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Static travel range augmentation of electrostatically actuated slender nano-cantilevers using particle swarm optimisation

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Abstract

Along with the electrostatic force and fringing field effect, the van der Waals (vdW) force acts on the electrostatically actuated nano-cantilever (EANC) when the separation between deformable and stationary electrodes is less than 20 nanometers. The vdW force can cause pull-in of the EANC even without the applied voltage when the nano-cantilever length exceeds its detachment length. The vdW force also causes a substantial curtailment of static pull-in instability parameters of the slender EANC compared to corresponding parameters obtained when this force is absent. This paper aims to utilise particle swarm optimisation (PSO) to arrive at the optimised beam width profile to augment the stable static travel range of the EANC having the length close to its detachment length. Continuous shape function having four parameters is utilised as the variable beam width. The weighted residual statement (GWRS) is obtained using the governing equation of the Bernoulli–Euler beam theory and Galerkin’s technique. Static pull-in instability parameters of referential prismatic and variable-width EANCs are evaluated by utilising the GWRS. PSO is employed to arrive at optimised parameters for the variable beam width. The penalty approach is used to impose constraints on design variables. Optimised width profiles of the EANC have been obtained for various values of design constraints and initial separation between electrodes. Static pull-in instability parameters of aforementioned EANCs are validated with corresponding results obtained by three-dimensional finite element simulations performed using COMSOL Multiphysics®. The optimised width profile of the EANC brings a significant augmentation in its stable static travel range.

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  1. Aerospace Structures Laboratory, Aerospace Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, 400076, India

    Kedar S. Pakhare, P. J. Guruprasad & Rameshchandra P. Shimpi

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Pakhare, K.S., Guruprasad, P.J. & Shimpi, R.P. Static travel range augmentation of electrostatically actuated slender nano-cantilevers using particle swarm optimisation. Arch Appl Mech 93, 2051–2080 (2023). https://doi.org/10.1007/s00419-023-02372-w

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