Wei-qiu Chen

Vibration of a functionally graded piezoelectric spherical shell filled with fluid

Nowadays piezoelectric composites are widely used as integrated structural elements including plates and shells. When the concept of functionally graded material is introduced, piezoelectric structures exhibit more advantages. The present paper focuses on the free vibration characteristic of a fluid-filled spherical shell, which consists of functionally graded piezoceramic. The radial inhomogeneity is approached by an approximate laminated model. To obtain a three-dimensional solution more conveniently and efficiently, a mixed method based on state space method is employed. At the end of this paper, some numerical examples are presented, in which the effect of related parameters on the vibration is discussed.

The symplectic method for plane problem of Functionally Graded Piezoelectric Materials

This paper applies the symplectic method to solve the plane problem of functional graded piezoelectric materials (FGPM) whose elastic stiffness, piezoelectric and dielectric constants vary exponentially with the axial coordinate. After introducing the displacements (the electrical potential function) and their conjugate stress (electric displacement), the problem is formulated within the frame of state space and it is solved using the method of separation of variables along with the eigenfunction expansion technique. Compared with that for homogeneous materials, the operator matrix is not in an exact Hamiltonian form, but it has similar properties. This operator matrix is called the shifted-Hamiltonian matrix since the eigenvalues are symmetric with respect to -alpha/2, rather than zero in the normal Hamilton matrix. In this case, the symplectic adjoint eigenvalue of zero isnt itself but -alpha . In this paper the eigensolutions corresponding to zero and -alpha are gained which indicate certain physical essence of the problem that can not be revealed by other methods. These also can be degenerated to the ones for homogeneous materials after suppressing certain rigid motions.

Wave propagation in two-layered infinite composite piezoelectric hollow cylinder with imperfect interfaces

The focus of this paper is to study an infinite composite hollow cylinder consisting of a homogeneous piezoelectric layer and a functionally graded elastic layer. A general linear spring-layer model is employed to characterize the interface between the two layers, which may be perfect or imperfect. Directly based on the three-dimensional exact equations of elasticity and piezoelasticity, the state space formulations are developed. An analytical characteristic equation is presented, from which the dispersion of wave propagating in the cylinder can be investigated. In numerical examples, different modes of wave propagation and the effects of some parameters on the dispersion curves are discussed.

Saint-Venant solutions for functionally graded piezoelectric beams with transverse polarization

The symplectic method is employed to investigate the functionally graded piezoelectric beam which is polarized in the thickness direction. The material constants vary along the length in an identical exponential form. The method uses both the displacements and their conjugate stress as variables so that the problem is reformulated in a state space. Using the method of separation of variables, the problem is further reduced to analyzing eigenvalues and their eigensolutions. The Saint-Venant eigensolutions corresponding to the eigenvalues of zero and ¯α which may be classified into 0-group and ¯α-group are solved. They satisfy the adjoint symplectic orthogonality relations. The 0-group eigensolutions are found identical with those for the homogenous materials, representing rigid-body translations and rotations and uniform electric potential. But the ¯α-group eigensolutions are different. However, they degenerate to the ones for the homogeneous materials with the related rigid motions restrained.

Geometrical non-linear finite element analysis of piezoelectric materials based on ABAQUS

The nonlinear piezoelectric finite element method, which includes geometrical nonlinearity and material nonlinearity, has gained more and more popularity and been studied by more and more researchers. A large deformation finite element analysis is presented for piezoelectric materials and structures in this paper. Green-Lagrenge strains for large deformation are incorporated into the linear piezoelectric equations. The formulations of the secant stiffness matrix and tangent stiffness matrix are presented, and the Newton-Raphson method has been used to solve the nonlinear equations. Based on the finite element package ABAQUS, eight-node plane geometrical nonlinear piezoelectric element is developed. The results using this user-developed element are found the same as those based on the piezoelectric element embedded in ABAQUS for geometrical nonlinear analysis. It indicates that ABAQUS can be used as a convenient platform for developing nonlinear piezoelectric finite element so as to study various nonlinear piezoelectric problems.

Bending of piezoelectric bimorph plates under a coupled action of electric and thermal fields

The bending of piezoelectric bimorph plates subject to electric and thermal loadings is investigated. Based on the constitutive equations for the generalized plane stress problems of piezoelectric materials, the stresses and the electric displacements of piezoelectric bimorph plates with different configurations are obtained by virtue of Kirchhoffs hypothesis and Saint-Venants hypothesis. Analytical expressions for the deflection of piezoelectric bimorph cantilever as an actuator are obtained.

Free vibration of multiferroic simply supported circular cylindrical panels

Two dimensional equations are derived for multiferroic circular cylindrical panels with small aspect ratio. The displacement, electrical potential and magnetic potential are assumed to be of zero-order of the radial thickness. The frequency equation is presented for a multiferroic cylindrical panel composed of CoFe2O3 and BaTiO3 with four edges simply supported. Numerical examples show clearly the effects of half-wave numbers in the axial and circumferential directions on the frequency parameters.

Delamination detection in laminated composite beams using electro-mechanical impedance signatures

This paper focuses on the delamination detection in composite beams using electro-mechanical impedance (EMI) signatures, which is directly related to the structures mechanical impedance. A model of a laminated beam including a delamination as well as installed PZT transducers is presented. Furthermore, the model has to take into account the dynamic behavior of the piezoelectric patches and simulate the presence of the imperfect bonding between the PZT patch and the host laminate based on a classic shear lag law. Then, an analytical expression of impedance involving information on the size and the position of a delamination in this coupled smart structure system is derived via the reverberation matrix method (RMM). Comparison with existent experimental and numerical results is presented to validate the present analysis. The numerical simulations allow us to study more closely the influence of some geometrical parameters such as sensor size and position. The analysis in this paper provides necessary theoretical basis for delamination detection in composite structures.

Reverberation-ray analysis of orthotropic piezoelectric laminates with imperfect interfaces

The static and dynamic problems of an imperfectly bonded, orthotropic, piezoelectric laminate in cylindrical bending are investigated based on the equations of piezoelasticity. A general spring layer is adopted to model the bonding imperfections at the interfaces of the laminate. The formulations of reverberation-ray analysis are developed. The approach is verified by comparing the results with those obtained from the state space method.

Modeling of multilayered acoustic wave devices with the method of reverberation-ray matrix

The method of reverberation-ray matrix (MRRM) are modified and extended to the analysis of wave propagation in multilayered acoustic wave devices based on three-dimensional linear piezoelectricity. By the plane wave solution assumption, state equations are established whose solutions are expressed with unknown wave amplitudes. Within the framework of MRRM, the phase and scattering relations are properly set up to determine the unknowns without involving exponentially growing functions and matrix inversion operations in an easy and uniform way. Thus the present MRRM is unconditionally stable and free from limitations to the frequency, the thickness of individual layers and the total number of layers. The surface waves, the interface waves and the bulk waves are all included in the formulation. Therefore, the present formulation applies to SAW devices as well as BAW devices. Numerical examples are given to illustrate the well performance of the proposed formulation of MRRM for the analysis of free waves in multilayered acoustic wave devices.