Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Abstract

Each guided elastic wave mode is composed of propagating and non-propagating branches. Non-propagating branches associated with complex wavenumbers are substantially different from the propagating ones. Accurate calculation of the transcendental dispersion equation for complex wavenumbers and arbitrary ranges of frequencies is usually very difficult, especially for demanding cases such as those involving composite materials and curved structures. In this article, an extended Legendre orthogonal polynomial method is presented to determine non-propagating waves in a functionally graded piezoelectric cylindrical shell. The extended Legendre orthogonal polynomial method can obtain complete solutions without the tedious iterative search. Results are compared with those published earlier to validate the extended Legendre orthogonal polynomial method, and the convergence of this method is also discussed. Dispersion characteristics of the non-propagating waves in various graded piezoelectric cylindrical shells are studied and three-dimensional dispersion curves are plotted. The effects of piezoelectricity, graded fields, and the mechanical and electrical boundary conditions on dispersion curves are illustrated. The displacement amplitude, stress, and electric potential distributions are also analyzed in detail. Numerical results show that the extended Legendre orthogonal polynomial method is very efficient to retrieve the guided waves of any nature and the modes of all orders.