Nonlinear dynamics of temperature-dependent fiber-reinforced composite MEMS resonators under multi-harmonic excitations

Abstract

This study focuses on the nonlinear vibration of a fully clamped microcomposite beam reinforced by temperature-dependent curvilinear fibers under the double action of a uniform temperature rise and lateral harmonic force in a viscous medium. The Euler–Bernoulli beam theory is used to model the composite microbeam made of a polymer matrix reinforced with temperature-dependent curvilinear fibers. The von Kármán theory is here used to model the geometric nonlinearity, whereas the modified couple stress theory (CST) is employed to derive the partial form of nonlinear equations governing dynamics of the system. The Galerkin approach is used to modify the partial differential equation to a nonlinear ordinary differential equation, which is, then, solved analytically by means of the method of multiple time scale, to investigate the nonlinear dynamic behavior of the system in secondary resonance. Finally, a parametric analysis investigates the effect of different parameters, such as uniform temperature rise, material length scale parameter, fiber path angels, equation of the fiber path angle, and excitation amplitude, on the dynamic behavior of the system in superharmonic and subharmonic resonance, with useful insights for many engineering applications.