A fixed point iteration approach for analyzing the pull-in dynamics of beam-type electromechanical actuators

Abstract

In this paper, a numerical approach is suggested to find a semi-analytical solution for the common nonlinear boundary value problems (BVPs) of cantilever-type micro-electromechanical system (MEMS) and nano-electromechanical system (NEMS) with a set of model parameters. The nonlinear BVPs that are studied involve the states of the single and double cantilever-shaped beams under the influence of Casimir and Van der Waals force for proper distances of separation. The method is based upon an integral operator that is formed considering Green’s function connected with the execution of Picard’s or Mann’s fixed point schemes. The numerical results for different cases of beam are presented and compared with those obtained by previous works to show the applicability, efficiency, and high accuracy of the suggested method.

KEYWORDS:

• Fixed point iteration
• Green’s function
• nonlinear boundary value problems
• Casimir force
• Van der Waals force

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 34B15

Disclosure statement

No potential conflict of interest was reported by the authors.