Coupled nonlinear size-dependent behaviour of microbeams

The nonlinear resonant behaviour of a microbeam, subject to a distributed harmonic excitation force, is investigated numerically taking into account the longitudinal as well as the transverse displacement. Hamilton's principle is employed to derive the coupled longitudinal-transverse nonlinear partial differential equations of motion based on the modified couple stress theory. The discretized form of the equations of motion is obtained by applying the Galerkin technique. The pseudo-arclength continuation technique is then employed to solve the discretized equations of motion numerically. Different types of bifurcations as well as the stability of solution branches are determined. The numerical results are presented in the form of frequency-response and force-response curves for different sets of parameters. The effect of taking into account the longitudinal displacement is highlighted.