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 idealized 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 the fluid structure interaction.
1 Introduction.- 2 Integral Equation Formulations of the Exterior Helmholtz Problem.- 2.1 Introduction.- 2.2 Basic Integral Equation Formulations.- 2.2.1 Indirect Integral Equation Formulations of the Exterior Helmholtz Problem.- 2.2.2 Direct Integral Equation Formulations of the Exterior Helmholtz Problem.- 2.3 Basic Integral Equation Theory.- 2.4 Improved Integral Equation Formulations.- 2.4.1 Indirect Formulations.- 2.4.2 The Method of Schenck and Related Direct Formulations.- 2.4.3 The Burton and Miller Formulation.- 2.4.4 Modified Green's Function Formulations.- 2.4.5 Comparison of Approaches.- 3 Numerical Solution of the Exterior Helmholtz Problem.- 3.1 Numerical Methods for Solving Integral Equations.- 3.1.1 Nystrom Method.- 3.1.2 Degenerate Kernel Method.- 3.1.3 Projection Methods.- 3.1.4 An Application of the Collocation Method.- 3.2 Surface Representation.- 3.3 Numerical Quadrature.- 3.3.1 Axisymmetric Elements.- 3.3.2 Three-Dimensional Elements.- 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.- 4.2.1 Finite Element Analysis of an Axisymmetric Structure.- 4.2.2 Finite Element Analysis of a Three-Dimensional 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.
Series: Lecture Notes in Engineering
Number Of Pages: 108
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99
Weight (kg): 0.2