FE-Based Surface Elastic Wave Analysis of a Two-Dimensional Periodic Half-Space

Abstract

This paper presents a numerical method for surface elastic waves in a half-space possessing a two-dimensional periodicity. The solution is expressed by plane waves in the vertical direction, while it is approximated by finite elements in the horizontal plane. By virtue of the Bloch's theorem, the problem is reduced to equations of motion in a unit cell. The vertical wavenumbers satisfying the equations in the unit cell are determined by solving an eigenvalue problem with respect to the wavenumbers. As numerical examples, periodic arrays of piles embedded in a ground are analyzed. In the analyses piles made of concrete and a soft material are considered with arrangements given by the square and the triangular honeycomb lattices. Under these conditions, the influences of the stiffness and the lattice pattern of piles on the band structure are investigated.