The polarization vectors at the interface and the secular equation for Stoneley waves in monoclinic bimaterials

Abstract

Stoneley waves propagating in the direction of the x 1 –axis in a bimaterial consisting of two half–spaces x 2 ⩾ 0 and x 2 ⩽ 0 of dissimilar anisotropic elastic materials are considered. Several invariants, independent of x 2 , that relate the displacement and the stress are obtained for a general anisotropic elastic bimaterial. We then study the case when both materials have the symmetry plane at x 2 = 0 (or x 1 = 0). The displacement and the traction at the interface x 2 = 0 describe two separate elliptic paths. They are polarized on planes that contain the x 2 –axis (or x 1 –axis). Moreover, the x 2 –axis (or x 1 –axis) is one of the principal axes of the ellipse. In the rest of the paper we consider special monoclinic bimaterials with the symmetry plane at x 2 = 0, x 1 = 0 or x 3 = 0. The elastic constants for the two monoclinic materials are identical except that those elastic constants that would vanish if the material were orthotropic have the opposite sign for the two materials. It is shown that one of the ellipses degenerates into a line along a coordinate axis while the other ellipse is on a coordinate plane normal to this coordinate axis. When the symmetry plane is at x 3 = 0, both ellipses degenerate into lines along the x 1 – and x 2 –axes. Explicit expressions of the polarization vectors and the secular equation are presented for all three monoclinic bimaterials.