Surface-bonded Piezoelectric Actuators Research Articles

Adaptive multimodal surface patterning on a cylindrical shell panel using piezoelectric actuators

The present study demonstrates the feasibility of creating adaptive multimodal surface patterns on an otherwise featureless cylindrical shell surface with the help of surface-bonded piezoelectric actuators. These patterns can be tuned to transform into a periodic shape that spreads equally over the domain or can have the form of a localized dimple that is concentrated only over a portion of the domain of the structure. The possibility of controlling the number, location, and temporal order of these patterns by smart actuation is established. This tunability, in both topographic patterns and their feature locations, can offer dynamic and switchable functionalities for fruitful applications.

Finite element modeling and analysis of adhesive layer effects in surface-bonded piezoelectric sensors and actuators including non-uniform thickness

A finite element model for multi-functional structures containing surface-bonded piezoelectric patches is proposed with two main objectives: to reduce the computational cost of detailed and accurate analyses; and to fully account for the adhesive layer between structure and patches, including non-uniform thickness. The proposed model is verified and used to assess the effect of adhesive layer properties on the performance of piezoelectric sensors and actuators, based on frequency responses and effective electromechanical coupling coefficient. Results indicate that increases of bonding layer thickness and thickness non-uniformity are not always detrimental to the actuation/sensing performance and could be explored as design parameters.

Excitation method and electromechanical coupling dynamic model of a novel torsional piezoelectric actuator

Torsional piezoelectric actuators have been widely applied in many fields due to their specific vibration mode. However, the conventional torsional vibration piezoelectric actuators require circumferentially polarized piezoelectric ceramics or special structural designs, increasing manufacturing difficulty and processing costs, and seriously limiting their applications. In order to solve these problems, a novel excitation method of torsional vibration is proposed in this study through the arrangement of the regular piezoelectric ceramic plates polarized along their thickness direction, and then two surface-bonded type torsional piezoelectric actuators are constructed to stimulate the odd and even order torsional vibration modes, respectively. A novel transfer matrix model of describing the torsional vibration, which involves in the mechanical and electrical properties, is created first for the piezoelectric composite beam element. Then a general electromechanical coupling dynamic model is developed to reveal dynamic behaviors of the proposed surface-bonded type torsional piezoelectric actuators. In addition, the finite element simulation and experimental investigations are carried out to confirm the validation of the proposed excitation method of torsional vibration and to verify the correctness of the developed electromechanical coupling dynamic model. The comparisons showed that the results calculated by the developed theoretical model, simulated by the finite element method, and tested by the experiments matched well, indicating that the developed electromechanical coupling dynamic model is correctness and the excitation method of torsional vibration is effective. Finally, the output characteristics of the two proposed actuator prototypes are measured, further confirming the feasibility of the proposed torsional vibration excitation method.

Adaptive active vibration control for piezoelectric smart structure with online hysteresis identification and compensation

Smart structure vibration reduction based on adaptive active vibration control has become a hot research spot in recent years. A filtered-U least mean square algorithm based on an infinite impulse response filter structure is used to solve the interference of controller output to reference signal. The filtered-U least mean square algorithm is very suitable for the nonlinear vibration control of the flexible structure. This study focuses on the analysis and implementation of an adaptive active vibration control system for smart structure with a surface-bonded piezoelectric actuator. The piezoelectric actuator contained in the secondary path has nonlinear hysteresis property. The nonlinear hysteresis property will cause a nonlinear relationship between the structural vibration response and the control voltage, which deteriorates the robustness and control effect of the adaptive control. This study designs an improved version of the filtered-U least mean square algorithm with online hysteresis identification and compensation (filtered-U least mean square–online hysteresis identification and compensation) based on a discrete Prandtl–Ishlinskii model. The Prandtl–Ishlinskii model parameters of the nonlinear hysteresis property are identified online based on the least mean square algorithm. Based on the identified Prandtl–Ishlinskii model parameters, an inverse hysteresis compensator is established for feedforward compensation in the secondary path. Simulation results show that the proposed method can dynamically compensate the hysteresis nonlinearity of the secondary path, linearizing the nonlinear hysteresis. The vibration reduction effect of the proposed method is obviously better than that of other competing methods. A piezoelectric smart cantilever plate with PZT (or lead zirconate titanate, Pb (Zr, Ti)) actuators and sensors is designed to demonstrate the validity and efficiency of the proposed method by experiments. Experiment results demonstrate that the adverse effect of nonlinear hysteresis is eliminated well after feedforward hysteresis compensation is introduced; the unexpected frequency vibration caused by the hysteresis property is suppressed. The proposed methodology possesses an important advantage in application of the adaptive active vibration control of the piezoelectric smart structure.

