Optimization of vibrating structures to reduce radiated noise

In this work, we propose an approach for reducing radiated noise from `light' fluid-loaded structures, such as, for example, vibrating structures in air. In this approach, we optimize the structure so as to minimize the dynamic compliance (defined as the input power) of the structure. We show that minimizing the dynamic compliance results in substantial reductions in the radiated sound power from the structure. The main advantage of this approach is that the redesign to minimize the dynamic compliance moves the natural frequencies of the structure away from the driving frequency thereby reducing the vibration levels of the structure, which in turn results in a reduction in the radiated sound power as an indirect benefit. Thus, the need for an acoustic and the associated sensitivity analysis is completely bypassed (although, in this work, we do carry out an acoustic analysis to demonstrate the reduction in sound power levels), making the strategy efficient compared to existing strategies in the literature which try to minimize some measure of noise directly. We show the effectiveness of the proposed approach by means of several examples involving both topology and stiffener optimization, for vibrating beam, plate and shell-type structures.