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