Enhancement of travel range of electrostatically driven fixed-fixed micro beam in static and dynamic mode using mutated particle swarm optimization

Abstract

Particle swarm optimization (PSO) is a substantially exercised technique for optimizing structural design problems. One major snag of particle swarm optimization is a possibility of premature convergence, observed in the specific cases where global optimum is encircled by the solutions having higher objective function values. These territories are unexplored and swarm can fall into local optimum. The present work proposes to suggest one of the variants of the PSO algorithm to enhance the reliability. In the proposed algorithm, during each iteration, few particles will be chosen to follow worst solution, this would enable to perform exploration and exploitation of design space simultaneously. Hence, the probability of not getting caught into local optima gets augmented which gives better assurance to the achieved solution. The mutated particle swarm optimization (MPSO) is efficaciously employed for shape optimization of electrostatically driven fixed-fixed microbeams to augment the static and dynamic travel range. The geometry of fixed-fixed microbeams is optimized using continuous, smooth, parametric functions of width and thickness. For structural analysis, Rayleigh–Ritz energy method is utilized to compute the static and dynamic pull-in parameters. Nonlinear design constraints of engineering interest are implemented through penalty approach. Using modified particle swarm optimization, width and thickness profiles of fixed-fixed microbeams that result in maximum pull-in displacement have been obtained. Augmented pull-in parameters for optimized geometry of microbeams have been endorsed using 3-D finite element analysis. The optimization parameters reveal maximum rise in the static pull-in displacement by 41.25% and dynamic pull-in displacement by 39.15% of fixed-fixed microbeam compared to referential prismatic microbeam. Efficacy of mutated particle swarm optimization is emphasized through 18 representative cases. Mutated particle swarm optimization converges in around 20% of time in comparison with the hybrid simulated annealing, without getting trapped into local minimum in all the test cases.