Optimal distribution of active piezoelectric elements for noise attenuation in sandwich panels

ABSTRACT In this paper, a multiobjective optimization approach for obtaining the optimal distribution of surface-bonded piezoelectric sensors and actuators for noise attenuation in sandwich panels is presented. The noise attenuation is achieved by using negative velocity feedback control with co-located sensors and actuators. The control gains are also optimized in order to obtain the most efficient noise attenuation in a given frequency band. An in-house implementation of a viscoelastic soft core sandwich plate finite element, including surface-bonded piezoelectric sensors and actuators with active control capabilities, is used for obtaining the frequency response of the panels. The sound transmission capability of the panels is evaluated using the radiated sound power, along with the Rayleigh integral approach, which is suitable for lightly coupled structural/acoustic problems. The Direct MultiSearch (DMS) optimization algorithm is used to minimize the added weight due to the piezoelectric material, minimizing also the number of required controllers and maximizing the noise attenuation. The total length of the radiated sound power curve is shown to be an effective measure of noise attenuation in a given frequency band. Trade-off Pareto fronts and the obtained optimal configurations are presented and discussed.

Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal–ceramic–metal layers in thermal environment using Reddy's third-order shear deformation shell theory

ABSTRACTBased on Reddy's third-order shear deformation shell theory, this paper studied the nonlinear buckling and postbuckling response of imperfect Sigmoid functionally graded circular cylindrical shells in a thermal environment with an outer surface-bonded piezoelectric actuator. Material properties are temperature dependent and graded in the thickness direction with two shell's outer surfaces rich of metal and ceramic in the middle (S-FGM). The shell is subjected to uniform external pressure, axial compressive, electrical loads and resting on elastic foundations. The obtained numerical results are validated by comparing with other results reported in the open literature.

Thermal buckling and postbuckling analysis of piezoelectric FGM beams based on high-order shear deformation theory

ABSTRACTThis article deals with the thermal buckling and postbuckling of functionally graded material (FGM) beams with surface-bonded piezoelectric actuators based on physical neutral surface concept and high-order shear deformation theory including von Kármán strain–displacement relationships. The beams are exposed to a uniform temperature field and electric field, the material properties of FGM layers are temperature-dependent and vary in the thickness direction. The approximate solutions of piezoelectric FGM beams for thermal buckling and postbuckling are obtained by a two-step perturbation method, meanwhile, the analytical solutions of Timoshenko beam model and Euler beam model are also presented. The validity of the present work can be confirmed by comparisons with previous results. The effects of the applied actuator voltage, beam geometry as well as volume fraction index of FGM beam on the critical buckling temperature, and postbuckling load–deflection relationships are investigated.

Hybrid Position Feedback Controller for Inducing Cross-Well Motion of Bistable Structures

A hybrid position feedback controller based on the well-known positive position feedback controller for bistable structures is presented. The proposed controller is a hybrid unstable-then-stable position feedback controller, which is a second-order single-degree-of-freedom system in nature. The controller takes advantage of the resonant mode of a bistable system about one equilibrium position, destabilizes the system, and dynamically induces snapthrough between the two equilibria. The proposed method is demonstrated on a bistable unsymmetric cross-ply composite platelike structure with surface-bonded piezoelectric actuators. The control scheme is shown to eliminate undesirable cross-well oscillations leading to a monotonic state crossover. An experimentally validated parametric analysis is also presented. Essential properties observed in theoretical and numerical analyses, such as the nondynamic stability and stability gain limit for the positive position feedback controller and the wide unstable bandwidth for the negative position feedback controller, are validated with experiments.

Thermo-electro-mechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections

This paper presents thermo-electro-mechanical postbuckling analysis of geometrically imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) hybrid beams that are integrated with surface-bonded piezoelectric actuators. The material properties of FG-CNTRCs are assumed to be temperature-dependent and graded in the thickness direction. By using a generic imperfection function, various possible imperfections with different shapes and locations in the beam are considered. The theoretical formulations are based on the first-order shear deformation beam theory with von-Kármán nonlinearity. A differential quadrature approximation based iteration process is employed to obtain the postbuckling equilibrium path of piezoelectric FG-CNTRC hybrid beams under thermo-electro-mechanical loading. Parametric studies are conducted to examine the effect of geometric imperfection, distribution pattern and volume fraction of carbon nanotubes, temperature rise, actuator voltage, beam geometry and boundary conditions on the thermo-electro-mechanical postbuckling behaviour. The results show that the thermo-electro-mechanical postbuckling is considerably affected by the imperfection mode, half-wave number, location and amplitude, as well as the temperature rise and boundary conditions. The effect of applied actuator voltage is much less pronounced but tends to be relatively more noticeable as the slenderness ratio increases.

