We explore the suppression of geometrically nonlinear vibrations of a flexible structure by using nonlinear switching shunt damping circuits, namely the Synchronized Switch Damping on Short (SSDS) circuit and the Synchronized Switch Damping on Inductor (SSDI) circuit. Following the early research on linear shunt circuits, the use of nonlinear switching shunts was explored for damping of linear resonance behavior of flexible structures in the early 2000s. However, such flexible structures can easily undergo undesired bifurcations and exhibit large-amplitude nonlinear oscillations that coexist with small oscillations in their frequency response. Suppression of such nonlinear vibrations and resulting bifurcations with linear resistive-inductive circuits is impractical due to extremely large inductance requirements. In the present work, the focus is placed on a strongly nonlinear and weakly coupled flexible structure for suppressing its large-amplitude periodic response branch resulting from saddle-node bifurcations. The Duffing-like structure of interest exhibits nonlinear hardening behavior of predominantly cubic stiffness under primary resonance excitation. Purely resistive linear shunting, SSDS, and SSDI damping techniques are employed and compared with the baseline (near short-circuit) frequency response curves (up- and down-sweep) of the nonlinear structure. Specifically it is shown that the SSDI circuit can substantially reduce the large-amplitude branch, offering the possibility of entirely suppressing undesired large-amplitude bifurcations of the nonlinear system up to certain excitation levels in order to achieve low-amplitude single-valued frequency response. Coupled nonlinear modeling, numerical simulations, and experimental validations are presented.

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