Consistent transmitting boundary conditions with a reduced number of eigenmodes for wave propagation in elastic media

Abstract

The consistent transmitting boundary condition is a powerful numerical technique for frequency domain analysis of wave problems in unbounded elastic media. A second-order complex-valued eigen-problem is associated with this method and the computed eigenmodes are used to formulate the nodal forces acting on the lateral boundaries of a Cartesian computational domain. Usually, all eigenmodes are computed and used in the consistent transmitting boundary conditions to simulate the infinite extent of the elastic medium. In this paper, it is demonstrated that by selecting a reduced number of relevant eigenmodes it is possible to produce similar results and consequently reduce the overall computational cost. This is highly desirable for soil–structure interaction problems involving wide ranges of frequencies and large-size domains with many sub-layers. The efficiency of the proposed approach is investigated by considering, first, the case of foundation vibration over rigid bedrock and, second, the effectiveness of a wave barrier to reduce the transmitted vibrations caused by a surface harmonic loading.