocity. Under certain conditions, the coupled flow/structure system is found to resonate, exhibiting a synchronized, almost sinusoidal interfacial motion with relatively long streamwise correlation.

This work investigates the design of a new class of three dimensional tensegrity tower structures with nodes lying on a cylinder. The novel aspect of the proposed topology is the fact that all bars in all stages are oriented in the same way, clockwise or counterclockwise. We investigate the existence of conditions for static equilibrium of such towers with an arbitrary number of stages and uniform force distribution.

Optical jitter degrades the pointing and imaging performance of precision optical systems. When a correlated measurement of the disturbance is available, improved control performance can be attained. In this research, an adaptive optimal sensing strategy for optical systems is proposed. An array of reference sensors makes it possible to estimate the disturbance and model the disturbance-to-reference paths. The least-square algorithm is applied for the disturbance model estimation. A sensor scoring algorithm is then used to select an optimal disturbance reference from the available reference signals. The optimal disturbance reference is comprised of sensors which are well correlated with the disturbance. This disturbance reference is then fed forward and used in an adaptive generalized predictive control design. This adaptive control approach is advantageous in the presence of time-varying or uncertain disturbances. The proposed technique is applied to an experimental test bed in which an array of accelerometer sensors measures the structural vibration of optical elements. Reduction of the structural vibration of optical components is attained using a fast steering mirror which results in a reduction of the corresponding jitter. Performance using optimally selected disturbance reference is shown to be better than for system in which a disturbance reference signal is chosen to be the sensor with the lowest score.

Progress as well as future challenges of wavelet analysis of signal processing for Smart Structures will be assessed. Wavelet analysis has provided two major capabilities: noise reduction and data compression. Wavelet phase determination is particularly useful for wavefront sensors based on interferometry: Mach-Zehnder, Michelson, shearing and Fabry-Perot interferometers. This capability will be applied to future Smart Structures applications.

In this article, recent investigations into the dynamic behavior of a sensor diaphragm under initial tension are presented. A comprehensive mechanics model based on a plate with in-plane tension is presented and analyzed to examine the transition from plate behavior to membrane behavior. It is shown that, for certain tension parameter values, it is appropriate to model the diaphragm as a plate-membrane structure rather than as a membrane. In the nonlinear analysis, the effect of cubic nonlinearity is studied when the excitation frequency is either close to one-third of the first natural frequency or the first natural frequency. The nonlinear effects limit the sensor bandwidth and dynamic range. The study shows that both of the nonlinear effects can be attenuated by decreasing the diaphragm thickness and applying an appropriate tension to realize the desired first natural frequency while reducing the strength of the nonlinearity. The analyses and related results should be valuable for carrying out the design of circular diaphragms for various sensor applications, in particular, for designing sensors on small scales.

We suggest using distributed fiber Bragg sensors systems which were developed locally at Langley Research Center carefully placed on the wing surface to collect strain component information at each location. Then we used the fact that the rate change of slope in the definition of linear strain is very small and can be treated as a constant. Thereby the strain distribution information of a morphed surface can be reduced into a distribution of local slope information of a flat surface. In other words a morphed curve surface is replaced by the collection of individual flat surface of different slope. By assembling the height of individual flat surface, the morphed curved surface can be approximated. A more sophisticated graphic routine can be utilized to restore the curved morphed surface. With this information, the morphed wing can be further adjusted and controlled. A numerical demonstration is presented.

There are numerous applications where a voice coil actuator is used for position control and it is not desirable to have a physical position sensor for feedback. This paper proposes a technique for sensorless position estimation of a linear voice coil transducer using sliding mode observers. The method exploits the fact that some voice coil designs possess position-dependent force and back-emf parameters due to their geometrical properties. Using an observer structure that incorporates these position-dependent parameters of the transducer allows the coil position to be observed from a current measurement. The nonlinear model developed for the voice coil is validated and experimental results are presented and discussed. Observability is proven and the results are incorporated into a sliding mode position feedback control algorithm.

The (approximate) diagonalization of symmetric matrices has been studied in the past in the context of distributed control of an array of collocated smart actuators and sensors. For distributed control using a two dimensional array of actuators and sensors, it is more natural to describe the system transfer function as a complex tensor rather than a complex matrix. In this paper, we study the problem of approximately diagonalizing a transfer function tensor via the tensor singular value decomposition (TSVD) for a locally spatially invariant system, and study its application along with the technique of recursive orthogonal transforms to achieve distributed control for a smart structure.

