Multipole expansion of Green’s function for guided waves in a transversely isotropic plate

다국어 초록 (Multilingual Abstract)

The multipole expansion of Green’s function in a transversely isotropic plate is derived based on the eigenfunction expansion method.
For the derivation, Green’s function is expressed in a bilinear form composed of the regular and singular Lamb-type (or shear-horizontal)wave eigenfunctions. The specific form of the derived Green’s function facilitates the handling of general scattering problems in an elasticplate when numerical methods such as the methods of the null-field integral equations are employed. In the derivation, the integraltransform of an arbitrary guided wave field is first constructed by the Lamb-type and shear horizontal wave eigenfunctions that work asthe kernel functions. After showing that the thickness-dependent parts of the eigenfunctions are orthogonal to each other in the transformedspace, Green’s function is explicitly derived by using the orthogonality. As an application of the derived Green’s function, a scatteringproblem is solved by the transition matrix method.

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