Nonlinear motion characteristics of microarches under axial loads based on modified couple stress theory

The aim of the present study is to investigate the geometrically nonlinear size-dependent bending as well as resonant behaviour over the bent state of a microarch under an axial load. In particular, an axial load is applied on the system causing the initial curvature to increase by giving rise to a new bent configuration. A distributed harmonic transverse force is then exerted on the microarch and the nonlinear resonant response of the system over the new deflected configuration is investigated. The nonlinear partial differential equation of motion is obtained via Hamilton's principle based on the modified couple stress theory. The equation is discretized into a set of nonlinear ordinary differential equations through use of the Galerkin scheme. The pseudo-arclength continuation technique is then applied to the resultant set of ordinary differential equations. First, for the unforced system in the transverse direction, the axial load is increased and the new deflected configuration of the system is plotted versus the axial compression load; the nonlinear resonant response over the deflected configuration is then investigated through constructing frequency-response and force-response curves.