Analysis of laminated piezoelectric composite plates using an inverse hyperbolic coupled plate theory

This paper presents a non-polynomial coupled plate theory for smart composite structures employing inverse hyperbolic displacement and electric potential functions. The theory is utilized towards analysis of composite piezoelectric plates operating in sensor and actuator modes. Particularly, the following three cases are studied: (i) passive laminated composite structure, (ii) composite piezoelectric plate actuator and (iii) unimorph and bimorph piezoelectric plate sensors. Analytical solutions are obtained for simply supported plates under static electrical and mechanical loads. These results are validated with existing 3D elasticity solutions and compared with other plate theory solutions. Furthermore, parametric studies are performed to determine the effect of loading, span-to-thickness ratio and lamination sequence on the response of the piezoelectric plate. Finally, the theory is applied to a transverse shear sensing device which utilizes transverse shear-electric field coupling in piezoelectric materials. This effect is often ignored in literature.It is observed that the maximum percentage error of the present theory, when compared with 3D results, is less than 3%, which is lower than other higher order plate theories.     

集成结构振动主动控制和抑制

采用一种新的压电板单元,建立了含有分布压电传感元件和执行元件的集成结构的有限元动力模型。研究了这种集成结构在常增益负速度反馈控制规律作用下,振动的主动控制与抑制的问题,并提出了集成结构振动主动控制和抑制的一般方法。最后,提供了数值示例,说明本文提出方法的有效性。     

Free vibration analysis of piezoelectric coupled annular plates with variable thickness

This paper presents the free vibration analysis of piezoelectric coupled annular plates with variable thickness on the basis of the Mindlin plate theory. No work has yet been done on piezoelectric laminated plates while the thickness is variable. Two piezoelectric layers are embedded on the upper and lower surfaces of the host plate. The host plate thickness is linearly increased in the radial direction while the piezoelectric layers thicknesses remain constant along the radial direction. Different combinations of three types of boundary conditions i.e. clamped, simply supported, and free end conditions are considered at the inner and outer edges of plate. The Maxwell static electricity equation in piezoelectric layers is satisfied using a quadratic distribution of electric potential along the thickness. The natural frequencies are obtained utilizing a Rayleigh–Ritz energy approach and are validated by comparing with those obtained by finite element analysis. A good compliance is observed between numerical solution and finite element analysis. Convergence study is performed in order to verify the numerical stability of the present method. The effects of different geometrical parameters such as the thickness of piezoelectric layers and the angle of host plate on the natural frequencies of the assembly are investigated.     

Analysis of wave propagation in functionally graded piezoelectric composite plates reinforced with graphene platelets

This paper presents a semi-analytical approach to investigate wave propagation characteristics in functionally graded graphene reinforced piezoelectric composite plates. Three patterns of graphene platelets (GPLs) describe the layer-wise variation of material properties in the thickness direction. Based on the Reissner-Mindlin plate theory and the isogeometric analysis, elastodynamic wave equation for the piezoelectric composite plate is derived by Hamilton’s principle and parameterized with the non-uniform rational B-splines (NURBS). The equation is transformed into a second-order polynomial eigenvalue problem with regard to wave dispersion. Then, the semi-analytical approach is validated by comparing with the existing results and the convergence on computing dispersion behaviors is also demonstrated. The effects of various distributions, volume fraction, size parameters and piezoelectricity of GPLs as well as different geometry parameters of the composite plate on dispersion characteristics are discussed in detail. The results show great potential of graphene reinforcements in design of smart composite structures and application for structural health monitoring.     

Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field

This work investigates the bending of a simply supported functionally graded piezoelectric plate under an in-plane magnetic field. The extended sinusoidal plate theory for piezoelectric plate is adopted. The governing equations are derived by the principle of the virtual work considering the Lorentz magnetic force obtained from the Maxwell's relation. The effect of magnetic field, electric loading and gradient index on the displacement, electric potential, stress and electric displacement are numerically presented and discussed in detail. These conclusions will be of particular interest to the future analysis of piezoelectric plate in magnetic field.     