Modelling and simulation of surface-bonded piezoelectric actuators with bending effects

In the modelling of thin-sheet piezoelectric actuators the effect of bending of the actuator itself is usually ignored. The current paper presents a model of a surface bonded piezoelectric actuator subjected to electric loading, which contains both the axial and bending deformations. The static electromechanical response of the actuator is studied under different mechanical and geometrical conditions to evaluate the effect of bending. An imperfectly bonded interface is proposed to simulate debonding and to study its effect on the actuation process. The problem is formulated as integral equations in terms of the interfacial shear and normal stresses, which are solved by using Chebyshev polynomials. Based on the solution, the effect of bending of the actuator upon load transfer is analysed. Illustrative examples are presented to show the effect of the material property, the geometry and the interfacial debonding on the response of the integrated structure.

Nonlinear thermo- electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations

In this paper, we study the nonlinear dynamic response of higher order shear deformable sandwich functionally graded circular cylindrical shells with outer surface-bonded piezoelectric actuator on elastic foundations subjected to thermo-electro-mechanical and damping loads. The sigmoid functionally graded material shells are made of the metal–ceramic–metal layers with temperature-dependent material properties. The governing equations are established based on Reddy’s third-order shear deformation theory using the stress function, the Galerkin method and the fourth-order Runge–Kutta method. Numerical results are given to demonstrate the influence of geometrical parameters, material properties, imperfection, elastic foundations, and thermo-electro-mechanical and damping loads on the nonlinear dynamic response of the shells. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature.

Laser Doppler imaging of delamination in a composite T-joint with remotely located ultrasonic actuators

This paper presents an experimental study on the interaction of ultrasonic guided waves with delamination in the web–flange interface of a co-cured, co-bonded composite T-joint. A complex interaction of waves is induced, first, by one, and, later, by two piezoceramic wafer(s) bonded on the inner surface of the flange. The flange surface velocity distributions are reconstructed from the scanning laser Doppler velocimeter (LDV) measurements to study the effect of a delamination overlapping the web–flange interface. The surface-bonded piezoelectric actuator(s) placed remotely on the flange produce primarily anti-symmetric wave incidence to the delamination. A two-stage wave mode conversion process, one due to the web and joint filler, and the other due to the delamination underneath the flange is observed. First, we address the problem of identification of delamination by ultrasonic contrast imaging of the web–flange interface using a single actuator. This study is extended further to enhance the ultrasonic contrast imaging at the web–flange interface using a standing wave. A quantitative methodology based on mode conversion strength is developed to monitor different structural features like free-edge, web–flange interface and delamination. The results show the complex nature of the conversion of flexural waves to in-plane waves through the deltoid and along the web–flange interface.

Unsymmetrical Buckling of Piezo-FGM Shallow Clamped Spherical Shells under Thermal Loading

The unsymmetrical buckling of clamped shallow spherical shells made of functionally graded material (FGM) and surface-bonded piezoelectric actuators under thermal load is studied in this paper. The governing equations are based on classical shell theory and the Sanders nonlinear kinematic equations. It is assumed that properties of the functionally graded material vary continuously through the thickness of the shell according to a power law distribution of the volume fractions of the constituent materials.

Improved finite element modeling of piezoelectric beam with edge debonded actuator for actuation authority and vibration behaviour

The main emphasis of the present work is to model a piezoelectric beam with edge debonded actuator by employing finite element method based layerwise shear deformation theory, to improve the accuracy with which the actuation authority and natural frequencies are computed. The surface-bonded piezoelectric actuators and the host beam are considered to rotate individually due to shear deformation, while they are assumed to undergo the same flexural deflection and slope. These modeling aspects have improved the accuracy of the computed results. Edge debonding of actuator is accounted in the model by modeling healthy and debonded regions of the beam individually and subsequently applying the displacement continuity conditions at the interfaces of different regions. The investigations are carried out to find the effect of different extents of edge debonding on the actuation authority and natural frequencies of the debonded piezoelectric beam. It is found from the numerical results that the behaviour of the beam with edge debonded actuator is affected considerably as regards to the actuation authority and marginally with respect to natural frequencies. Further it has been shown that, when an actuator is edge debonded it introduces the local modes besides displaying significant reduction in its actuation authority.

