Surface-bonded Piezoelectric Layers Research Articles

Nonlinear dynamical characteristics of carbon nanotube-reinforced composite beams with piezoelectric actuators and elastically restrained ends under thermo-electro-mechanical loads

Nonlinear free vibration and dynamical responses of carbon nanotube (CNT) reinforced composite beams with surface-bonded piezoelectric layers and tangentially restrained ends under thermo-electro-mechanical loads are investigated in this paper. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are estimated using an extended rule of mixture. Unlike previous studies, the present work considers the effects of tangentially elastic constraints of two ends on the nonlinear dynamic characteristics of hybrid beams. Motion equation is established within the framework of Euler-Bernoulli beam theory taking into account von Kármán nonlinearity. Analytical solution is assumed to satisfy simply supported boundary conditions and Galerkin procedure is employed to obtain a time ordinary differential equation including both quadratic and cubic nonlinear terms. This differential equation is numerically solved employing fourth-order Runge-Kutta scheme to determine the frequencies of nonlinear free vibration and nonlinear transient response. Parametric studies are executed to examine numerous influences on the nonlinear dynamical characteristics of hybrid nanocomposite beams. The study reveals that tangential constraints of ends substantially effect the frequencies and dynamic response of the beam, especially at elevated temperatures. The results also indicate that nonlinear dynamic responses can be controlled effectively by means of piezoelectric actuators and elasticity of tangential constraints of ends should be considered in design of piezo-CNTRC beams.

Thermo-electrical postbuckling behavior of carbon nanotubes-reinforced composite beams with piezoelectric layers and tangentially restrained ends

An analytical investigation on the buckling and postbuckling behavior of carbon nanotube-reinforced composite beams integrated with surface-bonded piezoelectric layers under uniform temperature rise is presented in this paper. Carbon nanotubes (CNTs) are reinforced into isotropic matrix through uniform distribution and functionally graded distributions. The properties of material constituents are assumed to be temperature-dependent and effective properties of CNT-reinforced composite are estimated using an extended rule of mixture. Equilibrium equations of the beams are established based on Euler-Bernoulli theory including von Kármán nonlinearity and solved using analytical solutions and Galerkin method. Critical temperatures and postbuckling load-deflection paths are determined using an iteration algorithm. Parametric studies are performed to examine the influences of CNT distribution and volume fraction, applied voltage, in-plane and out-of-plane conditions of the ends, slenderness, and thickness ratio of layers on the critical loads and postbuckling load carrying capacity of beams. Results reveal that CNT volume fraction and degree of in-plane ends constraint have slight and significant influences on the critical temperatures and thermal postbuckling paths, respectively. The study also finds that negative and positive voltages increase and decrease the thermal buckling temperatures of piezoelectric CNT-reinforced composite beams.

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Response of angle-ply laminated cylindrical shells with surface-bonded piezoelectric layers

A state-space method is developed to investigate the time-dependent behaviors of an angle-ply cylindrical shell in cylindrical bending with surface-bonded piezoelectric layers. Both the interfacial diffusion and sliding are considered to describe the properties of the imperfect interfaces. Particularly, a matrix reduction technique is adopted to establish the transfer relations between the elastic and piezoelectric layers of the laminated shell. Very different from our previous paper, in which an approximate numerical technique, i.e. power series expansion method, is used to deal with the time-dependent problems, the exact solutions are derived in the present analysis based on the piezoelasticity equations without any assumptions. Numerical results are finally obtained and the effects of imperfect interfaces on the electro-mechanical responses of the laminated shell are discussed.

Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations

The nonlinear dynamic and vibration behaviors of a cantilevered carbon nanotube-reinforced composite trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles are considered in this article. The plate is reinforced by single-walled carbon nanotubes and is exposed to subsonic airflow under combined parametric and external excitations. The large deflection von Karman plate assumptions and the classical laminated plate theory are applied to derive the governing equations of the motion of the piezoelectric nanocomposite laminated trapezoidal plate by using Hamilton's principle. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. The Galerkin's approach is used for transforming the nonlinear partial differential equations of motion into nonlinear two-degrees-of-freedom ordinary differential equations of cubic nonlinearities. The case of 1:3 internal resonance and primary resonance is considered, and the multiple scales method is employed. The aerodynamic pressure distribution formula is modeled by linear potential flow theory. The frequency and time history responses and phase portrait in free forced vibrations are obtained to analyze the nonlinear dynamic behavior of the plate. The effects of different parameters such as the plate geometry, volume fraction of carbon nanotubes, and different excitations on the nonlinear vibration of the thin laminated plate are also discussed. A complex softening nonlinearity with two peaks in the higher mode is observed in frequency response curves. The influence of electrical excitation with several amplitudes and frequencies on dynamic stability is investigated using time response curves.

