Asymptotics of wave motion in transversely isotropic plates

The present investigation is concerned with elastic wave motion in infinite transversely isotropic plate by asymptotic method. The differential equations for the flexural and extensional motions are derived from the system of three-dimensional dynamical equations of linear elasticity. All coefficients of the differential operator are presented as explicit functions of the material parameter γ=cs2/cl2, the ratio of the squared velocities of flexural (shear) and extensional (longitudinal) waves. The velocity dispersion equations for the flexural and extensional wave motions are deduced analytically from the three-dimensional analog of Rayleigh–Lamb frequency equation for plates. The approximations for long and short waves are also obtained. The dispersion curves for phase velocity and group velocity spectrum are shown graphically for flexural and extensional wave motions of the plate. The results for isotropic materials have been deduced as special cases.