Dynamics of a hybrid vibro-impact oscillator: canonical formalism

Hybrid vibro-impact (HVI) oscillations is a strongly nonlinear dynamical regime that involves both linear and collisions under periodic, impulsive, or stochastic excitation. This arises in various engineering systems, such as mechanical components tight rigid constraints, seismic-induced sloshing partially-filled liquid storage tanks, more. The adaptive nonlinearity of the HVI oscillator used by HVI-nonlinear energy sink an effective vibration mitigation solution for broad frequency range. Due to extreme this regime, traditional analytical methods are inapplicable description its transient dynamics. In current work, we model forced particle truncated quadratic potential well with infinite depth. slow flow dynamics system vicinity primary resonance described canonical transformation action-angle (AA) variables corresponding reduced manifold (RM). Two types bifurcation examined. former associated transition between HVI-regime vice versa, latter reaching chosen maximal level. boundaries on forcing parameters plane obtained analytically. level any given set analytically well. jumps type I crossing boundary obtained. underlying mechanisms govern occurrence bifurcations identified. They correspond two distinct scenarios: first scenario, gradually reaches threshold thus referred ”maximum” mechanism. second, potentially more dangerous abrupt transitions system’s response from relatively small value pattern related passage slow-flow phase trajectory through saddle point RM, “saddle” Both universal systems undergo escape All theoretical results complete agreement full-scale numerical simulations.