Piezoelectric Sandwich Research Articles

Free vibration of sandwich beams with graphene nanoplatelets reinforced piezoelectric face sheets

Owing to its exceptional physical properties, graphene is considered as an excellent reinforcement for composite materials. However, the existing higher-order models encounter significant hurdles when attempting to accurately predict the natural frequencies of sandwich beams with graphene nanoplatelets reinforced composite (GNPRC) piezoelectric face sheets. If transverse shear deformations are not accurately modeled, the dynamic behavior of piezoelectric sandwich beams will be noticeably influenced by the disparities of material properties at the interfaces of adjacent layers, as well as the inherent electromechanical coupling characteristic. To overcome these challenges, an advanced electro-mechanical coupling theory will be introduced for the vibration analysis of sandwich beams featuring GNPRC piezoelectric face sheets. Compared to previous higher-order models, the proposed beam model introduces an enhanced interlaminar shear stress field incorporating electromechanical properties. This improved stress field can be involved in the equations of motion based on the Hamilton principle, significantly enhancing the precision in analyzing the free vibration behavior of piezoelectric sandwich beams. Furthermore, a simplification of finite element implementation can be achieved by removing the second-order derivatives of in-plane displacements from the transverse shear stress field. Consequently, a C0-type three-node beam element is constructed for the dynamic analysis of sandwich beams with GNPRC piezoelectric face sheets. To validate the performance of the proposed theory, the 3D elasticity solutions and results obtained from alternative theoretical frameworks are used. Numerical results demonstrate that the present model offers superior accuracy over the existing higher-order theories. Additionally, a comprehensive parametric investigation is conducted to explore the influence of key parameters on the free vibration characteristics of piezoelectric sandwich beams.

Non-linear bending analysis and control of graphene-platelets-reinforced porous sandwich plates with piezoelectric layer subjected to electromechanical loading

Piezoelectric materials as the controlling element have been widely utilized to produce intelligent engineering structures, while these smart structures may fail to realize effective control of composite structures with large deformations. However, investigations on such issues are less reported in published literature, as an accurate and efficient model is required to well forecast the geometrically nonlinear behaviors of smart sandwich structures. As a result, a novel sinusoidal Legendre global-local higher-order shear deformation plate theory (SLHSDT) has been developed to accurately capture geometrically nonlinear behaviors of piezoelectric sandwich plates. The proposed model can fulfill the compatible conditions of transverse shear stresses and contain transverse normal strain, which can ensure precision in predicting electromechanical behaviors. The multi-patch isogeometric analysis (IGA) method for sandwich plates partially bonded with piezoelectric layers is proposed to overcome C1-continuity between patches for the first time. Moreover, the Newmark-β method and Newton-Raphson technique are attempted to solve the nonlinear equations. The present model has been utilized to investigate electromechanical behaviors of laminated structures with piezoelectric layers, which has been compared with the published results. In addition, experiments on macro fiber composite (MFC) integrated sandwich plates have been also carried out in the present work, which can effectively verify the performance of proposed model. Subsequently, the proposed model is employed to study electromechanical behaviors of the five-layer piezoelectric sandwich plates containing internal pores and graphene platelets. Then, influences of the porosity coefficient and GPLs weight fraction on the nonlinear electromechanical behaviors of sandwich plates are investigated. Eventually, the active control on nonlinear behaviors of piezoelectric porous sandwich plates with GPLs reinforcement is studied by using a closed-loop control system, and an effective approach slowing down large deformation has been proposed by selecting an appropriate distribution of GPLs along the thickness direction.

