Optimal dynamic vibration absorber design for minimizing the band-averaged input power using the residue theorem

This paper deals with an efficient strategy to improve the vibro-acoustic behavior of a structure over frequency bands. Genetic Algorithms are used to identify the optimal resonance frequency and location of Dynamic Vibration Absorbers (DVAs) which minimize the band-averaged input power into a plate, leading to an indirect reduction of the radiated acoustic power and global vibration. Instead of classic numerical quadrature schemes, the residue theorem is used to evaluate the band-averaged input power. This results into a considerable reduction of computational effort, as it requires only few function evaluations at complex frequencies, regardless of the analyzed bandwidth. The structural response is simulated by using the Wave Based Method (WBM). Besides an increased convergence rate as compared to classical element-based techniques, the WBM is also free in determining the optimal position of the DVAs, not restricting it to nodal grid locations. Moreover, when point connections are taken into account, only a small part of the WB matrices needs to be recomputed at each iteration, resulting in a strong reduction of the computation time. Numerical examples illustrate the benefits and the efficiency of the proposed optimization strategy.