The Wave Propagation And Harmonic Response Analysis Of A Laminated Piezoelectric Beam With An Arbitrary Delamination

Appearance of the smart structure improved the self-apperception capability, repair capability and control adjusting capability of materials. Because of positive and negative piezoelectric effects, piezoelectric materials have become one of important materials making smart structure. And laminated piezoelectric structure is one of the important forms of smart structure and applies very widely .But delamination phenomenon can arise in this kind of structure, so bearing capability of the structure can be reduced obviously and damages could be occurred. Based on Timoshenko beam theory and third-order shear deformation beam theory, basic equations of dynamics and reasonable displacement functions are induced by using wave propagation theory to analyse the dynamical response and effects of delamination parameters on dynamical response in this paper. The main work in dissertation includes:(1) Synthetic introduction of basic concepts about laminated piezoelectric-elastic beam. Based on electriomechanical coupling effects of piezoelectric materials, Timoshenko beam theory and third–order shear deformation theory, the basic dynamical equations of laminated piezoelectric beam are obtained, and methods to solve dispersion relation and dynamical response are brought up.(2) By utilizing Timoshenko beam theory, harmonic response of piezo-elastic laminated beam with arbitrary delamination is performed, and dispersion relation, analytical solutions of displacement and electric potential are obtained. The influence of geometric parameters of delamination on displacements of beam and electric potential in piezoelectric layer are discussed through numerical results.(3) By utilizing third–order shear deformation beam theory, harmonic response of piezo-elastic laminated beam with arbitrary delamination is performed, and dispersion relation, analytical solutions of displacement and electric potential are obtained. The results of third-order and first-order are compared through numerical examples, and the application scopes of first-order and high order shear deformation theory are given.The main work of this paper is using separated areas to describe piezo-elastic beam with delamination, which makes it easier to describe of length and location of delamination. And first-order and third-order shear deformation beam theory are utilized to assume the displacement shape functions, and electric potential is simplified by considering of long wave. The cantilever piezo-elastic beam are analysed by using wave theory and considering of no external charge, and dispersion relation, analytical solutions of displacement and electric potential are obtained, also the effects of parameters of delamination on displacements and electric potential are given. The results provide theoretical basis for new inspection of delamination.