Transient radiation and scattering from fluid-loaded oscillators, membranes, and plates

Abstract

Transient radiation and scattering from fluid-loaded mechanical oscillators, membranes, and plates is addressed using time domain methods. The pressure field is expressed as a sum of convolution integrals that involve appropriately defined space and time-dependent modal impulse responses and modal velocities. A general set of coupled convolution integral equations is developed to relate the time-dependent modal coefficients of the velocity to the modal forces for the vibrators of interest. The form of the coupled convolution integral equations is noted to be the same for the case of spatially discrete or continuous vibrators, and the equations are readily solved by a ‘‘marching forward in time’’ procedure. Some numerical results for the special case of a planar-baffled single-degree-of-freedom oscillator and a plate or membrane are presented. These results clearly illustrate the effects of time-dependent radiation-induced forces on the response of the vibrators. In general, a decrease in the in vacuo natural frequency and a change in the quality factors are clearly observed in the low- and midfrequency regions for a vibrator. In the high-frequency region, decreased quality factor and settling time are observed due to radiation damping.