This text considers the problem of the dynamic fluid-structure interaction between a finite elastic structure and the acoustic field in an unbounded fluid-filled exterior domain. The exterior acoustic field is modelled through a boundary integral equation over the structure surface. However, the classical boundary integral equation formulations of this problem either have no solutions or do not have unique solutions at certain characteristic frequencies (which depend on the surface geometry) and it is necessary to employ modified boundary integral equation formulations which are valid for all frequencies. The particular approach adopted here involves an arbitrary coupling parameter and the effect that this parameter has on the stability and accuracy of the numerical method used to solve the integral equation is examined. The boundary integral analysis of the exterior acoustic problem is coupled with a finite element analysis of the elastic structure in order to investigate the interaction between the dynamic behaviour of the structure and the associated acoustic field. Recently there has been some controversy over whether or not the coupled problem also suffers from the non-uniqueness problems associated with the classical integral equation formulations of the exterior acoustic problem. This question is resolved by demonstrating that .the solution to the coupled problem is not unique at the characteristic frequencies and that it is necessary to employ an integral equation formulation valid for all frequencies.

Klappentext

This text considers computational techniques for the analysis of the dynamic fluid-structure interaction between a finite elastic structure and the associated acoustic field in the surrounding medium. Detailed attention is paid to almost all aspects of a complete solution to the fluid-structure interaction problem. Starting from the mathematical formulation, as partial differential equations, of the idealised problem, the text takes the reader through reformulation of the problem as boundary integral and variational equations, followed by a comprehensive study of their numerical solution by boundary and finite element methods, to details of actual experiments using sonar transducers in a test tank. The presentation is aimed at postgraduate students and researchers in engineering, science and mathematics who may be working in the areas of boundary integral methods, finite element methods, acoustics, and, of course, the fluid structure interaction.

Inhalt
1 Introduction.- 2 Integral Equation Formulations of the Exterior Helmholtz Problem.- 2.1 Introduction.- 2.2 Basic Integral Equation Formulations.- 2.3 Basic Integral Equation Theory.- 2.4 Improved Integral Equation Formulations.- 3 Numerical Solution of the Exterior Helmholtz Problem.- 3.1 Numerical Methods for Solving Integral Equations.- 3.2 Surface Representation.- 3.3 Numerical Quadrature.- 3.4 The Choice of the Coupling Parameter.- 3.5 Numerical Results.- 4 The Dynamic Fluid-Structure Interaction Problem.- 4.1 Introduction.- 4.2 Finite Element Analysis of the Structure.- 4.3 The Coupled Equations of Motion.- 4.4 The Conditioning of the Coupled Equations.- 4.5 Numerical Results.- 5 The Determination of the Response from Sonar Transducers.- 5.1 An Introduction to Piezoelectric Sonar Transducers.- 5.2 Loading on the Structure.- 5.3 Experimental Determination of the Response.- 5.4 Results and Conclusions.- References.- Appendix A. An Analytical Solution for a Hollow Elastic Sphere in an Acoustic Medium.