Abstract
A system of coupled vector boundary integral equations (BIEs) is formulated to study the transmission of time–harmonic waves through elastic inclusions bonded to a three–dimensional elastic matrix of infinite extent, within the framework of isotropic, linear elasticity. Displacements and tractions on transmitting (scattering) boundaries appear explicitly in the integral equations as the only unknowns. The numerical solution procedure, which uses quadratic isoparametric elements for modelling purposes, is based on nodal collocation of regularized BIEs free from principal–value integrals. A modification of the CHIEF formulation of acoustics is used to overcome the nonuniqueness of the BIE solution at the fictitious eigenfrequencies. The modification of the BIEs for forced vibrations of finite composite bodies is presented. Numerical solutions are presented for forced vibrations of a layered sphere and for scattering of plane and spherical waves from spherical inclusions to demonstrate the accuracy of the formulation.
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