Experimentally characterising the dynamical landscape of an active MEMS cantilever

Experimental continuation describes a collection of techniques for constructing bifurcation diagrams by tracking steady-states and/or periodic responses directly in a physical experiment, without the need for a mathematical model. This approach has been used to characterise the nonlinear dynamics of macro-scale systems, which operate at relatively slow timescales. In this work we show that experimental continuation can be adapted to a wide range of engineering applications, namely, the technologically important class of micro-electromechanical systems (MEMS) — which are smaller, highly nonlinear, and operate at much faster timescales. The MEMS device is operated in a parameter range for which the cantilever undergoes self-oscillations at a natural frequency of just under 100 kHz, without external forcing. We investigate nonlinear responses to external, periodic excitation via a sequence of one-parameter response curves. Our experiments are model-free and use control-based continuation to map stable and unstable periodic responses of active MEMS cantilevers. Consequently, we expose the dynamic landscape by rendering a surface that features multi-valued responses across a range of forcing frequencies and amplitudes. An atypical, non-Duffing-like bifurcation structure is revealed. Thus, we showcase experimental continuation as a viable tool for investigating fast-timescale nonlinear oscillators. Our work encourages the integration of control-based testing schemes into standard engineering practice by showing that control-based continuation is an accessible tool for nonlinear analyses of a broader range of engineering applications.