Dynamics of Layered Structures with Bonded Piezoelectric Material

For the proper design of plate and shell composite structures with piezoelectric patches bonded to the surfaces of a host structure, appropriate finite elements are presented. The linear piezoelectric effect is taken into account so that the displacements and the electric potential serve as independent variables. The electric potential can be condensed on the element level and does not enter the system of equations. This condensation has the advantage of a more efficient calculation especially for dynamic problems. With dynamic examples the two formulations are compared with each other and with solutions from the literature, which prove the accuracy and the efficiency of the formulations.     

Compressive and thermal postbuckling behaviors of laminated plates with piezoelectric fiber reinforced composite actuators

This paper studied compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise for a shear deformable laminated plate with piezoelectric fiber reinforced composite (PFRC) actuators based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The material properties are assumed to be temperature-dependent and the initial geometric imperfection of the plate is considered. The compressive and thermal postbuckling behaviors of perfect, imperfect, symmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded PFRC actuators are conducted under different sets of thermal and electric loading conditions. The results reveal that, the applied voltage usually has a small effect on the postbuckling load–deflection relationship of the plate with PFRC actuators in the compressive buckling case, whereas the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators.     

Modelling of multilayer transducer by means of the graph and structural numbers method

This paper presents the characteristics of piezoelectric plate vibration. Model of simple system were shown. The equations of piezoelectric plate have been derived in terms of longitudinal displacement and electric potential. Three ports system for investigated model was determined. Analysis was done by means the graph and structural numbers method. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electro-dynamic analysis of smart nanoclay-reinforced plates with integrated piezoelectric layers

Integrating engineering structures with piezoelectric layers as actuator and/or sensor offers smart sandwich structures with controllable static and dynamic deflections. In this paper, a smart sandwich plate consisting of a light nanoclay-reinforced composite core and two piezoelectric face sheets is considered. The static and dynamic behaviors of the proposed smart plate are obtained using their governing coupled electro-mechanical system of equations. In order to facilitate the governing equations, a mesh-free method based on moving least square (MLS) shape function and first order shear deformation (FSDT) is developed and implemented. Two morphologies of intercalated stack and exfoliated nanoclay dispersions are considered in the distribution of the nanoclay into the polymeric matrix. The effects of morphology and volume fraction of the nanoclay, time-dependent loading, and essential boundary condition on the static and dynamic behavior of the smart piezoelectric-integrated nanocomposite plates are examined. In the dynamic analysis, resonance and amplitude modulation phenomena are studied. It is observed that the use of nanoclay, especially with exfoliated morphology, improves the static and the free vibration responses of the smart sandwich plates. Moreover, the frequency of the applied mechanical load has a significant effect on the electro-dynamic response of the proposed smart sandwich plates.     

Application for generating characteristics of free and bonded systems

The present paper is the continuation of earlier publications with stack of piezoelectric plates. This work is an author's idea of application for generating characteristics of piezoelectric systems. The presented program, called Piezo3D, allows for generation a single piezoelectric plate graphs as well as complex, free and bonded systems. An additional advantage is the ability to obtain the 3D graphs, in which the characteristics of the test graph can be based not only on frequency, but also on other parameters such as the thickness of the plate. The application is written in the numerical software "Matlab". (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strongly-coupled modelling and analysis of energy harvesting devices

A monolithic approach is proposed that provides simultaneous modelling and analysis of the harvester, which involves surface-coupled fluid-structure interaction, volume-coupled electro- mechanics and a controlling energy harvesting circuit for applications in energy harvesting. A space-time finite element approximation is used for numerical solution of the weighted residual form of the governing equations of the flow-driven piezoelectric energy harvesting device. This method enables time-domain investigation of different types of structures (plate, shells) subject to exterior/interior flow with varying cross sections, material compositions, and attached electrical circuits with respect to the electrical power output generated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear vibration of hybrid laminated plates resting on elastic foundations in thermal environments

This paper deals with large amplitude vibration of hybrid laminated plates containing piezoelectric layers resting on an elastic foundation in thermal environments. The motion equation of the plate that includes plate-foundation interaction is based on a higher order shear deformation plate theory and solved by a two-step perturbation technique. The thermo-piezoelectric effects are also included and the material properties of both orthotropic layers and piezoelectric layers are assumed to be temperature-dependent. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions. The results show that the foundation stiffness and stacking sequence have a significant effect on the nonlinear vibration characteristics of the hybrid laminated plate. The results also reveal that the temperature rise reduces the natural frequency, but it only has a small effect on the nonlinear to linear frequency ratios of the hybrid laminated plate. The results confirm that the effect of the applied voltage on the natural frequency and the nonlinear to linear frequency ratios of the hybrid laminated plate is marginal except the plate is sufficiently thin.     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

