Scattering analysis of guided waves in a plate using the T-matrix method

Abstract

in wavefunction expansion method, wave fields are expanded in terms of the eigenfunctions for the governing wave equation. We aim to solve problems that have not been solved before by previously existing wavefunction expansion methods and thus adopt the transition matrix formalism that has been well known for bulk wave scattering problems. In this formalism, the relation between the coefficient vector of a scattered field and that of an incident field is given by the transition matrix.

For this reason, we first derive the Green's function by employing integral transform whose transform kernel is the eigenfunctions for Lamb and SH waves. Then, we develop the extended boundary condition method based on the null-field integral equation by using the derived Green's function. By using the extended boundary condition method, the T matrix for a single scatterer such as an elastic inclusion, a hole, a step thickness increase or reduction can be calculated. And the multiple scattering solution for these scatterers can be also obtained by using the single scatterer T matrices. We also derive the general properties of the T matrix which represent the reciprocity, energy conservation and time-reversal invariance.

Another development is a decomposition method particularly useful for solving scattering problems regarding arbitrarily shaped elastic inclusions. In this method, an elastic inclusion is decomposed into multiple small subscatterers and then a multiple scattering among subscatterers is calculated. By employing this approach, the restrictions imposed by the inherent problem of the extended boundary condition method can be relaxed and therefore elastic inclusions of various shapes and sizes can be covered.

The main focus of this dissertation is on development of semi-theoretical methods for scattering analysis of guided waves in plates. The area of concern is problems related to flat transversely isotropic plates which include single or multi-layer isotropic and functionally graded plates. Specifically, we focus on the development of wavefunction expansion methods based on the three-dimensional elasticity