VIBRATIONS OF SUBMERGED STRUCTURES IN A HEAVY ACOUSTIC MEDIUM USING RADIATION MODES

Abstract

A set of radiation modes developed in previous work (Chen and Ginsberg [1]) is further applied to the study of interactions between a heavy acoustic loading and an elastic structure. The coupling of the acoustic loading with the structure is carried out by using the radiation modes to decouple surface quantities into model components together with a condensation of the structural equation onto the normal displacement of the wetted surface. Transforming the equation variables into velocity modal co-ordinates yields the equation for the submerged structure of which the unknown variable is the set of radiation modal amplitudes. The formulation provides a direct connection of the system response to the radiation modes, which characterizes acoustic behavior both at the surface and far fields. The radiation modes are divided into strong radiators and weak radiators, based on their magnitudes of the eigenvalues associated with the modal representation. Additionally, the interaction mechanism of the modes having strong radiation with the modes having weak radiation is presented in the formulation and demonstrated by numerical examples. The radiation patterns due to strong radiation modes exhibit directional characteristics, where the modal pressure distributions at the far field are confined to specific directions in space. Numerical examples are provided by beginning with a submerged constant thickness shell studied previously. The subsequent example is the shell attached with concentrated masses at various locations in order to reflect the changing of surface acoustic response and the far field response in terms of alterations to the structure.