Mobility power flow (MPF) approach applied to fluid-loaded shells with ring discontinuities

The vibrational and acoustic characteristics of fluid-loaded, cylindrical shells with single or multiple, aperiodically-spaced ring discontinuities are studied using an approach based on the mobility power flow (MPF) method and a hybrid numerical/analytical method for the evaluation of the velocity Green's function of the shell. The discontinuities are associated with internal structures coupled to the shell via ring junctions. The approach is a framework allowing alternative shell and/or internal structure models to be used. The solution consists of the net vibrational power flow between the shell and internal structure(s) at the junction(s), the shell's velocity Green's function, and the far-field acoustic pressure. Use of the MPF method is advantageous because the net power flow solution can be used as a diagnostic tool in ascertaining the proper coupling between the shell and internal structure(s) at the junction(s). Results are presented for two canonical problems: an infinite, thin cylindrical shell, externally fluid-loaded by a heavy fluid, coupled internally to: (1) a single damped circular plate bulkhead, and (2) a double bulkhead consisting of two identical damped circular plates spaced a shell diameter apart. Two excitation mechanisms are considered for each model: (1) insonification of the shell by an obliquely-incident, acoustic plane wave, and (2) a radial ring load applied to the shell away from the junction(s). The shell's radial velocity Green's function and far-field acoustic pressure results are presented and analyzed to study the behavior of each model. In addition, a comparison of these results accentuates the qualitative difference in the behavior between the single and multiple junction models. When multiple internal structures are present, the results are strongly influenced by inter-junction coupling communicated through the shell and the fluid. Results are presented for circumferential modes n = 0 & 2. The qualitative differences in the results for modes n = 0 and n = 2 (indicative of all modes {dollar}n > 0{dollar}) are presented and discussed. Using the formulation, an analysis is presented to specifically associate the features identified in the far-field acoustic pressure and velocity Green's function response with the characteristics of the shell and internal plate bulkhead. The results for the single junction model demonstrate the significance of the shell's membrane waves on the reradiation of acoustic energy from the shell; however, when multiple junctions are present, inter-junction coupling results in a significant broad acoustic scattering pattern. Using the results and analysis presented here, a better understanding can be obtained of fluid-loaded shells, which can be used to reduce the strength of the acoustic pressure field produced by the shell.