Extension of the surface variational principle to nonaxisymmetric response of submerged thin shells of revolution

Abstract

Previously, the surface variational principle (SVP) was implemented for rigid and elastic submerged structures under axisymmetric excitations. More recent developments extended SVP to address nonaxisymmetric problems of acoustic radiation and scattering situations for rigid bodies of revolution. In this presentation, SVP is applied jointly with Hamilton’s principle governing nonaxisymmetric responses of elastic thin shells of revolution. Complex Fourier expansions of the azimuthal dependence are combined with Ritz expansions of the spatial dependence to represent the displacement field and surface pressure. This representation is equivalent to a wave-number decomposition of the surface response into a series of helical-type waves. By enforcing continuity of normal velocity on the fluid–structure interface, a set of coupled algebraic equations is formed for each azimuthal harmonic. Problems addressed here are radiation due to arbitrary loading, and scattering associated with arbitrary incidence of a plane wave on a stationary elastic thin shell. The rigid body modes are included in the scattering case. Numerical results are assessed for the convergence qualities of an SVP simulation, particularly regarding series length requirement as the frequency is increased. [Work support by ONR.]