Turbulent boundary layer (TBL) noise is considered a primary contribution to the interior noise present in commercial airliners. There are numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a potential challenge since physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions were assumed; however, realistic panels likely display a range of boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of transducers required to achieve the desired control. The impact of model uncertainties, specifically uncertain boundaries, on the selection of transducer locations for structural acoustic control is considered herein. The final goal of this work is the design of an aircraft panel structure that can reduce TBL noise transmission through the use of a completely adaptive, single-input, single-output control system. The feasibility of this goal is demonstrated through the creation of a detailed analytical solution, followed by the implementation of a test model in a transmission loss apparatus. Successfully realizing a control system robust to variations in boundary conditions can lead to the design and implementation of practical adaptive structures that could be used to control the transmission of sound to the interior of aircraft. Results from this research effort indicate it is possible to optimize the design of actuator and sensor location and aperture, minimizing the impact of boundary conditions on the desired structural acoustic control.

A nonlinear optimal control method is developed for magnetostrictive actuators used to actively attenuate plate vibration. Significant improvements in vibration control can be achieved when the magnetostrictive actuators are driven at moderate to high field levels. This results in nonlinearity and hysteresis which cannot be effectively compensated using linear control theory. This issue is addressed by introducing a homogenized energy model that accounts for nonlinear, hysteretic constitutive behavior into the control design. Numerical examples illustrate significant improvements in vibration attenuation when the nonlinear control method is implemented.

The objective of this paper is to provide an experimental verification of a new H-infinity control scheme on a flexible beam which uses a collocated PZT actuator/sensor pair. We use an analytical bound approach that provides an explicit expression of an upper bound on the H-infinity norm of the closed-loop system and an explicit parametrization of the corresponding output feedback control gains. The method has great computational advantages for large scale structural systems where the solution of H-infinity optimization problems using standard tools could be computationally prohibitive. Both experimental and numerical results are presented that provide a comparison of the performance and the computational requirements on the controller design using the standard H-infinity formulation and the proposed analytical bound approach.

The last decade has witnessed the discovery of materials combining shape memory behavior with ferromagnetic properties (FSMAs), see James & Wuttig1, James et al.2, Ullakko et al.3. These materials feature the so-called giant magnetostrain effect, which, in contrast to conventional magnetostriction is due motion of martensite twins. This effect has motivated the development of a new class of active materials transducers, which combine intrinsic sensing capabilities with superior actuation speed and improved efficiency when compared to conventional shape memory alloys. Currently, thin film technology is being developed intensively in order to pave the way for applications in micro- and nanotechnology. As an example, Kohl et al., recently proposed a novel actuation mechanism based on NiMnGa thin film technology, which makes use of both the ferromagnetic transition and the martensitic transformation allowing the realization of an almost perfect antagonism in a single component part. The implementation of the mechanism led to the award-winning development of an optical microscanner. Possible applications in nanotechnology arise, e.g., by combination of smart NiMnGa actuators with scanning probe technologies. The key aspect of Kohl's device is the fact that it employs electric heating for actuation, which requires a thermo-magneto-mechanical model for analysis. The research presented in this paper aims at the development of a model that simulates this particular material behavior. It is based on ideas originally developed for conventional shape memory alloy behavior, (Mueller & Achenbach, Achenbach, Seelecke, Seelecke & Mueller) and couples it with a simple expression for the nonlinear temperature- and position-dependent effective magnetic force. This early and strongly simplified version does not account for a full coupling between SMA behavior and ferromagnetism yet, and does not incorporate the hysteretic character of the magnetization phenomena either. It can however be used to explain the basic actuation mechanism and highlight the role of coupled magnetic and martensitic transformation with respect to the actuator performance. In particular will we be able to develop guidelines for desirable alloy compositions, such that the resulting transition temperatures guarantee optimized actuator performance.

