Abstract Summary
The Wave Based Method (WBM) is an indirect Trefftz Method, 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 midfrequency 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 vibroacoustics to soil halfspaces without significantly increasing the number of wave functions, and hence the number of unknown weighting values. As WBM domains are based on analytical solutions of their differential equations, these can directly be coupled to other adjoining continuous systems. In the proposed contribution, a Timoshenko beam is implemented to reduce the structure of an elastodynamic trench within a halfspace. The Timoshenko beam permits to simulate the mitigation effect of a trench against incoming waves, by allowing shear deformation and reducing the number of unknowns of the numerical model. The performance and accuracy of the Timoshenko beam is compared with the results of the full order model for an elastodynamic trench.
