Nonlinear size-dependent dynamics of microarches with modal interactions

This paper investigates the nonlinear dynamics of microarches with internal modal interactions; the nonlinear size-dependent motion characteristics are analyzed for the system with two-to-one and three-to-one internal resonances. The partial differential equation of motion is discretized into a set of second-order nonlinear ordinary differential equations via the application of the Galerkin scheme. The linear natural frequencies of the system are obtained by eliminating the nonlinearities; these are used to verify the occurrence of modal interactions. The nonlinear resonant dynamics are examined via the pseudo-arclength continuation technique for the systems with internal modal interactions.