Mitigating Grazing Bifurcation and Vibro-Impact Instability in Time-Frequency Domain - Kuo, Chi-Wei; Suh, C. Steve (Journal of Applied Nonlinear Dynamics, 2026)
Impact oscillators are found in many applications. It is common for these applications to undergo the inadvertent state of grazing bifurcation. Vibro-impact incited grazing and route-to-chaos are difficult to control. The Newtonian model of a vibro-impact system rich of complex nonlinear behaviors is considered for the mitigation of impact induced instability and grazing. A novel concept capable of simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is adopted to formulate a viable control solution. The concept has been demonstrated to be feasible for the control of dynamic instability including bifurcation and route-to-chaos in many nonlinear systems. The developed controller explores wavelet adaptive filters and filtered-x least mean square algorithm to the successful moderation of the grazing and dynamic instability of the non-smooth system. The qualitative behavior of the controlled impact oscillator follows a definitive fractal topology before settling into a stable manifold. The controlled response is categorically quasi-periodic and of the prescribed vibration amplitude and frequency spectrum.