Nonlinear resonant response of imperfect extensible Timoshenko microbeams

This paper investigates the nonlinear size-dependent dynamics of an imperfect Timoshenko microbeam, taking into account extensibility. Based on the modified couple stress theory, the nonlinear equations of motion for the longitudinal, transverse, and rotational motions are derived via Hamilton's energy method. A high-dimensional finite degree-of-freedom system of ordinary differential equations is obtained by the application of the Galerkin scheme. This set of equations is solved through use of the pseudo-arclength continuation method. A stability analysis is conducted via use of the Floquet theory. The resonant motion characteristics of the microbeam are examined by plotting the frequency-response and force-response curves. The effect of system parameters on the resonant response of the system is highlighted.