Piezoelectric Smart Structures Research Articles

Modelling and analysis of piezoelectric smart structures for vibration and noise control

The paper presents an overall numerical approach for the simulation and design of smart lightweight structures in order to control vibration and noise. The design process requires an overall virtual computer model, which includes the passive mechanical structure, the acoustic fluid, the active materials, such as piezoelectric patch actuators glued to the structure, as well as the controller. Based on the finite element method such an overall model is presented in the paper. An acoustic box is used to verify the computational approach by comparing simulated and measured results.

Nonlinear ferro-electro-elastic beam theory

Motivated by the uniqueness and potential of the nonlinear range of piezoelectric and ferroelectric smart materials and structures, a static physically nonlinear ferro-electro-elastic beam theory which takes the effect of domain switching into account is developed. The kinematic assumptions adopt the geometrically linear Bernoulli–Euler form for the mechanical components and a first-order theory for the electrical potential, and lay the basis for further augmentation to higher order theories. The beam theory includes the field equations that correspond to the static case, the boundary conditions and the constitutive equations of ferro-electro-elasticity. The general 3-D constitutive equations are reduced to comply with the beam theory and formulated as ordinary differential equations by means of a set of generalized electro-mechanical stiffnesses. A micromechanical constitutive model that accounts for the loading history and for the domain switching phenomenon is adopted and an iterative solution procedure that incorporates the micromechanical approach is suggested. A numerical example that demonstrates the impact of the domain switching on the nonlinear electromechanical static response of a ferro-electro-elastic beam is presented and discussed. The quantitative assessment of this behavior takes a step towards new structural applications that cope with or even take advantage of the nonlinear ferro-electro-elastic range.

Numerical and Experimental Study on Integration of Control Actions into the Finite Element Solutions in Smart Structures

Piezoelectric smart structures can be modeled using commercial finite element packages. Integration of control actions into the finite element model solutions (ICFES) can be done in ANSYS by using parametric design language. Simulation results can be obtained easily in smart structures by this method. In this work, cantilever smart structures consisting of aluminum beams and lead-zirconate-titanate (PZT) patches are considered. Two cases are studied numerically and experimentally in parallel. In the first case, a smart structure with a single PZT patch is used for the free vibration control under an initial tip displacement. In the second case, a smart structure with two PZT patches is used for the forced vibration control under harmonic excitation, where one of the PZT patches is used as vibration generating shaker while the other is used as vibration controlling actuator. For the two cases, modal analyses are done using chirp signals; Control OFF and Control ON responses in the time domain are obtained for various controller gains. A non-contact laser displacement sensor and strain gauges are utilized for the feedback signals. It is observed that all the simulation results agree with the experimental results.

Numerical and Experimental Study on Integration of Control Actions into the Finite Element Solutions in Smart Structures

Piezoelectric smart structures can be modeled using commercial finite element packages. Integration of control actions into the finite element model solutions (ICFES) can be done in ANSYS by using parametric design language. Simulation results can be obtained easily in smart structures by this method. In this work, cantilever smart structures consisting of aluminum beams and lead-zirconate-titanate (PZT) patches are considered. Two cases are studied numerically and experimentally in parallel. In the first case, a smart structure with a single PZT patch is used for the free vibration control under an initial tip displacement. In the second case, a smart structure with two PZT patches is used for the forced vibration control under harmonic excitation, where one of the PZT patches is used as vibration generating shaker while the other is used as vibration controlling actuator. For the two cases, modal analyses are done using chirp signals; Control OFF and Control ON responses in the time domain are obtained for various controller gains. A non-contact laser displacement sensor and strain gauges are utilized for the feedback signals. It is observed that all the simulation results agree with the experimental results.