Dynamic analysis of functionally graded carbon nanotube–reinforced shell structures with piezoelectric layers under dynamic loads

This research makes a first attempt to investigate the dynamic characteristics of functionally graded carbon nanotube–reinforced composite plates and shell structures with surface-bonded piezoelectric layers. A variational formulation is derived based on the linear double director shell theory to ensure realistic parabolic variation of transverse shear strain along the thickness direction. The assumed natural strains method is adopted to enhance the accuracy of the four-node piezoelectric shell element developed in this study. Numerical studies are conducted to validate the efficiency and numerical stability of the proposed model to predict the behavior of piezolaminated composite shell structures. Furthermore, dynamic responses are extended to functionally graded carbon nanotube–reinforced composite shells covered by two active layers. The host structure is reinforced by single-walled carbon nanotubes, which are assumed to be graded through the thickness direction with different types of distributions and embedded in a polymer matrix. The effect of the volume fractions, distribution type, and geometrical parameters of the carbon nanotubes is examined.

Geometrically non-linear analysis of FG-CNTRC shell structures with surface-bonded piezoelectric layers

This work makes a first attempt to conduct a geometrically non-linear analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) structures, with surface-bonded active layers, based on Kirchhoff shell theory. Uniform and three different distribution types of functionally graded nanocomposites are presented. These distributions are assumed to be uniaxially aligned in the axial direction and functionally graded in the shell thickness direction, while the electric potential through the thickness of the active layers is assumed to be linear. A comparison study is carried out in order to show the applicability of the current formulation applied to various shapes of shell structures. The effects of various parameters as volume fraction, distribution of nanotubes, geometrical characteristics as well as load boundary on non-linear behavior of the smart FG-CNTRC structures are investigated.

Exact analysis of imperfect angle-ply laminated panels with surface-bonded piezoelectric layers

The electromechanical behavior of an angle-ply laminated plate in cylindrical bending with surface-bonded piezoelectric layers is investigated. The interlaminar bonding of this smart laminate is described by a Kelvin–Voigt viscoelastic model. Besides, a matrix reduction method is employed to construct the transfer relations between the piezoelectric layer and the elastic strip. Based on the state-space approach, a state differential equation of the interfacial sliding displacements with respect to time variable is derived, from which the exact solutions are obtained in the time domain. Comparison with the existing techniques validates the high efficiency and excellent accuracy of the present analysis. Furthermore, the numerical results indicate that the intelligent laminate may lose partly or completely the load-bearing capacity and the function of sensor/actuators with time elapsing because of the viscoelastic interfaces.

Design of a kinematic vibration energy harvester for a smart bearing with piezoelectric/magnetic coupling

A new configuration of vibration energy harvester is proposed, to equip a smart bearing with a power supply. The case of rolling mill is analyzed, to allow the identification of some design issues, related to the proposed hybrid energy scavenger. The energy conversion is performed by a contactless plucking of a permanent magnet upon the tip mass of a flexible structure, with surface-bonded piezoelectric layers. Since the system is embedded into a mechanical bearing, the dynamic excitation is applied on the vibrating structure, constrained to its fixed ring, by a permanent magnet lying on the rotating ring surface.

Structural stability enhancement by nonlinear geometry design and piezoelectric layers

Vibration and stability analysis of nonlinearly tapered cone beams coupled with a piezoelectric layer under compressive axial load is conducted using a new semi-theoretical model based on the Adomian decomposition method and a modified mathematical procedure. The method is applied to tapered structures with perfectly surface-bonded piezoelectric layers and general boundary conditions to analytically derive the natural frequencies and mode shape functions for flutter and buckling analysis. Furthermore, from the optimum structural design perspective, the effects of follower force, geometrical tapering ratio, boundary condition, and applied voltage on piezoelectric layers on the structural stability are thoroughly studied and presented. Simulation results show that the stability of the beam can be noticeably enhanced by the external voltage because of a pair of tensile loads locally induced by the piezoelectric effect. Moreover, for certain boundary conditions and applied voltages, the nonlinear tapered design has much greater buckling and flutter capacities than does the uniform beam. Consequently, the ideal structural design for effective stability enhancement can be reached efficiently.