Modeling of size dependent buckling behavior of piezoelectric sandwich perforated nanobeams rested on elastic foundation with flexoelectricity

This article presents a size dependent mathematical model and an analytical solution methodology to accurately simulate and analyze the size dependent buckling behavior of piezoelectrically layered sandwich nanobeams with perforated core embedded in an elastic medium with flexoelectricity. The electric enthalpy energy function is expressed in terms of the electric and the flexoelectric effects. Regular squared cutouts perforation pattern is adopted for the perforated core. Closed forms for the equivalent geometrical parameters of perforated core are developed. The shear deformation effect is incroporated using the Timoshenko beam theory (TBT). To capture the nonlocality and the microstructure length scale effects, the nonlocal strain gradient elasticity theory is modified and adopted to include the electromechanical nonclassical effects. The Hamiltonian principle is utilized to derive the equilibrium equations. An analytical solution methodology is developed to derive closed forms for critical buckling loads. The developed solution procedure is implemented into a MATLAB software code. The accuracy of the developed procedure is verified by comparing obtained results with corresponding cases reported in the literature. Influences of different design variables on the electromechanical buckling behavior are explored through intensive parametric studies. Results obtained showed the significant effects of the flexoelectricity and the piezoelectric parameters on the size dependent buckling behavior of piezoelectric sandwich nanobeams with perforated core. Size dependent electromechanical as well as mechanical buckling behaviors could be controlled by adjusting these parameters. The developed procedure and the obtained numerical results are helpful in many technological and industrial applications as MEMS and NEMS.

Electro-mechanical analysis of piezoelectric sandwich structure

Piezoelectric sandwich structures are a fundamental construction in most piezoelectric devices. Accurately modeling their electro-mechanical response remains challenging due to complex coupling and interface phenomena. The Green’s function solution for electro-mechanical field of piezoelectric sandwich structures under a normal concentrated force, a basic case for common loadings, is derived using a new type of harmonic function and the Mirror Image Method. We investigate the distribution of the electro-mechanical field and the impact of material parameters and force direction on electromechanical components at the interfaces. This solution provides essential theoretical guidance for material selection and loading design in piezoelectric devices.

Nonlinear vibrations, bifurcations and chaos of piezoelectric composite lattice sandwich plate with four simply supported edges

This paper is devoted to investigate the nonlinear dynamics, bifurcation and chaos of the piezoelectric composite lattice sandwich plate with 1:3 internal resonance. Galerkin method is used to discretize the nonlinear partial differential governing equations of motion into the ordinary differential equations. The multi-scale method is used to obtain the modulation equations of the piezoelectric composite lattice sandwich plate in the polar coordinates and Cartesian coordinates in the primary and parametric resonances, respectively. Using Newton-Raphson method, the bifurcation diagrams of the steady-state equilibrium solution are obtained for the modulation equation with the change of the system parameters. The stability of the steady-state equilibrium solution is analyzed for the modulation equation. The existence of the static bifurcations, such as the saddle-node bifurcation, pitchfork bifurcation and Hopf dynamic bifurcations are found. The complex nonlinear jump phenomena caused by the existence of the multiple nonlinear steady-state solution regions are analyzed in detail. Fourth-order Runge-Kutta method is used to continue tracing the nonlinear periodic solution of the modulation equation in Cartesian coordinates. The time-history diagram, phase portrait and Poincaré map are obtained for the piezoelectric composite lattice sandwich plate in the nonlinear resonance. The dynamic process of the nonlinear periodic solution is described for the modulation equation from the limit cycle oscillation to the chaotic attractor in detail.

Nonlocal quasi-3d vibration/ analysis of three-layer nanoplate surrounded by Orthotropic Visco-Pasternak foundation by considering surface effects and neutral surface concept

