## Coupled boundary and finite element methods for the solution of the dynamic fluid-structure interaction problemThis 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. |

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### Contents

INTRODUCTION | 1 |

NUMERICAL SOLUTION OF THE EXTERIOR HELMHOLTZ PROB | 25 |

THE DYNAMIC FLUIDSTRUCTURE INTERACTION PROBLEM | 57 |

Copyright | |

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### Common terms and phrases

acoustic pressure acoustic radiation ANGULAR FREQUENCY applied approximation axisymmetric axisymmetric structure basis functions boundary condition boundary element method boundary integral equation boundary integral formulation Burton and Miller ceramic characteristic wavenumbers collocation method collocation point compact condition number coupled fluid-structure interaction coupled problem coupling parameter cylinder denoted direct formulation discretisation displacements eigenvalue elastic structure evaluating exterior acoustic field exterior acoustic problem exterior Helmholtz problem Figure finite element analysis finite element method fluid fluid-structure interaction fluid-structure interaction problem G D+ given Green's function Helmholtz equation hence integral equation formulation integral operator kernel layer potential Legend linear operator matrix metre from transducer Miller formulation natural frequencies Neumann problem nodes non-uniqueness null space numerical methods obtain piezoelectric product Gauss rule quadrature rule regularised Relative mean error Section shell of thickness solve surface Helmholtz equation surface velocity Theorem thickness 0.25m three-dimensional transducer unique solution values vector wavenumbers