Analytical and Numerical Models of the Sound Radiated by Fully Clamped Rectangular Vibrating Plates

I n the present work, fully clamped rectangular isotropic plates are investigated: the response under steady-state excitation determined by harmonic point force application is calculated, and the consequent sound radiation is evaluated. The study is carried out both analytically and numeri cally. At first, the analytical solution of the clamped-clamped plate motion equation is calculated by means of a MATLAB implementation. The solution is based on the Principle of Virtual Work, calculating the displacement as a function of frequency at the nodes of a rectangular mesh. The monopole approximation of Rayleigh’s integral is then used to estimate the sound radiation in free field propagation. The numerical solution is evaluated using COMSOL Multiphysics, employing the Finite Elements Method (FEM). The clamped plate is modeled as a shell and “Acoustic-Structure Boundary” coupling is employed. Furthermore, the optimization of force application point is performed, with the aim of maximizing the radiated sound pressure level or flattening the frequency response. Very good matching between analytical and numerical methods has been found. In conclusion, a reliable prediction model of the sound pressure radiated by clamped plates in the low frequency range is achieved.