The present article deals with the application of refined plate theory and surface effects to investigate the nonlocal free vibration behavior of a functionally graded nano-plate composed of two piezoelectric face sheets resting on Orthotropic Visco-Pasternak. Surface and nonlocal effects are applied using the surface piezoelectricity and stress-strain gradient theories. Surface effects, refined quasi-3D higher-order theory, neutral surface position and in-plane mechanical preloads are considered to study piezoelectric sandwich nano-plate with a functionally graded core in this study for the first time, simultaneously. The size-dependent governing equations are derived based on 2D and 3D refined theory using Hamilton’s principle and different boundary conditions are studied and investigated according to the semi-analytical solution method. Comparing the results of the vibration behavior of 2D and quasi-3D models, local and non-local models, and also, examining different foundations simultaneously can be said as one of the innovations of the current research. Finally, a parametric study is presented to examine the effects of different parameters such as surface effects, small scale parameters, mechanical preloads, thickness stretching effects, neutral surface position, non-homogeneous coefficient, applied voltage, different foundation constants, boundary conditions, geometrical ratios and different theories in details. It is indicated that the inclusion of surface effects and thickness stretching effects leads to a significant influence on the vibration behavior of three-layered nano-scale plates. The presented results in this article may provide useful guidance for the design and development of the next generation of nano-devices.

Thermal buckling characterization of nanocomposite beams activated by PZT with temperature-dependent characteristics considering the pyroelectricity

Employing piezoelectrically activated beam-like structures is extending in numerous applications for instance energy harvesters and sensors. On the other hand, advanced materials such as carbon nanotube-reinforced nanocomposites are widely implemented in making passive structures with the aim of using their advantages. For the first time, a study is established on the critical temperature of a piezoelectric sandwich aggregated CNTRC beam regarding the pyroelectricity. The stabilization contribution of pyroelectricity against the thermal buckling incidence of sandwich beams has been demonstrated specifically. It is found that the pyroelectricity develops the critical point for the temperature of a clamped-clamped piezoelectric sandwich non-reinforced beam.

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

AbstractWithin the framework of the consistent couple stress theory (CCST), we develop a Hermitian Cn (n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into nl microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian Cn FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian Cn polynomials. The accuracy and the convergence rate of our Hermitian Cn FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.

Free vibration and nonlinear dynamic response of sandwich plates with auxetic honeycomb core and piezoelectric face sheets

This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation.

Localized bending waves along the edge of a piezoelectric sandwich plate

Localized bending waves along the edge of a piezoelectric sandwich plate

Nonlinear Dynamic Bifurcation and Chaos Characteristics of Piezoelectric Composite Lattice Sandwich Plates

This paper investigates the nonlinear bifurcation and chaos characteristics of piezoelectric composite lattice sandwich plates at 1:3 internal resonance. The nonlinear vibration partial differential equation is first discretized to become an ordinary differential equation by applying the Galerkin method. The main resonance modulation equations and the parametric resonance for the external excitation frequency that is close to the system’s second-order modal frequency are then obtained by using the multiscale method. The Newton–Raphson method is subsequently applied to obtain the bifurcation diagram of the steady-state equilibrium of modulation equation with varying system parameters. The equilibrium stability is finally analyzed. We confirm the existence of static bifurcation such as saddle-node bifurcation, pitchfork bifurcation, and Hopf dynamic bifurcation. A detailed analysis is also conducted on the complex nonlinear jump phenomenon caused by the presence of multiple nonlinear steady-state solution regions. In the dynamic Hopf bifurcation interval, the fourth-order Runge–Kutta method is used to continue to track the dynamic periodic solution of the modulation equation in Cartesian coordinates. It is found that there are multiple boundary crises and attractor merging crises in the vibration system for piezoelectric composite lattice sandwich plates.

Composite sandwich plates with piezoelectric layers: Structural design, modal attributes and electric potential

This study investigates the electromechanical performance of piezoelectric sandwich plates both numerically and experimentally. The effect of different inner design parameters, namely the length-to-thickness, core-to-face thickness, boundary conditions and aspect ratio on both the eigenfrequency and electric potential attributes is assessed. Moreover, vibration amplitude-dependent effects are investigated. Polymer-based, sandwich plates are additively manufactured (AM) and commercially available PZT layers are surface-bonded and experimentally probed. AM smart plates are found to yield comparable eigenfrequency properties with the ones reported for fiber-reinforced smart sandwich composites. Low length-to-thickness, low core-to-face, and rectangular rather than square designs favor the electric potential performance.

