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math-ph2013★ 17 cited
The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces
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 es…
math-ph2012★ 131 cited
Analytical formulation of 3D dynamic homogenization for periodic elastic systems
A. N. Norris, A. L. Shuvalov, A. A. Kutsenko
Homogenization of the equations of motion for a three dimensional periodic elastic system is considered. Expressions are obtained for the fully dynamic effective material parameter…