Acoustic time-dependent loading on elastic shells of revolution using the internal source density and singular value decomposition method

Abstract

A new representation for the time-dependent surface pressure on a fluid-loaded shell of revolution with a prescribed space and time-dependent axisymmetric velocity distribution is presented. This representation, which is based on expanding the surface traction and velocity vectors into in-vacuo modal vector expansions with time-dependent coefficients, results in each time-dependent modal pressure coefficient being expressed as a sum of temporal convolution integrals which involve time-dependent modal radiation impulse responses and modal velocities. After presenting the formulation of the appropriate initial-boundary value problem, Fourier transform methods are introduced to obtain the corresponding Neumann boundary value problem. The solution of this latter problem is formulated as a minimum mean square error problem in which linear monopole harmonic distributions along the axis of the shell are introduced to determine the surface pressures resulting from the normal components of the modal vectors of interest. Singular value decomposition methods are then used to determine the harmonic monopole distributions. Modal decomposition and inverse Fourier transform methods are then used to evaluate the time-dependent modal radiation impulse responses. Numerical results are presented for the self and mutual modal radiation impulse responses for both spherical and spheroidal shells.