Magnetic Control of Vibrational Behavior of Smart FG Sandwich Plates with Honeycomb Core via a Quasi‐3D Plate Theory

Herein, vibrational behavior of functionally graded (FG) smart piezoelectric sandwich plates with honeycomb core resting on viscoelastic foundation under the effect of 2D magnetic field is presented. By varying the magnetic‐field magnitude and its direction, the vibrations can be controlled. The plate is composed of two FG piezoelectric layers bonded with honeycomb structure as a mid‐layer. Magnetic Lorentz force will be deduced via Maxwell's relations. A new quasi‐3D plate theory considering the shear and normal deformations is incorporated to evaluate the displacements. The governing equations of motion are introduced via Hamilton's principle. Galerkin technique is considered to solve the motion equations for different boundary conditions. Influences of the magnetic field, boundary conditions, electric voltage, and core thickness on the eigenfrequency of the FG sandwich piezoelectric plate are illustrated. It is found that considering the effect of the magnetic field on the smart devices increases their vibrations, which may lead to an increment in the energy harvested from them. Further, when the magnetic field is applied along the length of the rectangular plate, the vibrations are reduced and vice versa.

Dynamic analysis of graphene-reinforced sandwich plates with piezoelectric macro fiber composite face sheets

Graphene is considered as an ideal candidate for composite materials owing to the outstanding physical characteristics. However, existing higher-order shear deformation theories in the literature may meet severe challenges for the accurate prediction of natural frequencies of graphene-reinforced sandwich plates with piezoelectric macro fiber composite (MFC) face sheets. If transverse shear deformations cannot be described accurately, the dynamic behaviors of piezoelectric sandwich plates with graphene reinforcements will be significantly impacted by the large differences of material properties at interfaces of adjacent layers and electro-mechanical coupling characteristic. Thereby, a novel electro-mechanical coupling theory is to be proposed for the free vibration of graphene-reinforced sandwich plates with MFC face sheets. Based on the Reissner mixed variational theorem (RMVT), the precision of the interlaminar shear stresses including the electro-mechanical coupling effect can be improved. The modified interlaminar shear stress field is absorbed in the strain energy, which can enhance the accuracy of the free vibration response of piezoelectric sandwich plates. Additionally, the second-order derivatives of in-plane displacements have been eliminated from the interlaminar shear stress components, which can substantially simplify the finite element implementation. Thus, a simple C0-type finite element formulation is developed for the free vibration of piezoelectric sandwich plates with graphene reinforcements. The 3D elasticity solutions and the results obtained from other theories are used to evaluate the performance of the proposed theory. In comparison with the existing higher-order theories, the proposed theory can produce more accurate results. In addition, a comprehensive parametric study is conducted to explore the impacts of significant parameters on the free vibration behaviors of piezoelectric graphene-reinforced sandwich plates.

Wave Propagation Analysis of Functionally Graded Graphene-Reinforced Piezoelectric Sandwich Nanoplates via Nonlocal Strain Gradient Theory

This article elaborates on the dispersion of waves in piezoelectric sandwich nanoplates resting on a viscoelastic foundation. The nanoplate comprises a functionally graded (FG) graphene-reinforced composite core layer with two piezoelectric surface layers. By combining the Halpin–Tsai model and related mixture rules, the properties of the composite material have been obtained. The Euler–Lagrange equation is obtained using the third-order shear deformation theory (TSDT) and Hamilton’s principle. Subsequently, based on the nonlocal strain gradient theory (NSGT), the equation of motion is presented. Finally, the effects of scale parameters, hygrothermal conditions, graphene distribution, and viscoelastic foundation on the propagation characteristics are numerically studied. The results reveal that the scale effect is more evident when the wave number is larger. Furthermore, critical damping increases with a rise in the wavenumber and Winkler modulus.

