Forced System with Vibro-impact Energy Sink: Chaotic Strongly Modulated Responses

AbstractThe paper treats forced response of primary linear oscillator with vibro-impact energy sink. This system exhibits some features of dynamics, which resemble forced systems with other types of nonlinear energy sinks, such as steady-state and strongly modulated responses. However, the differences are crucial: in the system with vibro-impact sink the strongly modulated response consists of randomly distributed periods of resonant and non-resonant motion. This salient feature allows us to identify this type of dynamic behavior as chaotic strongly modulated response (CSMR). It is demonstrated, that the CSMR exists due to special structure of a slow invariant manifold (SIM), which is derived with the help of a multiple-scale analysis of the system. In the considered system, this manifold has only one stable and one unstable branch. This feature defines new class of universality for the nonlinear energy sinks. In the system with the vibro-impact sink, such responses are observed even for very low level of the external forcing. This feature makes such system viable for possible energy harvesting applications

Analysis of a vibro-impact nonlinear energy sink: theoretical and numerical developments

Recently, it has been demonstrated that a Vibro-Impact type Nonlinear Energy Sink (VI-NES) can be used efficiently to mitigate vibration of a Linear Oscillator (LO) under transient loading and harmonic force. In this paper, a design optimization procedure of an optimal VI-NES coupled to LO for energy pumping is presented theoretically and numerically. Due to the small mass ratio between the flying mass of the VI-NES and LO, the obtained equation of motion is possible to use the method of multiple scales in the case of 1:1 resonance. It is showed that there exist different response regimes like Strongly Modulated Response (SMR) proved to be the most efficient reponse regime for vibration reduction. An optimization procedure is presented and the results are verified numerically

Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results

This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results.National Science Foundation (U.S.) (Grant CMMI-1100722

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer