Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

Abstract

AbstractConsistent transmitting boundaries for time‐domain analyses of scalar‐ and elastic‐wave propagation in horizontally layered anisotropic or transversely isotropic waveguides are developed. Governing equations and corresponding consistent nodal forces are derived for scalar and elastic waves in layered waveguides for which finite‐element discretization is considered in the vertical layering direction. Auxiliary variables for the horizontal derivatives and integrals of displacements are introduced to modify the governing equations and the nodal forces. The desired consistent transmitting boundaries applicable to time‐domain analyses of scalar‐ and elastic‐wave propagation in isotropic and anisotropic waveguides are then derived. The transmitting boundary for a scalar wave satisfies the criteria for an accurate and well‐posed boundary condition and shows convergent, accurate, and stable behaviors for a variety of scalar‐wave propagation problems in waveguides. Although the boundary for an elastic wave is demonstrated as convergent and stable for elastic‐wave propagation problems in waveguides, limited accuracy is observed in the numerical examples. Nevertheless, the newly proposed approach is expected to provide another way to solve elastic‐wave propagation problems.