Nonlinear oscillations of viscoelastic microcantilever beam based on modified strain gradient theory

A viscoelastic microcantilever beam is analytically analyzed based on the modified strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening effect theory and discretized by Galerkin method. Inner damping, nonlinear curvature effect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and stiffness, as well as modeling the size effect using modified coupled stress or modified strain gradient theories. First-mode nonlinear frequency and time response of the viscoelastic microcantilever beam are analytically evaluated using multiple time scale method and then, validated through numerical findings. The obtained results indicate that nonlinear terms have an appreciable effect on natural frequency and time response of a viscoelastic microcantilever. Moreover, further investigations suggest that due to the size effects, natural frequency would drastically increase, especially when the thickness of the beam and the length scale parameter are comparable. The findings elaborate the significance of size effects in analyzing the mechanical behavior of small-scale structures. (C) 2021 Sharif University of Technology. All rights reserved.