Wave based method for flexural vibration of thin plate with general elastically restrained edges

Wave based method is a numerical technique to predict steady-state vibration and solve vibroacoustic problems. It is a deterministic approach that is acknowledged to be more efficient than the element based methods in the mid-frequency range. The wave based method for plates with prescribed boundary conditions has been proposed and verified for the ideal constraint cases such as clamped, free and simply supported. To deal with different kind of or more realistic boundary conditions, this paper proposes a modified wave based method. The method is aimed at analyzing the flexural vibration of thin plates with general elastically restrained edges, and it can also consider the damping effect associated with the edge restraint. A number of numerical validation examples are shown, where the plate edges are uniform, non-uniform or partially supported. Within the examples, the responses of the plate under different edge conditions are compared, including elastic supports with different translational and rotational stiffness and damping parameters, rigid supports like clamped and simply supported, and free edges. For all the considered cases, the proposed method is proved to be effective, though the convergence performance is influenced by the boundary conditions. More wave functions may be required for simply supported, non-uniform or partially supported cases.