Membrane and Flexural Waves on Thin Shells

Abstract

Membrane and flexural waves are limiting short wavelength solutions of the equations of motion for arbitrarily curved, smooth shells. Each distinct wave type is found using a geometrical or ray method based upon asymptotics in the small parameters h/R, where h is thickness and R a minimum radius of curvature. Useful, asymptotic formulae are found for the normal displacement associated with membrane waves, group velocities, and other physically significant quantities. Ray paths on a conical shell are illustrated for each wave type, and it is found that flexural rays form a caustic near the vertex.