Problems of passive topological design optimization of structures against vibration and noise have only been undertaken during the last decade, cf. [
] and papers cited therein. The problems have dealt with maximization of intrinsic properties like fundamental eigenfrequencies, higher order eigenfrequencies and eigenfrequency gaps of freely vibrating structures, and minimization of the dynamic compliance of structures subjected to forced vibration [
Unlike earlier work on topological design against vibration and noise, the present paper takes into account the interaction between the structure and the acoustic medium. Thus, our paper deals with passive topological design optimization of vibrating elastic continuum structures with the objective of minimizing the total sound power radiation from the structural surfaces into a surrounding acoustic medium. The volume, admissible design domain and boundary conditions of the structure are prescribed. The structural vibrations are assumed to be excited by a time-harmonic mechanical loading with prescribed forcing frequency and amplitude, and structural damping is not considered. A bi-material model, which is an extended form of the SIMP model, is employed for the topology optimization. This implies that the boundary shape of the structure is not changed during the design process, which leads to a great simplification of the sensitivity analysis since the calculation associated with the shape gradients of the acoustic pressure loading is avoided.
It is assumed that air is the acoustic medium and that a feedback coupling between the acoustic medium and the structure can be neglected. Certain conditions are assumed, under which the sound power radiated from the structural surface can be estimated by using a simplified approach [
] instead of solving the Helmholz integral equation. This implies that the computational cost of the structural-acoustical analysis can be considerably reduced. Numerical results are presented for plate and pipe-like structures with different sets of boundary conditions.