Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-structure Interaction Problem |
Contents
INTEGRAL EQUATION FORMULATIONS OF THE EXTERIOR | 2 |
NUMERICAL SOLUTION OF THE EXTERIOR HELMHOLTZ PROB | 25 |
5 | 40 |
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ANGULAR FREQUENCY approximation axisymmetric 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 eigenvalue elastic structure evaluating exterior acoustic problem Əng Figure finite element analysis finite element method fluid-structure interaction fluid-structure interaction problem given Gk p,q Green's function Helmholtz equation integral equation formulation integral operator layer potential matrix metre from transducer Miller formulation natural frequencies Neumann problem nodes null space numbers of elements obtain piezoelectric product Gauss rule quadratic quadrature rule regularised RELATIVE MEAN ERROR scattering Section shell of thickness singular sonar transducer spherical shell surface Helmholtz equation surface velocity Theorem thickness 0.25m three-dimensional transducer unique solution values vector wavenumbers дп дпр მა მი მყ