Scattering from shells with internal structural loading. Part I. General theory.

Abstract

This paper starts a series of systematic analytical studies on sound scattering from cylindrical shells with various forms of internal structural loading. The objectives of these studies are to understand the physical phenomena involved in the scattering process and to identify dominant mechanisms that control the acoustical behavior of internally loaded shells in the mid-frequency region. It is hoped that these studies will also help to establish physical principles and modeling techniques which enable orderly treatment of complicated internal structures in sound scattering problems. In the present paper, a general formulation is given for the sound-shell-internals-coupled problem with exact solutions that can easily accommodate different forms of internal loading. Solutions are explicitly expressed in terms of two coupling matrices, respectively, representing the geometric and dynamic effects of internal loading. The first matrix is completely determined by the loci at which the internal structures are attached to the shell, independently of the details of the internal system. The dynamic coupling between the shell and its internals is entirely accounted for by the second matrix which relates the forces exerted on the shell by the internal structures to the shell displacements at the attachment points. This matrix can be found by considering the dynamics of the internal structures alone and involves only properties of the internal system. Examples are given for some forms of internal loading, which clearly illustrate the methodology employed and are of practical interest. Detailed analyses and discussions of the derived results will be given in a companion paper. (Y.-P. Guo, following abstract.) [Work supported by ONR.]