Nonlinear dynamics of a microscale beam based on the modified couple stress theory

In the present study, the nonlinear resonant dynamics of a microscale beam is studied numerically. The nonlinear partial differential equation governing the motion of the system is derived based on the modified couple stress theory, employing Hamilton's principle. In order to take advantage of the available numerical techniques, the Galerkin method along with appropriate eigenfunctions are used to discretize the nonlinear partial differential equation of motion into a set of nonlinear ordinary differential equations with coupled terms. This set of equations is solved numerically by means of the pseudo-arclength continuation technique, which is capable of continuing both the stable and unstable solution branches as well as determining different types of bifurcations. The frequency response curves of the system are constructed. Moreover, the effect of different system parameters on the resonant dynamic response of the system is investigated.