A new approach to designing and controlling multiple artificial muscle actuators using Segmented Binary Control (SBC) is presented and is implemented using shape memory alloys (SMA). SMA actuators are segmented into many independently controlled, spatially discrete volumes, each contributing a small displacement to create a large motion. The segmented architecture of SMA wires is extended to a multi-axis actuator array by arranging them in a two-dimensional array. For multi axis case, the number of segments can be reduced by activating adjacent SMA wires with coupled segments. Coupled segments activate multiple actuators that the segment covers. Although independence of the adjacent SMA wires is reduced to a certain degree, coordinated movements are generated. The shape and position of the coupled segments can be designed using the "similarity" of output trajectories of each actuator. SBC is extended into Hysteresis Loop Control, which reduces the delay in the system by using four different temperatures instead of just two temperatures that the SBC uses. Thermoelectric devices are used to locally heat and cool the SMA wires. Single-axis experimental setup is built to verify and compare the SBC and HLC, and multi-axis array actuator system that uses SBC is built with ten SMA actuators in parallel.

Pseudoelastic shape memory alloys (SMAs) have great potential of shock absorption because of their large reversible strain and the "force-thresholding" characteristics, especially when used with geometric nonlinearity such as post-buckling deformation. Martensitic SMAs also have favorable shock absorption capacity with actuation capability. In this paper, we attempt to apply both pseudoelastic and martensitic SMAs to the design of the outer skins of mechanical and structural systems to give them significant shock tolerance. The shock isolation capability of pseudoelastic NiTi thin wire is firstly examined by low velocity weight-dropping tests. Then, as the first step toward the development of woven SMA-based shock absorbing skin, both pseudoelastic and martensitic SMA wires are woven to form mesh structures, and their shock absorbing characteristics are investigated. The tests suggest that the energy absorption capacity of the SMA mesh can be adjustable by combining appropriate amount of martensitic wires, even though that of the pseudoelastic SMA by itself is rather poor.

A simple yet accurate model of shape memory alloys (SMAs) is proposed, which can consider asymmetric tension-compression ferroelastic behavior. Features of this model are (1) energy-based transformation criterion, (2) partial transformation rule based on the micromechanical viewpoint, (3) required transformation energy in the form of a sum of two exponential functions in terms of phase volume fraction, and (4) energy balance equation including thermoelastic effect and dissipated energy due to interaction between the phases. In this ferroelastic model, three phases are considered, namely, an austenitic phase, a tensile stress induced martensitic phase, and a compressive stress induced martensitic phase. The tension-compression asymmetry is expressed by using different required transformation energy functions in different transformation directions and by using different intrinsic strains and Young's moduli in different phases. Stress-strain hysteresis loops for a SMA bar under tensile-compressive cyclic loading are simulated. The obtained result shows that the proposed model can well capture the asymmetric stress-strain loops for tension and compression, minor loops, and effects of temperature and strain rate. This indicates that this model would be a useful tool for understanding the mechanism of SMA behavior and designing smart structures with SMA elements.

Application of Rotational Isomeric State (RIS) theory to the prediction of Young's modulus of a solvated ionomer is considered. RIS theory directly addresses polymer chain conformation as it relates to mechanical response trends. Successful adaptation of this methodology to the prediction of elastic moduli would thus provide a powerful tool for guiding ionomer fabrication. The Mark-Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for a solvated Nafion case. The distribution of chain lengths is then fitted to a Probability Density Function by the Johnson Bounded distribution method. The fitting parameters, as they relate to the model predictions and physical structure of the polymer, are studied so that a means to extend RIS theory to the reliable prediction of ionomer stiffness may be identified.

Ionic polymer transducers exhibit coupling between the electrical, chemical, and mechanical domains, allowing their use as both sensors and actuators. Because of their compliance, light weight, and low voltage operation, ionic polymers have spawned an area of much research, although their fundamental mechanisms are still open for debate. While most of the existing models provide linear, dynamic approximations of the response, nonlinear characteristics have been observed experimentally. Some of these include the introduction of permanent strain in the step response and distortion in the forced response to harmonic excitations. Recent experimental results have shown that the solvent plays a significant role in the dynamic response of ionic polymer actuators. Given a single-frequency input voltage, the major difference from changing solvent materials was concluded to be a nonlinear distortion with varying influence, seen in both the actuation current and tip velocity measurements. These results compared the response of a water-based sample to a sample prepared with the ionic liquid EMI-Tf, where it was found that the voltage-to-current relationship was much more nonlinear in the water sample, while it was predominantly linear with the ionic liquid sample. This research looks to further explore this nonlinear distortion by incorporating a larger set of candidate solvent materials and investigating the impact of how changing properties affect the overall response. System identification techniques using the Volterra series are employed to aid in the characterization of the harmonic distortion. The knowledge gained in this study will provide useful information about the nature of the nonlinearity and some of the factors that affect its relative influence, which will assist physical model development.

