Publisher's Note

Abstract

This paper, for the first time, analyses the size-dependent global dynamics of imperfect axially forced microbeams and shows that how a small initial imperfection (due to improper manufacturing of microbeams) can substantially change the size-dependent global dynamical behaviour of the microsystem; moreover, it investigates the effect of small size of the microbeam on the appearance and vanishing different chaotic and quasiperiodic motions. More specifically, the continuous expressions for the size-dependent potential energy as well as kinetic energy of the microsystem are constructed and dynamically balanced via an energy method. A transformation to a reduced-order model is performed via a weighted-residual method. The bifurcation diagrams of Poincare maps are constructed by means of direct time-integrating the reduced-order model for the imperfect microsystem. Poincare sections, phase-plane diagrams, time histories, and fast Fourier transforms are also plotted for some cases in order to shed light on the size-dependent microsystem global dynamics.