Parametric vibrations of imperfect Timoshenko microbeams

Abstract

This paper examines the size-dependent nonlinear parametric vibrations of imperfect Timoshenko microbeams subject to a time-dependent axial load. Taking into account rotary inertia and shear deformation, the modified couple stress theory is employed so as to derive a continuous expression for the elastic potential energy of the system; the geometric imperfection is modelled via a small initial deflection in the transverse direction. The continuous model of the system is obtained via an energy balance method. A reduced-order model is obtained by means of a weighted residual method together with an assumed-mode technique. The double-dimensionalised form of the reduced-order model is solved by means of different numerical techniques and stability is analysed. It is shown that even small geometric imperfections may change the parametric response of the system not only quantitatively, but also qualitatively.