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

TL;DR

This paper models a hybrid cubic vibro-impact oscillator with nonlinear energy sink to analyze its complex bifurcation mechanisms and predict transient energy behavior for vibration mitigation.

Contribution

It introduces a novel hybrid oscillator model with multiple nonlinearities and identifies three bifurcation mechanisms, advancing understanding of its transient dynamics and energy dissipation capabilities.

Findings

Analytical prediction of maximum transient energy.

Identification of three bifurcation mechanisms.

Full analytical response curves of the system.

Abstract

Various dynamical engineering systems involve purely nonlinear stiffness that lacks linear properties even under the assumption of small displacements. The most common is the cubic nonlinearity that may stem from either geometric or material properties. Examples include flexible structural components, pre-tensioned cables, springs, and polymers. When subjected to tight rigid constraints collisions might take place, leading to an additional infinitely strong nonlinearity. The resulting dynamical regime involves both smooth nonlinear oscillations (SNOs) and a hybrid cubic vibro-impact (HCVI) regime. The adaptive nonlinearity of the HCVI oscillator is used by the HCVI-nonlinear energy sink (NES) as an effective mechanism for efficient vibration mitigation in broad energy and frequency ranges. Due to the multiple essential nonlinearities of the HCVI oscillator, traditional analytical methods are inapplicable for the description of its transient dynamics. 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. Unlike previous studies, three underlying dynamical mechanisms that govern the occurrence of bifurcations are identified: two maximum mechanisms and one saddle mechanism. 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.