Application of transformed differential quadrature to free vibration analysis of FG-CNTRC quadrilateral spherical panel with piezoelectric layers

In this work, a framework based on the differential quadrature (DQ) method for the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral spherical panels with surface-bonded piezoelectric layers is developed. The higher-order shear deformation theory is used to model the displacement fields of quadrilateral thin-to-moderately thick spherical panels. Hamilton’s principle together with Maxwell’s equation is applied to drive the differential governing equations and the related boundary conditions. The transformed differential quadrature (TDQ) method for the case of quadrilateral panels is established to discretize the governing partial differential equations. The benefit of this method is the usage of the transformed weighted coefficients, which are able to discretize partial differential equations in physical domain. This study exhibits that the TDQ approximation method shows a good convergence rate for quadrilateral curved panels. Furthermore, the accuracy and reliability of the proposed method are verified by comparing the results with the existing reference solutions or the results calculated by ANSYS software. The effects of CNTs volume fractions, CNTs distributions through the thickness, different boundary conditions and various panel geometrical parameters such as the panel thickness, piezoelectric thickness, side angle, and radius to length ratio on the natural frequency parameters are demonstrated. The article presents useful results for the design purpose of curved panels with complex geometries, for instance, achieving the optimal panel shape in order to pursuit the maximum structural stiffness.

Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method

The purpose of the present study is to introduce the application of carbon nanotubes (CNTs) and piezoelectric layers in suppressing the postbuckling deflection of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular sector plates. To achieve this objective, a structural model is developed based on the first-order shear deformation theory (FSDT) along with the von Karman geometrical nonlinearity. The distribution of electric potential across the thickness of piezoelectric layers is modeled by a combination of linear and sinusoidal functions and the closed circuit electrical boundary condition is taken into account for the top and bottom surfaces of the piezoelectric layers. Generalized differential quadrature method (GDQM) is implemented to discretize the nonlinear stability equations, boundary conditions and Maxwell equation. The nonlinear system of equations is solved via a direct iterative method. A detailed parametric study is conducted to explore effects of geometrical parameters, boundary conditions, piezoelectric materials, thickness of the piezoelectric layers, external electric voltage, CNT distribution, and volume fraction on the postbuckling responses of FG-CNTRC annular sector plates with surface-bonded piezoelectric layers. Results indicate that both volume fraction and distribution of CNTs play a key role in enhancing the postbuckling strength of CNTRC annular sector plates. It is found that the type of piezoelectric materials, thickness of piezoelectric layers and the external electric voltage have a significant effect on suppressing the postbuckling deflection of FG-CNTRC annular sector plates. It is also found that the distribution of CNTs plays a pivotal role in changing buckling mode shapes of CNTRC annular sector plates. Besides, the proposed solution procedure has shown clear advantages over existing methods and demonstrated itself as a general, stable and accurate numerical method in solving strongly coupled nonlinear partial differential equations.

Coupled thermo-electro-mechanical analysis of sandwiched hybrid functionally graded elastic material and piezoelectric plates under thermal loads

Based on Reissner’s mixed variational theorem, a weak-form formulation of finite layer methods is developed for the three-dimensional coupled thermo-electro-mechanical analysis of simply-supported, functionally graded elastic material plates integrated with surface-bonded piezoelectric layers and under thermal loads. The material properties of the functionally graded elastic material core are assumed to obey the power-law distributions varying through-the-thickness coordinate of the core according to the volume fractions of the constituents, and those of the functionally graded elastic material core and piezoelectric face sheets are also temperature dependent. The effective material properties of the functionally graded elastic material are estimated using the Mori-Tanaka scheme. Two different thermal conditions, i.e. the convection conditions and specified temperature conditions, on the top and bottom surfaces of the plate are considered. The accuracies and convergence rates of the finite layer methods with various orders used for expanding the elastic and electric variables in the thickness direction are assessed by comparing their solutions with the exact three-dimensional ones available in the literature.

Structural Modeling and Active Vibration Control of Smart FGM Plate through ANSYS

This paper presents a methodology to use the software ANSYS in modeling and active vibration control of a functionally graded (FGM) plate with upper and lower surface-bonded piezoelectric layers. First a FGM plate with piezoelectric layers is designed using APDL ANSYS. Then a modal analysis has been carried out to get the first five rank frequencies and mode shapes. A proportional–integral–derivative (PID) and a linear-quadratic-based output feedback controller are introduced to realize the vibration control through a closed loop. Results for various volume fraction indexes are presented.

Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers

The objective of this research is to scrutinize large amplitude vibration response of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular sector plates with surface-bonded piezoelectric layers. A nonlinear formulation is derived based on the first-order shear deformation theory (FSDT), von Karman geometrical nonlinearity along with the Hamilton principle. The distribution of electric potential through the thickness of the piezoelectric layers is simulated by a sinusoidal function. The closed circuit electrical boundary condition is taken into consideration for the top and bottom surfaces of the piezoelectric layers. The nonlinear dynamic equations, boundary conditions and Maxwell equation are discretized using the generalized differential quadrature method and direct iterative method is then employed to solve the nonlinear system of equations. The variation of nonlinear frequency versus the vibration amplitude is highlighted considering various influential parameters such as distribution and volume fraction of the CNTs, geometrical parameters, boundary conditions and the thickness of the piezoelectric layers. It is found that the dynamic responses of the CNTRC sector plate may be noticeably enhanced by adjusting values of the CNT volume fraction and distribution. The numerical results reveal that the increase in the nonlinear frequency descents at certain vibration amplitude owing to vibration mode redistribution.

Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

The second order statistics in terms of mean and standard deviation (SD) of normalized nonlinear transverse dynamic central deflection (NTDCD) response of un-damped elastically supported functionally graded materials (FGMs) beam with surface-bonded piezoelectric layers under the action of moving load are investigated in this paper. The random system properties such as Young's modulus, Poisson's ratio, density, thermal expansion coefficients, piezoelectric materials, volume fraction exponent and external loading are modeled as uncorrelated random variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics combined with Newton–Raphson technique through Newmark's time integrating scheme using finite element method (FEM). The non-uniform temperature distribution with temperature dependent material properties is taken into consideration for consideration of thermal loading. The one parameter Pasternak elastic foundation with Winkler cubic nonlinearity is considered as an elastic foundation. The stochastic based second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are adopted for the solution of nonlinear dynamic governing equation. The influences of volume fraction exponents, temperature increments, moving loads and velocity, nonlinearity, slenderness ratios, foundation parameters and external loadings with random system properties on the NTDCD are examined. The capability of present stochastic model in predicting the NTDCD statistics are compared by studying their convergence with the existing results those available in the literature.

Thermal buckling of FGEM plates integrated with surface-bonded piezoelectric layers and temperature-dependent material properties

ABSTRACTBased on Reissner’s mixed variational theorem (RMVT), a unified formulation of finite layer methods (FLMs) is developed for the quasi three-dimensional (3-D) thermal buckling analysis of simply-supported, sandwich piezoelectric plates embedded with a functionally graded elastic material (FGEM) core, the material properties of which are considered to be thickness- and temperature-dependent. The plate is subjected to a uniform temperature change and with open-/closed-circuit boundary conditions on the lateral surfaces. A 3-D linear buckling theory is used, in which a set of membrane stresses is assumed to exist just before buckling occurs, and these membrane stresses are determined using a set of predefined 3-D deformations for the pre-buckling state. The material properties of the FGEM core are assumed to obey the power-law distributions varying through the thickness coordinate of the core according to the volume fractions of the constituents. The effective material properties are estimated using the rule of mixtures and Mori-Tanaka’s model. The accuracies and convergence rates of the FLMs with various orders, as used for expanding the elastic and electric variables in the thickness direction, are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory

This paper reports on a study of active vibration control of functionally graded beams with upper and lower surface-bonded piezoelectric layers. The model is based on higher-order shear deformation theory and implemented using the finite element method (FEM). The proprieties of the functionally graded beam (FGB) are graded along the thickness direction. The piezoelectric actuator provides a damping effect on the FGB by means of a velocity feedback control algorithm. A Matlab program has been developed for the FGB model and compared with ANSYS APDL. Using Newmark’s method numerical solutions are obtained for the dynamic equations of FGB with piezoelectric layers. Numerical results show the effects of the constituent volume fraction and the influence the feedback control gain on the frequency and dynamic response of FGBs.

Modeling of the electromechanical coupling between crack propagation and piezoelectric behavior in active layers of smart devices

ABSTRACTIn this article, a new computational approach is investigated to predict the crack propagation inside some smart structures equipped with surface-bonded piezoelectric layers; meanwhile, the electromechanical coupling is exploited. The current industrial need of analyzing rather irregular geometries motivates resorting to a numerical approach. Therefore, the finite element method (FEM) is used to predict both the fracture behavior and the coupled response of piezoelectric material through a suitable interoperation of the two computational environments, available in some commercial code like the ABAQUS©. The two solutions are then coupled by means of a subroutine, in this case operated through the ISIGHT© tool. After a preliminary analysis and a validation, results of some numerical simulations are shown to highlight some significant peculiarities of the coupled behavior of the piezoelectric material.

On the energy harvesting via doubly curved piezoelectric panels

This article presents an analytical solution for power output from a doubly curved piezoelectric energy harvester. The energy harvester is made of an elastic core layer coupled with one or two surface-bonded piezoelectric layers. Five mechanical equations of motion together with Gauss’s equation are derived on the basis of first-order shell theory and solved simultaneously for simply supported mechanical boundary conditions. The influence of structural damping is taken into account using Rayleigh damping. The electromechanical frequency response functions that relate the power output and circuit load resistance are identified from the exact solutions. Finally, the performance of the system is analyzed extensively for different parameters such as type of energy harvester including unimorph and bimorph panel in series or parallel connections of piezoelectric layers, circuit load resistance, geometrical parameters, and material properties of core and piezoelectric layers.