On the Nonlinear Multi-Physics Dynamics of a Mechanical Oscillator Coupled to an Electro-Magnetic Circuit

The dynamics of a nonlinear electro-magneto-mechanical coupled system is addressed. Such a system exhibits a rich dynamic behavior arising from the involved quadratic nonlinearities that can be explored by relying on both analytical and numerical tools. It will be shown that the global multi-physics dynamic can be effectively handled to make the system functioning either as a sensor or an actuator for applications in the micro electromechanical context. Towards this goal, the roles played by the electro-magnetic and mechanical components in the resulting complex response, encompassing bifurcations as well as possible transitions from regular to chaotic motion, will be highlighted by means of Poincaré sections. Moreover, when the linear frequency of the circuit is larger than that of the mechanical oscillator, the dynamics exhibits slow and fast time scales. Therefore we analyze the mechanical oscillator forced (actuated) via harmonic voltage excitation of the electric circuit; when the forcing frequency is close to that of the mechanical oscillator, the long term dynamics are expected to evolve in a purely slow timescale, in the presence of dissipation, with no interaction with the fast time scale. We show this by assuming the existence of a slow invariant manifold, computing it analytically, and verifying its existence via numerical experiments on both full- and reduced-order systems.