A benchmark for free vibration and effective coupling of thick piezoelectric smartstructures

An experimental benchmark and its three-dimensional finite element (FE) simulation arepresented for free vibration and effective electromechanical coupling of thick smart beamsand plates bonded symmetrically on their upper/lower surfaces with a single pair of largepiezoceramic patches. The so-called modal effective electromechanical coupling coefficient,which is post-processed from free-vibration analyses under short-circuit and open-circuitelectrodes, is proposed as a unified free-vibration benchmarking comparator. For thispurpose, the tests are numerically modeled, analyzed, and correlated using the commercialANSYS® FE code. Realistic and desirable features were considered; they concern electrodeequipotentiality, piezoceramic patches poling orientations (here opposite), and an FEmodel electromechanical updating. The original experimental benchmark and its refinedmodeling and simulation outcomes could be of major interest to smart materials andstructures practitioners and researchers.

Integrated Optimization of Material Layout and Control Voltage for Piezoelectric Laminated Plates

Topology optimization techniques have recently been successfully applied to the design of piezoelectric smart structures. However, in previous formulations, the material layout is optimized under the condition of given electric actuation voltages. This imposes a restriction to the design problem and may consequently limit application of these approaches, particularly in complex shape control problems. The present article investigates the integrated optimization of structural topology and control voltage of piezoelectric laminated plates. The finite element analysis formulation of laminated plates with surface bonded piezoelectric layers is introduced first. The optimal design problem is then formulated based on an artificial material model with penalization for both mechanical and piezoelectric properties. In the formulated problem, the topologies of both host and actuation layers are optimized simultaneously with spatial distribution of control voltage. Several special cases of the proposed design problem are considered, and numerical techniques for sensitivity analysis and optimal solutions are proposed. Numerical examples are presented to demonstrate the validity and applicability of the proposed methods.

A segment based sequential least squares algorithm with optimum energy control fortracking the dynamic shapes of smart structures

This paper presents a segment based sequential least squares algorithm with optimumenergy control for tracking the dynamic shapes of piezoelectric smart structures. In thisalgorithm, integration of the square difference between the desired and achieved dynamicshapes over a time period is employed as an error function. The total electrical energyconsumption of all actuators is used as the other control target. Two controlschemes are studied: (a) minimization of the square error over a time periodwith energy constraint and (b) minimization of control energy with specifiedsquare error constraint. The Lagrange multiplier technique is used to consider theconstraint, in which the properties of the characteristic matrix and polynomials ofthe Lagrange multiplier are analysed. Based on the present analysis, a simpleand efficient algorithm is proposed; the relationship between permissible energyconstraint and achievable minimum square error is investigated. Numerical results arepresented for tracking twisting shape variations of a smart plate. Optimum energycontrol for reducing conflicting effects of the applied actuation voltages is alsodiscussed.

Direct model reference adaptive control (MRAC) design and simulation for the vibration suppression of piezoelectric smart structures

The paper presents control system design based on a non-linear model reference adaptive control law (MRAC) used for the vibration suppression of a smart piezoelectric mechanical structure. Numerical simulation of the proposed control system is performed based on the finite element (FE) model of the structure, modally reduced in order to meet the requirements of the control system design. First the MRAC problem is defined and a direct control algorithm described in the paper is suggested as a solution to the control problem. The basic MRAC algorithm is modified by augmenting the integral term of the control law in order to provide the robustness of the control system with respect to the stability. This approach provides preserving the boundness of the system states and adaptive gains, with small trackings error over large ranges of non-ideal conditions and uncertainties. The efficiency of the suggested control for the vibration suppression is tested and shown through a numerical simulation of the funnel-shaped piezoelectric structure.

A Development of Miniaturized Piezoelectric Actuator System for Mobile Smart Structures

A smart material actuator is required for a smart structure having multifunctional performance. Among the smart material actuators, piezoelectric actuator is known for its excellent large force generation in broad bandwidth in a compact size. However it needs relatively large actuation voltage requiring a bulky hardware system. This study is mainly concerned to develop a self-powered miniaturized piezoelectric actuator driver (MIPAD) controlled by a radio controller for small sized piezoelectric smart structures. It can receive command from other microprocessors or a remote radio controller. We designed a real hardware and it demonstrated good performances even though the driving system was very small. The MIPAD is expected to minimize the weight and size of the piezoelectric actuator system and it can be easily embedded into mobile smart structures.

Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study

The aim of this study is to investigate the efficiency of a system identification technique known as observer/Kalman filter identification (OKID) technique in the numerical simulation and experimental study of active vibration control of piezoelectric smart structures. Based on the structure responses determined by finite element method, an explicit state space model of the equivalent linear system is developed by employing OKID approach. The linear quadratic Gaussian (LQG) algorithm is employed for controller design. The control law is then incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Furthermore, a complete active vibration control system comprising the cantilever plate, the piezoelectric actuators, the accelerometers and the digital signal processor (DSP) board is set up to conduct the experimental investigation. A state space model characterizing the dynamics of the physical system is developed from experimental results using OKID approach for the purpose of control law design. The controller is then implemented by using a floating point TMS320VC33 DSP. Numerical examples by employing the proposed numerical simulation method, together with the experimental results obtained by using the active vibration control system, have demonstrated the validity and efficiency of OKID method in application of active vibration control of piezoelectric smart structures.

A sequential linear least square algorithm for tracking dynamic shapes of smart structures

This paper presents a sequential linear least square algorithm for tracking dynamic shapes of piezoelectric smart structures. The dynamic shape discussed in this paper is defined as a host structural shape varying with time, and the tracking technique is to find an electric voltage history for each piezoelectric device over a time period so that the desired structural movements can be achieved. In the theoretical formulation, dynamic equations of piezoelectric smart structures are introduced by finite element analysis, and then a solution procedure for a set of time-dependent electric voltages is derived by combining the linear least square method and the Houbolt numerical integration scheme. The formulation indicates that this algorithm can be used to find the time-dependent voltages for tracking structural movements of piezoelectric smart structures. The present novel formulation is then demonstrated through numerical examples for tracking dynamic shapes of piezoelectric smart beams and plates. The numerical results for the smart beam are compared with the experimental ones. It is shown that the present sequential linear least square algorithm is capable of efficiently simulating dynamic shape tracking for smart structures. Copyright © 2006 John Wiley & Sons, Ltd.

Driving Forces for Interfacial Fatigue Crack Growth by Piezoelectric Actuator

A new experimental technique for accelerated fatigue testing has recently been developed (Du, T.B., Liu, M., Seghi, S., Hsia, K.J., Economy, J. and Shang, J.K. 2001. “Piezoelectric Actuation of Crack Growth along Polymer-Metal Interfaces in Adhesive Bonds,’’ Journal of Material Research, 16(10):2885-2892). Using a piezoelectric actuator, cyclic loading can be applied at frequencies up to 20 kHz, several orders of magnitude higher than that achieved by a conventional mechanical cyclic loading technique. Moreover, the new technique using piezoelectric actuators directly addresses the debonding problem in piezoelectric multilayered smart structures. However, the threshold energy release rate for interfacial crack propagation, evaluated based on plane strain and linear piezoelectricity assumptions in (Du, T.B. 2001. “Durability of Polymer/Metal Interfaces under Cyclic Loading,” PhD Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, May), seems to be almost an order of magnitude lower than that measured by the conventional mechanical cyclic loading. In this article, we investigate the origin of such discrepancies, and find that the driving force provided by piezoelectric actuator is intrinsically three-dimensional in nature. To account for this effect, we develop both a plane strain model and a modified plane strain analytical model that takes into account the effects in the third dimension to evaluate the energy release rate. The results show that the plane strain solution underestimates the driving force. We also study the effect of nonlinear piezoelectricity on crack driving forces by performing detailed finite element simulations. The results show that the nonlinear piezoelectric effect is another important factor that contributes to the discrepancy between the results from the piezoelectric loading and that from the conventional mechanical loading.

