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.