Implementation of a Timoshenko beam within an elastodynamic halfspace modeled by the Wave Based Method

The Wave Based Method (WBM) is an indirect Trefftz approach, which uses weighted wave functions to approximate the field response of a boundary value problem. These wave functions weakly fulfill the underlying differential equations and pass through a weighted residual approach by applying boundary conditions. This method has firstly been introduced for vibroacoustic problems to simulate excitations in the mid-frequency range. The accuracy of the WBM strongly depends on the relation between the geometrical size of a boundary value problem and the applied excitation frequency. This permits to transfer the WBM from vibroacoustic applications to soil halfspaces without significantly increasing the number of wave functions, and hence the number of unknown weighting values. Within this paper, a coupling approach between a Timoshenko beam and adjoining WBM domains is introduced as an efficient procedure for the simulation of a trench with two side walls. This trench is installed as a wave barrier against an incoming Rayleigh wave. The performance and accuracy of this coupling approach are analyzed and compared with results from literature. Moreover, different materials are tested for the side walls to assess the mitigation efficiency of the trench.