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

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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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acoustic pressure ALUMINIUM ANGULAR FREQUENCY ANGULAR FREQUENCY RAD/SEC applied approximation axisymmetric axisymmetric structure basis functions boundary condition Boundary Element Method boundary integral equation boundary integral formulation bounded linear operator 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 finite element analysis finite element method fluid fluid-structure interaction problem given Green's function hence incident plane wave integral equation formulation integral operator layer potential Legend linear operator matrix metre from transducer Miller formulation natural frequencies Neumann problem nodes non-singular non-uniqueness null space numbers of elements 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 transducer unique solution values vector wavenumbers zero