This paper presents a new approach to numerical implementation of a classical Preisach model to hystersis modeling of Shape Memory Alloys (SMA). Classical Preisach hysteresis model is a phenomenological model and it offers various advantages over other models. After reviewing the basic properties of the classical Preisach model, this paper reveals one difficulty to numerically implement a classical Preisach model. Numerical simulations have to be done in two different cases: 1) when input ascends and 2) when input descends. Based on the geometrical interpretation, this paper proposed a unified approach to numerical implementation of a Preisach model and there is no need to consider the different cases. To demonstrate the effectiveness of the proposed numerical method, an experiment setup with an SMA wire with severe hysteresis is utilized. Experimental results convincingly demonstrate that the proposed method accurately captures the features of the hysteresis. Using the forward Preisach model, an approach to find the inverse model is presented for compensation purpose.

Numerical modeling of a three-dimensional acoustic field coupled with a piezoelectric-elastic structure demands significant computation load even on modern high speed computers. In particular, when the wavelength is much smaller than the field scale, the size of the coupled model and its computation time can be excessively large. In this paper, MHSV (Modal Hankel Singular Value) based model reduction technique is employed to minimize the size of the coupled model. This model reduction technique enables us to compare both the radiated and reflected waves from a piezoelectric-elastic source in three dimensional space. Thus, it considers the possibility to fully suppress reflected waves by radiating controlled wave in three dimensional space.

The present study describes a comprehensive investigation performed to study the effects of piezoceramic materials on the active damping of vibrating piezo-composite beams. The active damping is obtained by using an actuator and a sensor made of piezoceramic layers, acting in 'closed-loop'. By transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer, causes the beam to actively damp-out its vibrations. The voltage transferred from the sensor to the actuator has to be amplified through a feedback gain. An exact mathematical model based on a first order shear deformation theory (FSDT) was developed and described in order to study the effect of all four piezoelectric 'closed-loop' combinations (EE, SS, ES and SE). The first two combinations use only one piezoelectric mechanism, extension or shear, as both sensors and actuators, while the other two use piezoelectric mechanisms, extension and shear, in a combined 'closed-loop'. Using the present model, both natural and damped vibrations were calculated. Parametric studies were performed for investigating the required feedback gain, G, of each piezoelectric combination, and the effect of piezoelectric materials on damping higher frequencies was also studied.

Due to the extended application of piezoelectrics into a number of high performance structures, the necessity for accurate analysis of their behavior is of critical importance. In this work the dynamic analysis of a composite plate incorporating piezoelectric layers is presented. A 4-node plate finite element is developed. Discrete layer kinematic assumptions in combination with a thermal-electrical-mechanical coupled formulation takes place. This formulation enables the investigation of the response of a structure under the influence of different thermal and electrical conditions. Additionally, in order to investigate whether the kinematics assumptions implemented here are capable of capturing with accuracy the dynamic performance of both thin and thick structures, plates of different thicknesses are investigated.

Wave propagation characteristics can be computed analytically for simple geometries such as plates and cylinders but geometries that are more complex and waveguides comprising combinations of different materials require numerical analysis. Piezoelectric waveguide finite elements, which can model wave propagation in piezoelectric waveguides of arbitrary cross-section, were formulated and implemented. In these elements wave functions are used to describe the displacement variation along the waveguide with conventional finite element interpolation functions over the crosssection of the waveguide. The resulting two-dimensional element is very efficient for computing wave propagation in waveguides. The accuracy of the elements was verified by comparison with a three-dimensional finite element model with appropriate boundary conditions to represent a waveguide. An analytical expression was derived to compute the group velocities of waves in piezoelectric waveguides. Wavenumber and group velocity versus frequency curves were plotted for a piezoelectric waveguide with square cross-section. The elements were used to model 1-3 piezoelectric composite material. A unit cell, comprising one-quarter of the cross-section of the piezoelectric pillar and half the neighboring (non-piezoelectric) polymer was modeled with appropriate boundary conditions to represent the periodicity of the material. The results were verified with three-dimensional finite element modeling and the waveguide element model was found to be very accurate and efficient.

