Dynamics of a hybrid cubic vibro-impact oscillator and nonlinear energy sink

In the current work, we model HCVI oscillator by a forced particle in hybrid quartic-square potential well with infinite depth under periodic external forcing. The slow-flow dynamics of system is analyzed framework isolated resonance approximation canonical transformation to action–angle (AA) variables and corresponding reduced manifold (RM). Two types bifurcation are examined described analytically. former associated SNO-regime HCVI-regime vice versa, latter reaching chosen maximal transient energy level. Unlike previous studies, three underlying dynamical mechanisms that govern occurrence bifurcations identified: two maximum one saddle mechanism. first correspond gradual increase system’s response amplitude for proportional excitation intensity, corresponds an abrupt therefore more potentially hazardous when takes place engineering systems effective pumpingwhen HCVI-NES. Both mechanism universal undergo escape from well. predicted analytically over space parameters using iso-energy contours. curves obtained analytically, allowing full perspective on HCVI-oscillator response, HCVI-NES performances design optimization. All theoretical results supported numerical simulations.