Asymptotic analysis of the modes of wave propagation in a piezoelectric solid cylinder

An asymptotic method due to ’’Achenbach’’ is used to analyze the longitudinal and circumferential modes of wave propagation in a piezoelectric solid circular cylinder of crystal class (6 mm) or ceramics (∞m). Information obtained in this method is useful for the frequency spectrum at long wavelengths. In this method the displacement components, electric potential, and the frequency are expressed as power series of the dimensionless wavenumber, ε = 2π× radius/wavelength. Substituting these expansions in the field equations and the boundary conditions, a system of coupled second-order inhomogeneous ordinary differential equations with radial coordinate as the independent variable is obtained by collecting the terms of same order εm. Integration of such systems of differential equations yields the various terms in the series expansions for the above modes and for the whole range of frequencies, when the real valued dimensionless wavenumber is less than unity (0<ε<1). To test the correctness of the present scheme, the roots of the exact frequency equation are computed and the results thus obtained are compared with the results obtained in the present analysis.