Nonlinear dynamics of multi-layered microplates

[+] Author and Article Information
Mergen Ghayesh

School of Mechanical Engineering, University of Adelaide, South Australia 5005, Australia

1Corresponding author.

ASME doi:10.1115/1.4037596 History: Received May 20, 2017; Revised August 07, 2017


This paper, for the first time, investigates the nonlinear dynamics of a three-layered microplate. The von Kármán plate theory together with the modified couple stress theory (MCST) is employed to derive the nonlinear size-dependent transverse and in-plane equations of motion in a Hamiltonian framework. A nonconservative damping force of viscous type as well as an external excitation load consisting of a harmonic term is considered in the model. All the transverse and in-plane displacements and inertia are considered (not neglected) in both the theoretical modelling and numerical simulations; this leads to difficulties in the complex nonlinear model and simulations. These difficulties are overcome here by means of the systematic modelling of the kinetic and potential energies corresponding to each layer of the microplate and through use of a well-optimised numerical scheme. The effect of different arrangements and different material percentages of each layer on the force-amplitude and frequency-amplitude curves of the microsystem, with special attention to the effect of the length-scale parameter, are investigated. The results of this study are helpful in designing three-layered microplates in MEMS industry.

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