A vibration confinement is the act of restricting the vibration of a structure to a certain region on the structure. Confinement or restriction of vibrations to relatively unimportant areas helps in isolating vibration-sensitive components from vibratory disturbances and mitigating the damage of the components. In this research, an active vibration confinement technique based on full state feedback strategy, which was proposed by previous authors, is experimentally implemented and verified. The algorithm constructs a square matrix of the closed-loop eigenvectors and a rectangular matrix of the corresponding control vectors. Then, the control gain is uniquely determined by right-multiplying the inverse of the eigenvector matrix to the control vector matrix. The experiment is conducted for a pinned-pinned aluminum beam with two piezoelectric film sensors and two piezoceramic actuators bonded symmetrically along the beam. The vibration of the beam is estimated using an observer and the control actuation is realized using two piezoceramic patch actuators. Experimental results show that active vibration confinement can actually be realized for a lightly damped system with piezoceramic patch actuators.

Because the disturbances which govern the dynamical response of a structure cannot be precisely measured, and the system itself has many uncertainties, the development of control strategies that are implementable and that can accommodate uncertainties and imprecision are becoming a critical and challenging work. PID adaptive controller based on RBF Neural Networks Identifier is developed for structural control in this paper. The combined controller includes PID neural network controller and an identifier based on RBF neural networks. It was implemented on linear single degree of freedom system representation of structures subjected to external disturbances based on the El Centro (1940), Hachinohe (1988), Kobe (1995) and Northridge (1994) earthquake loadings. It is demonstrated that the neuro PID adaptive control method can effectively suppress the vibration of structures.

This paper presents the concept, control strategy, and simulations of suppressing the thruster-firing-induced vibration of satellites. First, a satellite vibration reduction concept of utilizing the UHM multifunctional platform is discussed, and the structural configurations of the platform as well as the combination of the platform and a satellite are described. A satellite-like frame with the platform is analyzed, and the predominant modes of the frame are determined. A MIMO adaptive control scheme is then developed to suppress the frame vibration, and a convergence factor vector concept is introduced to ease the multi-channel convergence rate control. This controller is adjusted based on the vibration information of the frame and drives the platform to isolate the vibration transmission from the firing thruster to the satellite structure. The entire system has ten actuators: four piezoelectric stack actuators and six piezoelectric patch actuators. Eleven vibration components of the frame and platform are controlled. Nine components are in the frame for the satellite vibration suppression, and two are in the top-device plate of the platform for the thruster vibration suppression. Finally, simulations are performed to suppress the vibration of the frame for three platform positions to simulate the misalignment correction of the satellite thrust vector. The results demonstrate that the entire frame vibration at its dominant frequency decreases to 7-10% of its uncontrolled value in the three platform positions, and the thruster vibration decreases to 7.5% of its uncontrolled value.

This paper reports damage detection and vibration control of a new smart board designed by mounting piezoelectric fibers with metal cores on the surface of a CFRP composite. Damage to the board is identified on the assumption that the piezoelectric fibers used as sensors and actuators are broken simultaneously at the damaged location. When such damage-induced breakage occurs, the piezoelectric fibers expand and contract between the root and the damaged position on the cantilever beam. Damaged positions are detected by focusing attention on this property. Furthermore, this deterioration of sensors and actuators caused by breaks in the piezoelectric fibers is a consideration in the design of the gain-scheduled controller. First, the length of the piezoelectric fibers is measured to derive a finite-element method (FEM) model of the cantilever beam. If the fiber length is shortened due to a break, there is a decrease not only in actuator performance but also in the sensor output. Thus, peak gain of the FEM model is calculated for the length of every piezoelectric fiber. Damage detection is based on the computed relation between peak gain and the damage position. Furthermore, a reduced-order model that considers only the first mode is derived for the controller design and transformed into a linear fractional transformation (LFT) representation for the gain-scheduled controller design. The position of the damage is the contributing parameter in the variation. Next, the gain-scheduled controller is designed using LFT representation. Finally, the simulation and experimental results of the damage detection and the gain-scheduled control are presented. These results show that our gain-scheduled controller can improve control performance when damage cause a break in the piezoelectric fiber.

The tracking control accuracy of the piezoelectric actuator (PEA) is limited due to their inherent hysteretic nonlinearity. Direct drive of PEA on a positioning stage with friction force causes control problems in static errors, varying dynamic frictional force, limit cycles and stick-slip, et al. An approximated PEA model is synthesized based on linear transfer function with two uncertainty parameters for time delay and frictional force effect. The frictional model of the motion stage in the presliding and sliding regimes is considered thoroughly. The H-infinite tracking controller is designed for compensating the hysteresis delay and frictional force in PEA actuated stage during positioning. The Iterative Learning Control (ILC) is implemented to reduce the unmodelled repetitive error from the frictional characteristics. Numerical simulations and experimental tests consolidate that the RMS positioning error can be close to the hardware reproducibility and accuracy level. Experimental results show the controlled piezo-stage can be potentially used for nano technology applications for precision engineering in industrial systems.

