Large-amplitude dynamical behaviour of microcantilevers

This paper aims at analysing the nonlinear size-dependent dynamics of a microcantilever based on the modified couple stress theory. Since one end of the microcantilever is free to move, the system undergoes large deformations; this necessitates the application of a nonlinear theory which is capable of taking into account curvature-related and inertial related nonlinearities. The expressions for the kinetic and potential energies are developed on the basis of the modified couple stress theory. The energy terms are balanced by the work of a base excitation by means of Hamilton's principle, yielding the continuous model for the system motion. Based on a weighted-residual method, this continuous model is reduced and then solved via an eigenvalue analysis (for the linear analysis) and a continuation method (for the nonlinear analysis); stability analysis is performed via the Floquet theory. It is shown that each source of nonlinearity, in the presence of the length-scale parameter, has a significant effect on the system dynamics. (C) 2016 Published by Elsevier Ltd.