Experimentally characterising the dynamical landscape of an active MEMS cantilever

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Abstract
Micro-and nano-electromechanical systems (M/NEMS) are in high demand for cutting-edge future technological solutions. Their strongly nonlinear nature is regarded as beneficial for optimising performance metrics for a wide range of engineering applications. As model-free experimentation remains limited to forward time observations, important dynamic features can be left uncharted, resulting in an incomplete dynamical landscape. Here we address this issue by employing experimental continuationa model-free technique for constructing bifurcation diagrams by tracking steady-states and/or periodic responses directly in a physical experiment. This approach is unexplored for investigating micro-scale systems with fast timescales. Our state-of-the-art experiment investigates an active MEMS cantilever operated as a self-oscillator with a natural frequency of 100 kHz; the fastest timescales of a mechanical system probed with experimental continuation. We explore the cantilever's nonlinear responses to external, periodic excitation via a sequence of one-parameter response curves. By experimentally mapping out the MEMS cantilever's stable and unstable periodic orbits, we expose the dynamic landscape by rendering a multi-valued response surface across a range of forcing frequencies and amplitudes. An atypical, non-Duffing-like bifurcation structure is revealed.

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