Optimization of static and dynamic travel range of electrostatically driven microbeams using particle swarm optimization

• Static and dynamic analysis of variable geometry microbeams using energy method.
• All microbeams are electrostatically driven and have variable width and thickness.
• Optimizing shape of microbeams using PSO and hybrid SA method.
• Comparison of convergence speed and optimized results using both the methods.
• Proposed optimized profiles of microbeams for maximizing pull-in displacement.

This paper examines the enhancement of static and dynamic travel range of electrostatically driven microbeams using shape optimization approach. Continuous functions of width and thickness are used for optimizing the geometry of both cantilever and fixed–fixed microbeams. Rayleigh–Ritz energy method is employed to compute the static and dynamic pull-in parameters. Particle swarm optimization and hybrid simulated annealing are used for shape optimization of microbeams. Constraints on design variables are imposed using penalty approach. Enhanced pull-in parameters obtained for variable geometry microbeams have been validated using 3-D finite element analysis. Optimized shapes of microbeams show significant improvement in static and dynamic travel range. Pull-in displacement is increased up to 54.92% for cantilever microbeam and 40.79% for fixed–fixed microbeam with hybrid simulated annealing. Effectiveness of particle swarm optimization is brought out through representative test cases. The convergence of the particle swarm optimization is approximately five times faster as compared to the hybrid simulated annealing, while maintaining the same level of accuracy.