The effect of substructures on the acoustic radiation from axisymmetric shells of finite length

Abstract

A modal-based method is developed to analyze the acoustic radiation of shells of finite length with internal substructures subjected to time-harmonic loads. In this method, a variational principle is used to determine the relationship between the distribution of velocity and pressure over the surface of the shell, and Lagrange multipliers are used to account for the interaction forces from the substructure motion. To identify the dominant physical characteristics of the fluid/shell/substructure response, a singularity decomposition is introduced. This decomposition uses the singular points of the response in complex wave-number space that are closest to the real axis. The response contributions from these singular points are found to be highly fluctuating, yet analytically simple functions of frequency. The remaining or residual response is a slowly varying function of frequency. To reduce computational effort, the singularity decomposition is combined with a frequency window method. The method is demonstrated for a cylindrical shell with elastic, hemispherical endcaps and internal circular panels. The effects of the substructure are illustrated by comparing the response of the shell/substructure system with corresponding results for an empty shell. It is shown that the substructures can significantly alter the near- and far-field acoustic response.