Improvement of the Wave Based Method for Thick Plate Vibrations

The numerical simulation of plate vibrations in the low frequency range is commonly performed with the Finite Element Method (FEM). In the so-called mid-frequency range, the computational load of the conventional FEM becomes generally too high for practical purposes and different kinds of calculation methods are needed. A deterministic method which can be used to calculate plate vibrations is the Wave Based Method (WBM). Since it has a high computational efficiency, it can tackle the mid-frequency range. In this paper, the convergence rate of the WBM using the Mindlin plate theory is investigated and a new selection of wave functions, distinguishing between travelling and evanescent waves, is proposed to improve the performance of the WBM. It is shown that the WBM for thick plates fails to calculate accurate results for certain types of boundary conditions if the plate becomes thinner. This problem is also resolved with the newly proposed selection of wave functions. The validation examples illustrate that the convergence rate and accuracy of the new wave function selection is generally higher compared to the conventional wave functions. In this paper, only examples with straight boundaries and point force excitation are considered.