Closed Loop Finite Element Modeling of Piezoelectric Smart Structures

The objective of this paper is to develop a general design and analysis scheme for actively controlled piezoelectric smart structures. The scheme involves dynamic modeling of a smart structure, designing control laws and closed‐loop simulation in a finite element environment. Based on the structure responses determined by finite element method, a modern system identification technique known as Observer/Kalman filter Identification (OKID) technique is used to determine the system Markov parameters. The Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system for control law design. The Linear Quadratic Gaussian (LQG) control law design technique is employed to design a control law. By using ANSYS parametric design language (APDL), the control law is incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Finally, numerical examples have demonstrated the validity and efficiency of the proposed design scheme. Without any further modifications, the design scheme can be readily applied to other complex smart structures.

Possibilities of Optimal and Adaptive Control Laws Design in Piezoelectric Smart Structures

AbstractPossibilities of the controller design for piezoelectric smart structures are considered in the paper. The modelbased approach, which relies on the finite element modal analysis of structures, is used. As an alternative, system identification is suggested in cases when the real plant or its prototype is available for studying. Dynamics of piezoelectric active materials used as actuators and sensors is taken into account in the modelling procedure. The aim of control is vibration suppression in the sense of magnitudes reduction as well as the isolation of undesirable frequencies from the response spectra. For known plant models and available a priori information on the type of excitation or disturbances, optimal LQ tracking control systems perform good behavior. Owing to the approximation of the real structure's behavior by the finite element model and by modal reduction, the full infinite‐dimensional dynamics of an elastic structure cannot be completely captured. Introduced inaccuracies could be compensated for if they are viewed as the source of the model parameters variation and therefore by employing adaptive control laws. The adaptive control design is considered from this point of view. The application possibilities are illustrated by examples of piezoelectrically controlled structures.

Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

In this paper, the incremental finite element equations for geometric non-linear analysis of piezoelectric smart structures are developed using a total Lagrange approach by using virtual velocity incremental variational principles. A four-node first order shear plate element model with reduced and selective integration is also developed. Geometrically non-linear transient vibration response and control of plates with piezoelectric patches subjected to pulse loads are investigated. Active damping is introduced on the plates by coupling a self-sensing and negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can introduce significant damping and suppress transient vibration effectively. The effects of the number and locations of the piezoelectric actuators on the control system are also discussed.

Effective electromechanical properties of transversely isotropic piezoelectric ceramics with microvoids

In most piezoelectric materials and smart structures, the presence of microvoids can hardly be avoided. In the present paper, detailed three-dimensional (3-D) finite element analyses based on the unit cell method are carried out to investigate the inherent relations between the effective properties and the non-uniform distributions of microscopic electromechanical coupling fields resulting from microvoids. The emphases are placed on the influences of void volume fraction, void distribution, void shape and configuration on the effective properties of voided piezoelectric ceramics. The influences rooting in the permeability of voids and piezoelectricity of matrix materials on the effective properties of voided piezoelectric ceramics are also studied. The results obtained by this study have prospective guiding significances to the structural integrity analyses and fabrication of piezoelectric ceramics.

Finite element analysis and design of actively controlled piezoelectric smart structures

A general purpose design scheme of actively controlled smart structures with piezoelectric sensors and actuators is presented in this study. The proposed scheme can make use of any finite element code with piezoelectric elements, and control design is carried out in state space form established on finite element modal analysis. Subsequent details of designing state/output feedback control are addressed. For the purpose of demonstration, a commercial finite element code complemented with output feedback control law is employed to design a set of structure systems for active vibration control. The validity and efficiency of present scheme is confirmed by comparing with available reported results. The present scheme can be adapted to the design of actively controlled smart structures with non-piezoelectric sensors or actuators.

