Reliability-based vibro-acoustic microstructural topology optimization

A reliability-based vibro-acoustic microstructural topology optimization (RBVAMTO) model taking into consideration the uncertainty of several design-independent parameters, such as the direction of the load, the excitation frequency, or their combinations is presented. The design objective is to minimize the sound power of the vibrating composite macrostructure that is assumed to be constructed by periodic micro unit cell filled up by two kinds of prescribed isotropic materials. The SIMP based bi-material interpolation model is employed at the micro-scale and the design variable is the relative material volume density of the micro unit cell. A design process consisting of the uncertainty analysis and vibro-acoustic microstructural topology optimization is proposed and implemented. The influences of different combination values of the normalized variables corresponding to the uncertainty parameters on the design results are investigated. Numerical examples show that in the vibro-acoustic microstructural design the uncertainty of the excitation frequency may play a very important role. It is also shown that when the normalized variable corresponding to the random excitation frequency takes the higher value, the optimum microstructural topology may not be so sensitive to perturbation of the loading direction. Monte Carlo simulation results demonstrate that the RBVAMTO designs normally lead to the optimum results that are more robust for perturbations of both the excitation frequency and the loading direction than the deterministic design.