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.