Experimental bifurcation analysis of a clamped beam with designed mechanical nonlinearity

We use control-based continuation (CBC) to perform an experimental bifurcation study of a periodically forced dual-beam. The nonlinearity is of geometric nature, provided by a thin, clamped beam. The overall system exhibits hysteresis and bistability in its open-loop frequency response due to a hardening, Duffing-like nonlinear stiffness, which can be designed or adjusted by choosing the properties of the thin beam. We employ local stabilising feedback control to implement CBC and track stable periodic solutions past the fold points. Thus obtained continuous solution branches are used to generate the solution surface over the plane of excitation amplitude and frequency. This surface features two curves of fold bifurcations that meet at a cusp point, and they delimit the experimentally observed bistability range of this nonlinear beam.