Characteristics of wave propagation in section-varying bar covered with piezoelectric layer

The wave propagation in the section-varying bar with piezoelectric layered is studied in this paper. The study aims at observing the general characteristics of wave in the laminated section-varying bar. The section-varying problem is described by the boundary varying function and the co-ordinate functions are utilized to denote the displacements in the laminated bar. The co-ordinate functions which can be used to express an arbitrary unique and continuous displacement field are polynomials in the radial co-ordinate r. Based on a matrix formulation of Hamilton’s principle, the dynamical equations associated with wave propagation in the laminated bar are established. The numerical solution of the dispersion curves for different section-varying extent and wave propagation distance are obtained by performing the variational operation and solving the eigenvalue problem where the wavenumber is considered to be known and the frequency is determined as an eigenvalue. The eigenvectors are coupled to the co-ordinate functions and determine the distribution of displacements over the cross-section. From the calculated results, the first three mode shapes of displacement fields and the first mode shapes of stress fields distribution along radial direction are shown in the paper.