Nonlinear dynamics of a microscale beam based on the modified couple stress theory

Nonlinear resonant response of imperfect extensible Timoshenko microbeams

“…Ş imşek (2010) analyzed the motion characteristics of an embedded microbeam under the action of a moving microparticle. These investigations were extended to nonlinear analyses, for example, by Ghayesh et al (2013aGhayesh et al ( , 2013d, who examined the size-dependent nonlinear behaviour of a microbeam on the basis of both the strain gradient and modified couple stress theories.…”

Chaotic motion of a parametrically excited microbeam

“…Many contributions on the dynamical behaviour and stability of microbeams can be found in the literature (Baghani, 2012;Ghayesh, Amabili, & Farokhi, 2013a;Ghayesh & Farokhi, 2013;S ßims ßek, 2010;S ßims ßek & Reddy, 2013;Tang, Ni, Wang, Luo, & Wang, 2014a); the first class of the literature analysed the free dynamics, while the second class examined the forced statics and dynamical behaviour of microbeams subject to a time-varying transverse force or a constant axial force, mainly with the aim of obtaining frequency-response curves for the former (of the second class) and post-buckling/bending amplitude for the latter case (of the second class). This paper is the first which analyses the sub and supercritical complex global dynamics of microbeams subject to a time-dependent axial load by constructing the bifurcation diagrams of Poincaré sections, with special consideration to period-n, quasiperiodic, and chaotic motions.…”

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

“…The Bernoulli-Euler beam theory along with the von-K arm an's geometric nonlinearity was used in this study. Ghayesh et al numerically studied the nonlinear resonant dynamics of a microbeam [22] for straight beam, and Farokhi et al [23] did the same for an initially curved beam. The Galerkin method along with appropriate eigenfunctions was used to discretize the nonlinear partial di erential equation of motion into a set of nonlinear ordinary di erential equations, and subsequently, the pseudo-arc length continuation technique was utilized to solve these equations.…”

“…Similar to the aforementioned linear models, the nonlinear static and dynamic analyses of microbeams were investigated using the numerical and theoretical methods by many researchers based on the modi ed couple stress theory [19][20][21][22][23]. Dai et al developed a new nonlinear theoretical model for cantilever microbeams [19] to explore the nonlinear dynamic behavior.…”