Elastodynamic Analysis Of Piezoelectric Rod Structures

Piezoelectric materials have been widely used to manufacture various sensors and actuators in the form of laminar layer, thin membrane and coat as sense organs in the areas of smart or intelligent structures because of its strong electriomechanical coupling effects. Piezoelectric composite layered rods structures have become one of the important functional devices in the application areas as aerospace engineering, smart structures, ocean exploration, energy fields and even biological engineering. Piezoelectric elements can be incorporated into a laminated composite structure, either by embedding it or by mounting it onto the surface of the host structure. With the developing of advanced technical and the growing demand for engineering practice, researches in this area have been further extended from pure piezoelectric properties into the properties of smart structures. By considering of broad application and encountering more problems in manufacture practice, researches of dynamical properties of piezoelectric materials have been further deepened. The study of characteristics of wave propagation in the laminated rods structures becomes one of the most important parts in dynamical property researches of smart structures and is very meaningful in theory and valuable in application.The main work in dissertation includes:(1)Based on the matrix formulation of Hamilton's principle and co-ordinated fuctions, the basic equations of wave propagation in laminated piezoelectric cylindrical bars (including section-varying) are derived. The wave dispersion curves are obtained by solving an eigenvalue problem. By the numerical examples, the factors of influence on distributions of dispersion curves, displacements and electric potential are discussed through numerical results. The influence of changes of cross section on the distributions of displacements and electric potential is studied.(2)The equations of wave propagation in plane bent piezoelectric rods, in 3D circular bent piezoelectric rods, and in 3D bent piezoelectric rods with arbitrary curvature are established in the orthogonal curvilinear coordinate system. The wave dispersion curves in the rods with different curvature are obtained by performing Galerkin integral and solving an eigenvalue problem. The differences of dispersion curves in piezoelectric bent rods and in elastic bent rods are discussed by the results of numerical examples. The influence of material parameters on dispersion relations is also discussed. And distributions of displacements and electric potential of the first three modes in the cross section and along the axes are studied.(3) Based on simplified the problem to one dimension, by performing Laplace transform and some relevant transforms in functions of a complex variable, dispersion relations in bent piezoelectric rods are obtained, then the relations between displacements and electric potential, and the dynamical response expressions of displacements and electric potential under stress impulse acting on end of the rod are derived. The dynamical response curves of displacements, stress and electric potential are discussed in the numerical examples, and the dynamical response characteristics under longitudinal impulse wave act on laminated piezoelectric rods are analysed.(4) Based finite deformation theory, the equations of geometrical nonlinear elastic wave propagation in the laminated piezoelectric rod are established. The method of successive approximation is used to assume the functions of displacement and electric potential and their relations are also obtained. By using perturbation method, the equations are solved and functions of displacements and electric potential are obtained. Distortion of shapes of nonlinear wave and effects of initial frequency and initial amplitude on nonlinear characteristics of wave propagation are discussed.