Resonance sound transmission into arbitrarily loaded submerged cylindrical shells

Abstract

We develop the fundamental exact analytical and computational model required to study the transmission of incident plane sound waves into submerged elastic cylindrical shells subjected to arbitrary forcing functions on their outer surface. We use the superposition principle in this linear problem to separate the contributions to the internally transmitted field caused by the incident wave from that of the surface excitation. This basic model uses the exact (2-D) formulation of elastodynamics to describe the shell motions, and that of general linear acoustics to describe the wave motion in the inner and outer fluids. We display the isobaric contours of the internally transmitted pressure fields, exhibiting their caustics and their progressive development as the frequency is increased within the band 0≤k3a≤10. The contour plots are generated for all possible combinations of forcing functions and insonification conditions with a view toward computing an advantage ratio PR which measures the gains that would result from sensing the internally transmitted field, rather than the field external to the shell at its surface. This advantage ratio is shown always to be greater than unity, and in many cases, much greater than unity. The effects of two basically different types of loads are analyzed via internal isobaric plots, and also by means of spectral plots computed at selected fixed points inside the shell. We observe an encouraging overall permanence of the caustic locations, at fixed frequencies, as the types of surface loads are varied. The present investigation of sound transmission into arbitrarily surface-loaded shells clearly demonstrates the filtering behavior of the shell in the frequency domain, and its focusing action in space. Hence, for moderate surface loads, the air-filled submerged shell analyzed here acts as a very effective sound concentrator, particularly near the resonances of its monopole mode.