LQR-based optimization of multiple tuned resonators for plate sound radiation reduction

A linear quadratic regulator based optimization problem is formulated in order to minimize the broad-band low-frequency domain vibration and acoustic response of a baffled simply supported plate by means of multiple optimally tuned mass–spring–damper systems. To this end, we propose a robust method to obtain a (stable) state–space model describing the far-field radiated sound power, also known as the radiation filter. The Kirchhoff plate equation, which describes the plate vibrations, is discretized based on the Rayleigh–Ritz method. The resulting state–space models of the plate and the mass–springdamper systems are coupled to the radiation filter. Finally, the optimal spring stiffness and damping values of each mass–spring–damper system are successfully obtained by minimizing the kinetic energy or the far-field radiated sound power of the plate for low computational cost. In general, the results indicate that tuned mass-spring-damper systems have great potential to reduce the broadband low frequency vibration and acoustic response of vibro-acoustic systems. From the results, it can be concluded that there are fundamental differences between the optimal TMD systems if one minimizes the kinetic energy or the far-field radiated sound power.