Response Green's function and acoustic scattering from a fluid-loaded cylindrical shell with discontinuities

Abstract

A classical problem in structural acoustics is the response and acoustic scattering from a fluid-loaded cylindrical shell with ring discontinuities, to excitation by incident acoustic waves. The solution for these type of problems is generally formulated using integral transforms to the wavenumber domain. The solution in the spatial domain is obtained by inverse transforming the wavenumber solution. The inverse transform is typically obtained using a contour integral approach which can handle the singularities of the inverse transform. A contour solution is required for every spatial location of interest. Structural damping can be introduced to remove the singularities from the integrand of the inverse transform, and the spatial solution obtained by performing the inverse transform numerically. However, damping can mask the influence of the fluid-loading. An alternative to these approaches to obtain the spatial solution is a hybrid numerical analytical method which does not require the introduction of structural damping, and therefore retains only the influence of the fluid-loading on the response and the scattering. Using this hybrid numerical/analytical approach, the response Green's function and the nearfield scattered pressure are obtained for a fluid-loaded shell with a wall thickness to radius ratio of 1%, excited by a circumferential ring load, which is representative of scattering by a ring impedance, excluding the shell to impedance interaction. Apart from the response Green's function and the nearfield scattered pressure, of interest in structural acoustics is the far field scattered pressure. A solution for the bistatic and monostatic scattering from a fluid-loaded cylindrical shell with one or two internal plate bulkheads is presented. The solution is based on knowledge of the junction forces between the shell and the internal plate bulkheads which are obtained using a mobility (or impedance) approach. The mobility functions are obtained using the hybrid method. Results for the response Green's function and the nearfield and farfield scattered pressures are presented for the circumferential modes n equals 0 and 2. The results for the n equals 2 case are representative of high order circumferential modes which include the presence of compressional and shear helical waves.