In this study the authors develop haptic systems for telerobotic surgery. In order to model the full range of tactile force exhibited from an MR damper a microstructural, kinetic theory-based model of Magnetorheological (MR) fluids has been developed. Microscale constitutive equations relating flow, stress, and particle orientation are produced. The model developed is fully vectorial and relationships between the stress tensor and the applied magnetic field vector are fully exploited. The higher accuracy of the model in this regard gives better force representations of highly compliant objects. This model is then applied in force feedback control of single degree of freedom (SDOF) and two degrees of freedom (2DOF) systems. Carbonyl iron powders with different particle sizes mixed with silicone oils with different viscosities are used to make several sample MR fluids. These MR fluid samples are then used in three different designed MR dampers. A State feedback control algorithm is employed to control a SDOF system and tracking a 2-D profile path using a special innovative MR force feedback joystick. The results indicate that the MR based force feedback dampers can be used as effective haptic devices. The systems designed and constructed in this paper can be extended to a three degree of freedom force feedback system appropriate for telerobotic surgery.

The shape control of thin, flexible structures has been studied primarily for edge-supported thin plates. For applications involving reconfigurable apertures such as membrane optics and active RF surfaces, corner-supported configurations may prove more applicable. Corner-supported adaptive structures allow for parabolic geometries, greater flexibility, and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Preliminary models have been developed for corner-supported thin plates actuated by isotropic piezoelectric actuators. However, typical piezoelectric materials are known to be orthotropic. This paper extends a previously-developed isotropic model for a corner-supported, thin, rectangular bimorph to a more general orthotropic model for a bimorph actuated by a two-dimensional array of segmented PVDF laminates. First, a model determining the deflected shape of an orthotropic laminate for a given distribution of voltages over the actuator array is derived. Second, symmetric actuation of a bimorph consisting of orthotropic material is simulated using orthogonally-oriented laminae. Finally, the results of the model are shown to agree well with layered-shell finite element simulations for simple and complex voltage distributions.

We present a computer model which allows us to explore the failure behavior of surface coatings. We use a quasi-static three-dimensional Lattice Spring Model coupled with the velocity Verlet algorithm to simulate surface coating on substrate systems. Fracture, elastic response, and shrinking are considered in our simulation method. The results provide a framework upon which the failure mechanisms of surface coatings can be investigated.

The transient response of delaminated smart composite laminates is studied using an improved layerwise laminate theory. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The Fermi-Dirac distribution function is combined with an improved layerwise laminate theory to model a smooth transition in the displacement and the strain fields of the delaminated interfaces during “breathing” of delaminated layers. Stress free boundary conditions are enforced at all free surfaces. Continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration of bimodular behavior caused by the contact impact of delaminated interfaces. Composite plate with surface-bonded or embedded sensors, subject to external loads, are also investigated to study the effects on transient responses due to various sizes and locations of delamination.

This paper presents a new form of the Bouc-Wen model called the normalized one. This form appears as a result of the analytical description of the limit cycle. The parameters that appear in this new form are the ones that influence in a direct way the shape of the hysteresis loop. This paper explores the relationship between these parameters and the behavior of the limit cycle.

The properties of the hybrid functions which consists of block-pulse functions plus Chebyshev polynomials are presented. By using these hybrid functions, the differential and integral expressions which arise in the radiative transfer equation are converted into some linear systems of differential equations which can be solved for the unknown coefficient. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results.

We propose a sensor calibration approach that is based on constructing statistical error models that capture the characteristics of the measurement errors. The approach is generic in the sense that it can be utilized in any arbitrary sensor modalities. The error models can be constructed either off-line or on-line and is derived using the nonparametric kernel density estimation techniques. Models constructed using various forms of the kernel smoothing functions are compared and contrasted using statistical evaluation methods. Based on the selected error model, we propose four alternatives to make the transition from the error model to the calibration model, which is represented by piece-wise polynomials. In addition, statistical validation and evaluation methods such as resubstitution, is used in order to establish the interval of confidence for both the error model and the calibration model. Traces of the acoustic signal-based distance measurements recorded by in-field deployed sensors are used as our demonstrative example. Furthermore, we discuss the broad range of applications of the error models and provide a tangible example on how adopting statistical error model as the optimization objective impacts the accuracy of the location discovery task for wireless ad-hoc sensor networks.

