The non-linear dynamics of electromagnetically actuated microbeam resonators with purely parametric excitations

• We investigate the behavior of an electromagnetically actuated microscale cantilever.
• We examine the effects of non-linearities on the system's near-resonant response.
• Nonlinear parametric excitations qualitatively alter the behavior of the system.
• Effective frequency response tuning mechanisms are highlighted.

Electromagnetic micro-transducers have been utilized in a number of distinct applications in recent years due, in large part, to their scalability, low power consumption, self-sensing capabilities and ease of integration with external hardware. In the present work, the highly non-linear dynamic behavior of a new class of parametrically excited, electromagnetically actuated microcantilevers is explored. The system is modeled using classical energy methods and its frequency response behavior is subsequently characterized using perturbation methods and bifurcation analysis. The recovered results provide a clear understanding of the effects of fifth-order non-linearities in a parametrically excited microresonator, and are currently guiding experimental work on electromagnetically actuated oscillators and microresonator arrays.