An inelastic micro/macro theory for hybrid smart/metal composites

Motivated by the emerging concept of including metal phases within piezoelectric and other smart structures and materials, this paper presents a micro/macro theory for determining the coupled thermo-electro-magneto-elasto-plastic behavior of arbitrary composite laminates. The approach involves two models capable of analyzing geometries that include inelastic materials. The first is the electro-magnetic generalized method of cells (EMGMC) (Micromechanical Prediction of the Effective Behavior of Fully Coupled Electro-Magneto-Thermo-Elastic Multiphase Composites, 2000. [1]) micromechanics model. EMGMC has been reformulated to improve its computational efficiency and has been extended to admit arbitrary anisotropic local material behavior (in terms of the thermal response, mechanical response, electric response, magnetic response, as well as the coupling behavior) and inelasticity. The second model is classical lamination theory, which has also been extended for arbitrary anisotropic material behavior and electro-magnetic and inelastic effects. The end result is a coupled theory that employs EMGMC to provide the homogenized behavior of the composite plies that constitute the thermo-electro-magneto-elasto-plastic laminate. Sample results, which address the inelastic response of a hybrid smart/metal matrix composite laminate, are presented.

Shape Control of Beams by Piezoelectric Actuators

The shape control of beams by piezoelectric actuators is addressed analytically. Solutions are presented for a beamsubjectedto differentboundaryconditions.Thesolutionsshowhowandhowmuchthepiezoelectricactuators can ine uence the shape of a beam. Several case studies arealso presented to show the applications of the analytical solutions in the various analyses relevant to shape control of beams by piezoelectric actuators. The limitation of the actuation forces produced by piezoelectric actuators makes it dife cult to realize global and local precise shape control. In this application, the actuation forces produced by piezoelectric actuators are used to change the shapes of e exible structures. Some work has been reported on the shape control of beams, plates, and shells during the past few years. Some numerical methods, includ- ing the Ritz method, 3,4 e nite difference method, 5 and e nite element method 6i 10 have been used to model and analyze the problems rel- evant to shape control of e exible structures by piezoelectric actua- tors. However, due to the approximation of the numerical methods, the reported results can only give rough information of the global shape changes of the structures induced by piezoelectric actuators. Theycannot showthe detailed localshapechange information,such as information on the slope or curvature change of a structure at one point. The detailed local shape change information induced by piezoelectricactuators,whichshowshowthepiezoelectricactuators can change the shape of a structure or what types of shape change the piezoelectric actuators can make to a structure, is important for the design and analysis of such a piezoelectric smart structure. To obtain this information, one needs to analytically solve the problem of shape control. In general, it is very dife cult and complicated to solveanalyticallytheproblemforatwo-dimensionalplate;however, a one-dimensional beam is another case, and an analytical solution can be possibly obtained with acceptable complexity. The conclu- sions for a two-dimensional plate can be drawn from those for a one-dimensional beam. Thispaperwillpresenttheanalyticalsolutionsofthedee ectionof a beam induced by both piezoelectric actuators and external forces. In accordance with the solutions, the detailed local shape change information induced by piezoelectric actuators will be addressed. Using the solutions, one can analytically perform various analyses relevant to the shape control of beams by piezoelectric actuators. Case studies will also be carried out to show the applications of the solution.

Piezoelectric smart structures for noise reduction in a cabin

The feasibility of piezoelectric smart structures for cabin noise problem is studied numerically and experimentally. A rectangular enclosure, one side of which is a plate while the other sides are assumed to be rigid, is considered as a cabin. A disk-shaped piezoelectric sensor and actuator are mounted on the plate structure and the sensor signal is returned to the actuator with a negative gain. An optimal design of the piezoelectric structure for active noise control of the cabin is performed. The design variables are the locations and sizes of the disk-shaped piezoelectric actuator and sensor and the actuator gain. To model the enclosure structure, a finite element method based on a combination of three dimensional piezoelectric, flat shell and transition elements is used. For the interior acoustic medium, the theoretical solution of a rectangular cavity in the absence of any elastic structures is used and the coupling effect is included in the finite element equation. The design optimigation is performed at resonance and off-resonance frequencies, with the results showing a remarkable noise reduction in the cavity. An experimental verification of the optimally designed configuration confirms the feasibility of piezoelectric smart structures in resolving cabin noise problems.