Minimization of sound radiation from vibrating bi-material structures using topology optimization

Up to now, work on topological design optimization of vibrating structures against noise radiation has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, and minimization of the dynamic compliance subject to harmonic loading on the structure. In this paper, we deal with topology optimization problems formulated directly with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. It is assumed that air is the acoustic medium and that a feedback coupling to the structure can be neglected. Certain conditions are assumed that imply that the sound power emission from the structural surface can be obtained in a simpler way than by solving Helmholz’ integral equation. Hereby, the computational cost of the structural-acoustical analysis is substantially reduced. Several numerical results are presented and discussed for plate- and pipe-like structures with different sets of boundary and loading conditions.