Traveling-wave decomposition of surface displacements associated with scattering by a cylindrical shell: Numerical evaluation displaying guided forward and backward wave properties

Abstract

Internal displacements of spherical shells subjected to steady sound waves in water have previously been computed by other researchers [e.g., R. Hickling et al., J. Acoust. Soc. Am. 92, 499 (1992)]. Such displacements can be perplexing to directly interpret with a guided wave representation because of the superposition of counterpropagating waves in a steady-state analysis. In this research the surface displacements of a cylinder were evaluated since they can be mathematically decomposed into counterpropagating circumferential traveling waves. (Unlike an analogous decomposition for spheres, the traveling-wave amplitudes in the cylinder case are regular at 0 and 180 deg.) By limiting attention to the radial displacements of the outer surface, it was also possible to display the response to short-tone bursts and thereby distinguish between counterpropagating wave packets. Both the steady-state and burst response situations clearly manifest waves launched on the shell. Shells studied include 2.5% and 10% thick SS304 shells with coincidence frequency excitations of the subsonic a0− Lamb wave and high-frequency (near kLh≊π) excitation of a negative group velocity Lamb wave.