Nonlinear coupled dynamics of shear deformable microbeams

The nonlinear dynamics of a shear deformable microbeam is investigated in this paper. Based on the modified couple stress theory, the equations of motion for the longitudinal, transverse, and rotational motions are obtained by balancing the energies of the system with the works of external excitation loads via Hamilton’s principle. These nonlinear partial differential equations are discretized by means of the Galerkin method together with an assumed-mode technique. The resultant nonlinear equations are solved via the pseudo-arclength continuation method and a direct time-integration technique. Nonlinear dynamical characteristics of the system are presented in the form of frequency-response curves, force-response plots, time traces, phase-plane portraits, and fast Fourier transforms.