Plate sound radiation reduction by means of multiple tuned mass dampers

The dynamical response of a plate is reduced passively by using multiple Tuned Mass-Spring-Damper (TMSD) systems. It is assumed that the plate is thin, simply supported, and excited by a normal incident plane wave. As a result of the first assumption, the out of plane motion of the plate can be modeled by the Euler-Bernoulli equation, which is discretized using the Galerkin Method. Here, the TMSD systems are spaced periodically over the plate surface and the total mass of the TMSD systems if fixed. The optimal stiffness and damping values of the TMSD systems are obtained by solving a minimization problem based on the H2-norm of the modal velocity of the plate. Results show that a significant reduction in the dynamical response of a single and multiple plate modes can be achieved. Based on the results, it is expected that TMSD systems can also effectively be applied to low-frequency passive acoustic shielding applications due to the fact that the radiated sound power of a thin walled structure is closely related to its velocity response.