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

Experimental and Numerical Methods for the Evaluation of Sound Radiated by Vibrating Panels Excited by Electromagnetic Shakers in Automotive Applications

Numerical simulations are increasingly employed in the automotive industry to optimize the design stage, reduce prototype testing, and shorten the time to market. The aim of the presented research is the development of a fast and reliable method for the prediction of the sound field generated outside a vehicle by vibrating panels under electromagnetic shaker excitation. Despite that multi-physics numerical simulation software already link mechanical vibrations to their acoustic effect, they show a drawback when calculating the exterior sound field produced by a vibrating panel: the presence of a car model to separate front and rear radiations avoiding the acoustic short circuit, and an air volume surrounding it are required, thus increasing the model complexity and calculation time. Both problems can be overcome with the presented methodology: only the mechanical vibration of the panel is solved numerically, and the radiated sound field is then calculated postprocessing, relying on Rayleigh’s integral. At first, the method’s validation is presented through laboratory experiments; then, a real vehicle panel is analyzed. Comparisons between the finite element method (FEM) simulations and experimental measurements showed very good agreement while keeping the calculation time low for both the laboratory and on-vehicle tests