We have developed an on-line sensor calibration scheme that employes a additional single source as the external stimulus that creats differential sensor readings used for calibration. The key idea of our approach is to use an actuator to produce differential simultaneous excitement of all sensors over a number of time frames while the environment the sensors are deployed in is relatively inactive. The sensor calibration functions are derived in such a way that all sensors (or a group of sensors) agree on the effect of the actuator in the most consistent way. More specifically, we utilizes the maximal likelihood principle and a nonlinear system optimization solver to derive the calibration functions of arbitrary complexity and accuracy. The approach has the following noble properties: i) it is maximally localized in that each sensor only needs to communicate with one other sensor in order to be calibrated; ii) the number of time steps that are required for calibration is very low. Therefore, the approach is both communication and time efficitent. We present two variants of the approach: i) one where only two neighboring sensors have to communicate in order to conduct calibration; ii) one that utilizes an integer linear programming (ILP) formulation to provably minimize the required number of packets that must be sent for calibration. We evaluate the techniques using traces from light sensors recorded by in-field deployed sensors, and statistical evaluations are conducted in order to obtain the interval of confidence to support all the results.

In this paper, a finite element method to simulate the overall behavior of ultrasonic motor (USM) is proposed. Firstly, an iterative algorithm using ABAQUS^® version 6.4 to solve the contact problem with piezoelectric actuation is presented. In each iteration, the dynamic responses of stator actuated by piezoelectric force and updated contact force are solved, from which static (or steady state) contact between deformed stator and rotor are estimated. For the dynamics of stator, three dimensional solid elements are adopted and direct integration method is used because modal-based procedures do not adequately transform the electric loads into modal loads. Rayleigh damping is adopted with the ratio set to 0.5%. For the contact between deformed stator and rotor, Lagrange multiplier method is used to impose the normal and tangential contact constraints between the stator and rotor respectively. Based on the proposed procedure, given the applied torque, axial force, and piezoelectric drive voltages as inputs, the general measures of motor performance are obtained and compared with published numerical and experimental results. The approach presented here provides a more accurate framework with moderate computational cost for modeling USM and serves as a design tool for optimizing prototypes.

This paper proposes an effective vibration control algorithm using a smart damping system for vibration mitigation. The proposed algorithm, which extends Lyapunov stability theory into a unified system, enables to correct the errors in quantization by its increased stability. The validity of this design method is proved in the experiment on a control model of three-storied building structure. Smart damper is used for shear mode MR damper in the experiment, and its control effectiveness is evaluated. In order to make a more accurate control model experimentally, model updating is performed on the basis of the analysis of dynamic characteristics of structure and of the mathematical analysis of a lumped mass model, and then it employs a state space model redefined by structural property matrix. In this vibration control experiment, control effect under the influence of each different earthquake magnitude is evaluated to various performance index, and thus the algorithm presented here is proved to be valid.

In this paper, we present a new algorithm to implement the homogenized energy hysteresis model with thermal relaxation for both ferroelectric and ferromagnetic materials. The approach conserves most of the accuracy of the original algorithm, but enables all erfc and exp functions to be calculated in advance, thereby requiring that only basic mathematical operations be performed in real time. This is done without a signicant increase in memory usage. Using this approach, execution time of the model has been seen to improve by a factor of 70 for some applications, whereas the error only increases by five ten thousandths (0.05%) of the saturation polarization/magnetization. The model with negligible relaxation is also given, as it is used to illustrate some optimizations. Emphasis is placed on the ecient computation of these models, and theoretical development is left to the references.

