Reducing Radiated Sound Power by Minimizing the Dynamic Compliance

Since the input power due to a periodic load on a structure is equal to the sum of the power dissipated in the structure and the acoustic power radiated to the surroundings, it is not obvious that redesigning the structure so as to minimize the input power results in a reduction of the radiated sound power. In this work, we present numerical evidence to show that dramatic reductions in sound power radiated from a structure immersed in a light fluid such as air can be achieved by using topology optimization techniques to minimize the input power due to the periodic loading. Minimizing the input power moves the natural frequencies of the structure away from the driving frequencies thereby reducing the vibrations, and hence the radiated power. The numerical examples show that in the case of baffled plates, the reduction obtained in the emitted sound power obtained by minimizing the input power is almost as much as that obtained by minimizing the sound power directly; however, the proposed technique circumvents the need to solve the acoustical equations, thereby resulting in considerable saving in computational cost.