1303.5114 (A. N. Norris et al.)

The matrix sign function for solving surface wave problems in
homogeneous and laterally periodic elastic half-spaces    [PDF]

A. N. Norris, A. L. Shuvalov, A. A. Kutsenko

The matrix sign function is shown to provide a simple and direct method to derive some fundamental results in the theory of surface waves in anisotropic materials. It is used to establish a shortcut to the basic formulas of the Barnett-Lothe integral formalism and to obtain an explicit solution of the algebraic matrix Riccati equation for the surface impedance. The matrix sign function allows the Barnett-Lothe formalism to be readily generalized for the problem of finding the surface wave speed in a periodically inhomogeneous half-space with material properties that are independent of depth. No partial wave solutions need to be found; the surface wave dispersion equation is formulated instead in terms of blocks of the matrix sign function of i times the Stroh matrix.

View original: http://arxiv.org/abs/1303.5114