Metaheuristic optimisation of an elastic metamaterial for robust vibration control

Abstract

Parametric uncertainty in a structure can reduce modelling accuracy, leading to a reduction in the efficacy of a vibration suppression system. The suppression of modal vibration with robustness to parametric uncertainty has been demonstrated using multiple tuned-vibration-absorbers (TVAs) with distributed resonance frequencies. In this paper, an Elastic Metamaterial (EMM) unit cell consisting of multiple single-degree-offreedom resonators is defined for the absorption of vibration in a cantilever beam. A genetic algorithm (GA), hybrid genetic algorithm (HGA) and particle swarm optimisation (PSO) are compared in their ability to optimise the resonance frequencies of the unit cell to minimise the mean kinetic energy gain of the EMM, on a beam with parametric variation. Firstly, all optimisation procedures are able to produce an EMM unit cell with good robustness to parametric uncertainty. When the optimisations are run until convergence, the PSO is shown to achieve the best fitness value, but with an increase in computation time compared to the GA. The HGA achieves a better fitness value than the GA but computation time is inflated by a factor greater than 50. By also running until a time constraint is met, it is shown that the GA and PSO perform similarly for the same time-limit.