Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5022712 | International Journal of Engineering Science | 2017 | 14 Pages |
Abstract
The nonlinear oscillations of viscoelastic microplates is addressed in this paper based on the modified couple stress theory (MCST). Employing the Kirchhoff plate theory, both out-of-plane and in-plane motions as well as the corresponding inertia are taken into account; an internal damping mechanism, based on Kelvin-Voigt model, is employed to model the behaviour of the material. The strain energy, the kinetic energy, the work done by the viscous parts of the classical and non-classical stresses, and the work of the external time-dependent force are obtained and implemented into Hamilton's framework so as to derive a set of fully coupled nonlinear partial differential equations (PDEs) for motions in the out-of-plane and in-plane directions. The Galerkin scheme is utilized to reduce the set of viscoelastically coupled nonlinear PDEs into a set of nonlinear ordinary differential equations (ODEs). Thereupon, this set of equations is transformed into a new set of size-dependent viscoelastically coupled nonlinear first-order ODEs and then is solved with the aid of a continuation scheme. The nonlinear oscillations is thoroughly investigated through conducting extensive numerical simulations and plotting force-response and frequency-response diagrams of the viscoelastic microsystem. The results reveal that the contributions of the nonlinear damping terms, arising due to employing a viscoelastic model, in the response of the viscoelastic microsystem increase substantially when the forcing amplitude is increased. Moreover, the concurrent presence of the nonlinear amplitude-dependent damping mechanism and the length-scale parameter affects the resonant response of the microplate significantly in both linear and nonlinear senses.
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Authors
Hamed Farokhi, Mergen H. Ghayesh, Alireza Gholipour, Mohammad Tavallaeinejad,