C.F. Lü

Three-Dimensional Pyroelectric Analysis of a Functionally Graded Piezoelectric Hollow Sphere

A three-dimensional analytical piezothermoelastic solution is presented for a functionally graded piezoelectric spherical shell subjected to various thermal boundary conditions applied on the inner and outer surfaces. Material properties are assumed to vary along the radius, r, obeying a power law. Both the thermal field and the pyroelectric responses are resolved using the state space method. On introducing three displacement and two stress functions, two independent kinds of state equations are derived from the basic equations of piezoelectricity. It is interesting that the first kind is a homogeneous equation only related to the purely elastic behavior of the sphere, yet the second has an inhomogeneous term associated with the thermal effect to determine the pyroelectric responses. The state equations are solved by expanding the field variables into series of spherical harmonic functions. Numerical examples are performed to investigate the influence of material inhomogeneity on the pyroelectric responses of the spherical shell.

Elastic waves in piezoelectric cylinders with sectorial cross-section

On the basis of linear theory of three-dimensional piezoelasticity, the propagation of elastic waves in piezoelectric cylindrical waveguides with sectorial cross-section is analyzed. Dispersion relations in analytical forms are obtained for various boundary conditions. Numerical results including real, imaginary and complex branches of full dispersion spectra are presented to show the essential characteristics of the waves. The problem was currently investigated by V. Puzyrev [Int. J. Solids Struct. 2010 (47) 2115–2122], but, unfortunately, many misprints/mistakes can be found therein. What we do here is to correct these mistakes and present the right numerical results.

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.

Semi-analytical solution for orthotropic multiferroic laminates

The dynamic responses of an orthotropic, multiferroic laminate in cylindrical bending are investigated based on the three dimensional equations. A semi-analytical approach, which makes a hybrid use of the method of state space method (SSM) and the differential quadrature method (DQM), is employed. This semi-analytical approach allows us to efficiently analyze laminates with arbitrary boundary conditions at the two ends. The approach is verified by comparing the results with those for simply-supported conditions that are obtained exactly via SSM. The effects of some parameters on the dynamic responses are discussed.

Exact solution for simply supported multiferroic laminates with imperfect interfaces

Exact solutions are derived for simply-supported, orthotropic, multiferroic laminates with imperfect thermal interfaces, subject to mechanical, electric, magnetic, and thermal loads. The assumption of cylindrical bending is adopted. The interface is described as thermally weakly (or highly) conducting, as well as mechanically, electrically and magnetically compliant. The state space method is adopted, which is very convenient and efficient for multilayered structures. Numerical results are presented to validate the formulation and to illustrate the influence of the interfacial imperfection on the various field variables.

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.