Natural Frequencies and Mode Shapes for Vibrations of Rectangular and Circular Membranes: A Numerical Study

The main goal of present study is to simulate vibrations of rectangular and circular membranes using COMSOL software. In the simulation procedure, two rectangular and one circular membranes with constant thickness have been modeled in COMSOL software. For rectangular and circular membranes, external edges along the perimeter considered to be fixed at zero displacement to simulate the boundary conditions as the Dirichlet boundary conditions. Then natural frequencies and mode shapes are obtained by considering an initial displacement, for simulated membranes. In order to validate the results, two-dimensional wave equation solved for rectangular membranes by considering the Dirichlet boundary conditions. Natural frequencies are derived from the wave equation analytically and are consistent with COMSOL simulations with less than 1% difference.