Thermal Buckling Analysis of Piezoelectric Functionally Graded Plates with Temperature-Dependent Properties

In this study, the thermal buckling analysis of hybrid laminated plates made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators referred to as (P/FGM)s are investigated. Material properties for both substrate FGM layers and piezoelectric layers are temperature-dependent. Uniform temperature rise as a thermal load and constant applied actuator voltage are considered for this analysis. By definition of four new analytic functions, the five coupled governing stability equations, which are derived based on the first-order shear deformation plate theory, are converted into fourth-order and second-order decoupled partial differential equations (PDEs). Considering a Levy-type solution, these two PDEs are reduced to two ordinary differential equations. One of these equations is solved using an accurate analytical solution, which is named as power series Frobenius method. The effects of parameters, such as the plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer, gradient index, actuator voltage, and the temperature dependency on the critical buckling temperature difference, are illustrated and explained. The critical buckling temperatures of (P/FGM)s with six various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.

AN ANALYTICAL APPROACH FOR BUCKLING BEHAVIOR OF TEMPERATURE-DEPENDENT LAMINATED PIEZOELECTRIC FUNCTIONALLY GRADED PLATES UNDER THERMO-ELECTRO-MECHANICAL LOADINGS AND DIFFERENT END SUPPORTS

In this paper, we examine the buckling behavior of piezoelectric laminated plate made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators and is subjected to a combined action of uniform temperature change, inplane forces, and applied actuator voltage. Temperature-dependent material properties are assumed for both the substrate FGM layer and piezoelectric layers. Employing an analytical approach, five coupled governing stability equations, which were derived based on the first-order shear deformation plate theory, are converted into a fourth-order and a second-order decoupled partial differential equations. Then, an accurate analytical solution is proposed to solve them. Parametric studies are also undertaken, and show the effects of applied actuator voltage, volume fraction exponents, plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer and temperature dependency, on the buckling load of the plate.

Axisymmetric snap-through behavior of Piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading

Snap-through buckling of shallow clamped spherical shells made of functionally graded material (FGM) and surface-bonded piezoelectric actuators under the thermo-electro-mechanical loading is studied in this paper. The governing equations are based on the classical shell theory and the Sanders nonlinear kinematics equations. It is assumed that the property of the functionally graded materials vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituent materials. The constituent materials of the functionally graded shell are assumed to be mixture of ceramic and metal. The results show that the axisymmetric buckling of Piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading is of snap-through type. The intensity of buckling is dependent on the geometry of the shell, value of thermo-electro-mechanical loading and type of thermal loading.

Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates

Abstract The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Karman geometrical nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.

Three-dimensional dynamic responses of carbon nanotube–reinforced composite plates with surface-bonded piezoelectric layers using Reissner’s mixed variational theorem–based finite layer methods

A unified formulation of finite layer methods based on the Reissner’s mixed variational theorem is developed for the three-dimensional dynamic responses of simply supported, functionally graded carbon nanotube–reinforced composite plates with surface-bonded piezoelectric sensor and actuator layers and closed- and open-circuit surface conditions. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations in the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement (flux) components. The relevant orders used for expansion of these variables in the thickness coordinate can be freely chosen, such as linear, quadratic, or cubic ones. Four different through-thickness distributions of carbon nanotubes in the carbon nanotube–reinforced composite layer are considered, and the effective material properties of the layer are estimated using the rule of mixtures. The accuracy and convergence rate of the frequency parameters of the sandwiched hybrid carbon nanotube–reinforced composite and piezoelectric plates obtained using assorted Reissner’s mixed variational theorem–based finite layer methods are assessed by comparing their solutions with the exact three-dimensional solutions available in the literature.

Stability of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers and under bi-axial compression

Based on Reissner’s mixed variational theorem (RMVT), we develop a unified formulation of finite layer methods (FLMs) for the three-dimensional (3D) buckling analysis of simply-supported, functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates with surface-bonded piezoelectric actuator and sensor layers and under bi-axial compressive loads. In this work, a set of membrane stresses is assumed to exist just before instability occurs, and determined using the predefined 3D deformations for the prebuckling state. The carbon nanotubes (CNTs) are considered to be uniformly distributed (UD), and FG rhombus- and X-type variations through the thickness coordinate, and the effective material properties of the FG CNTRC layer are evaluated using the rule of mixtures, and two different surface conditions, open- and closed-circuit, are considered. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations for the field variables of each individual layer, respectively. The accuracy and convergence of the FLMs with various orders used for the expansion of each field variable in the thickness are assessed by comparing their solutions with the exact 3D ones available in the literature.