An in vacuo modal expansion method to determine the transient response of fluid-loaded planar vibrators

Abstract

A general approach is presented to evaluate the vibratory response of fluid-loaded planar vibrators to broadband time dependent excitations for either radiation or scattering problems. The velocity of the vibrator is expressed as a sum of the products of the in vacuo modes and the time dependent modal velocities. In contrast to the in vacuo case, the modal velocities are coupled due to fluid loading. A set of coupled convolution integral equations for the time dependent modal velocities is developed and rearranged to facilitate their numerical solution. Analytical expressions are obtained for the impulse responses of the pc fluid-loaded admittances. These impulse responses which are the modal velocities when the pc or high-frequency approximation is made for the effect of fluid loading, are then used to compute the modal velocities when the effect of coupling is included. Since the known terms in the coupled convolution integral equations are very easily obtained, a large number of modes can be included in the analysis. Numerical results are presented to illustrate the effect of coupling on the velocity responses of simply supported plates to convecting line excitations and clamped circular plates to impacts.