Finite deformations of thin shells with piezoelectric sensors and actuators

We treat coupled electromechanical problem of finite deformations of piezoelectric shells with the help of the direct approach. A shell is considered as a material surface with mechanical degrees of freedom of particles and with an additional field variable, namely electric potential on the electrodes. This results both in the nonlinear system of equations of piezoelectric shells and in the appropriate numerical scheme. Application of the direct approach is preceded with the three-dimensional asymptotic analysis of a linear electromechanical problem for a non-homogeneous piezoelectric plate, which provides the constitutive relations for the nonlinear theory. As a sample problem, we present finite element analysis of deformation and local buckling of cylindrical panel, equipped with piezoelectric sensors. The latter influence the mechanical behavior and produce signals, which can be interpreted in terms of structural entities. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hamilton等参元与智能叠层板的半解析法

根据压电材料修正后的Hellinger-Reissner(H-R)变分原理,建立了各向异性压电材料4节点Hamilton等参元的一般形式．为智能叠层板自由振动问题和带有压电块的叠层悬臂梁的瞬态响应等问题提出了一种新的半解析法．数学模型的基本步骤:将压电层和主体层看成独立的三维体,在平面内离散各层,分别建立各层的方程;根据主体层和压电层在连接界面上广义应力和广义位移的连续条件,联立主体层和压电层的方程得到全结构的控制方程．等参元不限制智能板侧面的几何边界形状、板的厚度和层数,有广泛的应用领域．     

Optimal placement of distributed actuators for a controlled smart elastic plate

The performance and the efficiency of smart structures controlled by piezoelectric wafers decisively depend on the locations of the actuators and sensors. For the evaluation and testing of time consuming numerical optimisation techniques, which are currently a part of our research, benchmark examples are required. As such a benchmark example a simply supported plate structure is inverstigated, where the active controlled behaviour can still be described analytically. In the paper the optimisation algorithm is briefly described and the results of a typical example are presented.     

Exact solution for Transient bending of a circular plate integrated with piezoelectric layers

This paper presents the exact, explicit solution for the transient motion of a circular plate surface bonded by two piezoelectric layers, based on Kirchhoff plate model. The distribution of eclectic potential along the thickness direction is simulated by a quadratic function so that the Maxwell static electricity equation is satisfied. The piezoelectric layers are electrically grounded over the edge and electrodes at the two surfaces of the piezoelectric layers are shortly connected. The differential equations of motion are solved for simply supported and clamped boundary conditions. The solutions are expressed by elementary Bessel functions and obtained via exact inverse Laplace transform.     

The static shape control for intelligent structures

A finite element formulation is presented for modeling the plate structure containing distributed piezoelectric sensors and actuators (S/As). A new plate bending element for analysis of the plate with distributed piezoelectric S/As is developed. This element saves much memory and computation time. Using the bending plate element, a general method of static shape control for the intelligent structure is put forth. Two examples are given to illustrate the application of the method presented in this paper. The purpose of the first example is to check the accuracy of the finite element method presented in this paper. The second example is to study the problem of the static shape control for the intelligent structure. It is concluded that the shape of the intelligent structure can reach the desired shape through passive control or active control.     

Plates made of piezoelectric materials: When are they really piezoelectric?

This paper aims at presenting in a synthetic way mathematical results that have been rigorously and recently derived by the authors. These results deal with the simplified but accurate modeling of linearly piezoelectric thin plates. It is shown how mathematical tools lead to two different situations linked to either sensors or actuators devices. Moreover we enlighten the fact that for some piezoelectric crystal classes, the coupling between the electrical and the mechanical effects disappear in the plate. Finally, we furnish a detailed example of such models in the case of a plate constituted by a 222 symmetry class material.     

Transient analysis of a potential pulse in a piezoelectric (622) crystal plate

Transient analysis of the wave propagation due to an electric potential pulse concentrated at a point on the boundary of an infinite piezoelectric plate of the crystal class (622) resting on an infinite elastic medium is considered. The electric potential is studied for an exponential pulse and step pulse. Numerical results are obtained for theβ-quartz plate that rests on aluminium half-space.