Semi-analytical solutions of static and dynamic degenerate, nondegenerate and functionally graded electro-elastic multilayered plates

In this paper mathematical modelling and semi-analytical solutions are elaborated based on the extended Stroh-like formalism for 3-D static problems of electro-elastic mono and multilayered plates. For the dynamic analysis of such structures under various excitation types, a time trigonometric series was coupled with the Stroh-like formalism. The unknown coefficient vectors are solution of the resulted eigenvalue problems and the solution is obtained in the associated basis. Mechanical and electrical forces are applied on the top and/or bottom layer and may take arbitrary forms. A flexible matrix formulation is elaborated to easily account for arbitrary mechanical and electrical surface loads and excitations. The methodological approach focuses on various aspects including the electro-elastic effects, the degeneracy of elastic isotropic materials as well as the effect of the graded material’s factor. Analytical solutions are obtained for the static behavior of degenerate and non-degenerate Elastic FGM plates, where the eigenvalues and eigenvectors are explicitly given. Mainly, semi-analytical solutions are presented for the dynamic behavior of piezoelectric sandwich plates by coupling Stroh-like formalism and trigonometric series. The presented methodological approach is applied to the dynamical analysis of sandwich plates under various excitation forms, namely sinusoidal, rectangular and sawtooth excitation pulses. The obtained numerical results demonstrate the effect of the graded factor, degeneracy and the applied surface load as well as of the excitation on mechanical and electrical responses for various laminated plates.

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

An analytical and experimental study on adaptive active vibration control of sandwich beam

A novel composite sandwich beam with adaptive active control system is proposed for low-frequency vibration reduction, and the experimental investigation on adaptive closed-loop vibration control is carried out. The macro fiber composite (MFC) piezoelectric patches and filtered-x least mean square (Fx-LMS) algorithm are employed to construct the adaptive closed-loop control system. An improved analytical model considering the effects of MFC piezoelectric patches is proposed to calculate the vibration characteristics of the composite sandwich beam. It provides a theoretical basis for the design of adaptive control scheme. The accuracy of present analytical model is verified by the results of experiment and numerical simulation. The adaptive vibration control is implemented analytically and experimentally, and the results demonstrate that the low-frequency vibration of the composite sandwich beam can be greatly and quickly suppressed by the proposed adaptive closed-loop control system. Moreover, vibrations induced by complex multi-frequency excitation with different amplitudes can be effectively reduced by using the proposed adaptive control system. The novelty of this work lies in the proposed adaptive closed-loop vibration control system and improved analytical method for piezoelectric composite sandwich beam. The study provides a novel design of real-time control system for the low-frequency vibration of composite sandwich structures.

Dynamic Analysis of a Piezoelectrically Layered Perforated Nonlocal Strain Gradient Nanobeam with Flexoelectricity

This study presents a mathematical size-dependent model capable of investigating the dynamic behavior of a sandwich perforated nanobeam incorporating the flexoelectricity effect. The nonlocal strain gradient elasticity theory is developed for both continuum mechanics and flexoelectricity. Closed forms of the equivalent perforated geometrical variables are developed. The Hamiltonian principle is exploited to derive the governing equation of motion of the sandwich beam including the flexoelectric effect. Closed forms for the eigen values are derived for different boundary conditions. The accuracy of the developed model is verified by comparing the obtained results with the available published results. Parametric studies are conducted to explore the effects of the perforation parameters, geometric dimensions, nonclassical parameters, flexoelectric parameters, as well as the piezoelectric parameters on the vibration behavior of a piezoelectric perforated sandwich nanobeam. The obtained results demonstrate that both the flexoelectric and piezoelectric parameters increased the vibration frequency of the nanobeam. The nonlocal parameter reduced the natural vibration frequency due to a decrease in the stiffness of the structures. However, the strain gradient parameter increased the stiffness of the structures and hence increased the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the ration of the value of the nonlocal parameter to the strain gradient parameter. This model can be employed in the analysis and design of NEMS, nanosensors, and nanoactuators.

Mantari’s Higher-Order Shear Deformation Theory of Sandwich Beam with CNTRC Face Layers with Porous Core Under Thermal Loading

In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.