An idea about software PnP (Plug & Play) is put forward according to the hardware PnP. And base on this idea, a virtual flexible digital signal processing system (FVDSPS) is carried out. FVDSPS is composed of a main control center, many sub-function modules and other hardware I/O modules. Main control center sends out commands to sub-function modules, and manages running orders, parameters and results of sub-functions. The software kernel of FVDSPS is DSP (Digital Signal Processing) module, which communicates with the main control center through some protocols, accept commands or send requirements. The data sharing and exchanging between the main control center and the DSP modules are carried out and managed by the files system of the Windows Operation System through the effective communication. FVDSPS real orients objects, orients engineers and orients engineering problems. With FVDSPS, users can freely plug and play, and fast reconfigure a signal process system according to engineering problems without programming. What you see is what you get. Thus, an engineer can orient engineering problems directly, pay more attention to engineering problems, and promote the flexibility, reliability and veracity of testing system. Because FVDSPS orients TCP/IP protocol, through Internet, testing engineers, technology experts can be connected freely without space. Engineering problems can be resolved fast and effectively. FVDSPS can be used in many fields such as instruments and meter, fault diagnosis, device maintenance and quality control.

A multiagent framework for data acquisition, analysis, and diagnosis in health management is proposed. It uses the contract net protocol, a protocol for high-level distributed problem solving that provides adaptive and flexible solutions where task decomposition and assignment of subtasks is natural. Java is used to wrap implementations of existing techniques for individual tasks, such as neural networks or fuzzy rule bases for fault classification. The Java wrapping supplies an agent interface that allows an implementation to participate in the contract net protocol. This framework is demonstrated with a simple Java prototype that monitors a laboratory specimen that generates acoustic emission signals due to fracture-induced failure. A multiagent system that conforms to our framework can focus resources as well as select important data and extract important information. Such a system is extensible and decentralized, and redundancy in it provides fault tolerance and graceful degradation. Finally, the flexibility inherent in such a system allows new strategies to develop on the fly. The behavior of a non-trivial concurrent system (such as multiagent systems) is too complex and uncontrollable to be thoroughly tested, so methods have been developed to check the design of a concurrent system against formal specifications of the system’s behavior. We review one such method-model checking with SPIN-and discuss how it can be used to verify control aspects of multiagent systems that conform to our framework.

In the linear static theory of thermoelasticity, the body force analogy dates back to Duhamel. In its classical form, it reads: Consider the static deformation of an isotropic linear thermoelastic body under the action of a given temperature. Then the thermal stresses can be obtained by addition of an imaginary pressure to the isothermal stresses, which follow by solving the isothermal governing equations with certain imaginary body forces and surface tractions. Moreover, the thermal displacements due to the given temperature are identical to the isothermal displacements due to the imaginary body forces and surface tractions. In the present paper, a dynamic extension of this body force analogy is presented in the framework of the three-dimensional theory of linear anisotropic elastodynamics with eigenstrains. Our formulation thus includes not only effects such as thermal expansion strains or piezoelectric expansion strains, but also inelastic parts of strains in the framework of a geometrically linear theory. We treat two problems, namely a problem with a given distribution of eigenstrains and with assigned body and surface forces, and a second problem without eigenstrains, but with an auxiliary system of body and surface forces, which we determine such that the required body force analogy holds. It turns out that all what is needed for an extension of the classical static analogy to dynamics is the requirement of identical initial conditions and displacement boundary conditions in the two problems under consideration. We finally present the proper form of the jump conditions for balance of momentum that must be taken into account in the auxiliary problem in order that the body force analogy holds in the presence of a singular surface also.

Previous work at NASA Langley Research Center (LaRC) involved fabrication and testing of composite beams with embedded, pre-strained shape memory alloy (SMA) ribbons within the beam structures. That study also provided comparison of experimental results with numerical predictions from a research code making use of a new thermoelastic model for shape memory alloy hybrid composite (SMAHC) structures. The previous work showed qualitative validation of the numerical model. However, deficiencies in the experimental-numerical correlation were noted and hypotheses for the discrepancies were given for further investigation. The goal of this work is to refine the experimental measurement and numerical modeling approaches in order to better understand the discrepancies, improve the correlation between prediction and measurement, and provide rigorous quantitative validation of the numerical analysis/design tool. The experimental investigation is refined by a more thorough test procedure and incorporation of higher fidelity measurements such as infrared thermography and projection moire interferometry. The numerical results are produced by a recently commercialized version of the constitutive model as implemented in ABAQUS and are refined by incorporation of additional measured parameters such as geometric imperfection. Thermal buckling, post-buckling, and random responses to thermal and inertial (base acceleration) loads are studied. The results demonstrate the effectiveness of SMAHC structures in controlling static and dynamic responses by adaptive stiffening. Excellent agreement is achieved between the predicted and measured results of the static and dynamic thermomechanical response, thereby providing quantitative validation of the numerical tool.