scholarly journals Dynamics of Cubic and Vibro-Impact Nonlinear Energy Sink: Analytical, Numerical, and Experimental Analysis

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Tao Li ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Steady State ◽  
Invariant Manifold ◽  
General Equation ◽  
Analytical Procedure ◽  
Multiple Scales ◽  
Nonlinear Energy Sink ◽  
Periodic Forcing ◽  
State Response ◽  
Energy Sink ◽  
Nonlinear Energy

This paper is devoted to study and compare dynamics of primary linear oscillator (LO) coupled to cubic and vibro-impact (VI) nonlinear energy sink (NES) under transient and periodic forcing. The classic analytical procedure combining the approach of invariant manifold and multiple scales is extended from the analysis of steady-state resonance to other regimes, especially strongly modulated response (SMR). A general equation governing the variation of motion along the slow invariant manifold (SIM) is obtained. Numerical results show its convenience to explain the transition from steady-state response to SMR and the characteristics of SMR for periodic forcing. Targeted energy transfer (TET) under transient forcing can also be well understood. Experimental results from LO coupled to VI NES under periodic forcing confirm the existence of SMR and its properties (e.g., chaotic). They also verify the feasibility of the general equation to explain complicated case like SMR in experiments.

scholarly journals Chatter Control in Turning Process with a Nonlinear Energy Sink

2013 ◽  
Vol 698 ◽  
pp. 89-98 ◽  
Author(s):  
Etienne Gourc ◽  
Sébastien Seguy ◽  
Guilhem Michon ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Turning Process ◽  
Strongly Coupled ◽  
Different Types ◽  
Chatter Control ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Cubic Stiffness

This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

scholarly journals Theoretical and Experimental Study of an Harmonically Forced Vibro-Impact Nonlinear Energy Sink

2013 ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Mass Ratio ◽  
Strongly Coupled ◽  
Electrodynamic Shaker ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Good Agreement

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. In this paper, the dynamic response of an harmonically forced LO, strongly coupled to a VI-NES is investigated theoretically and experimentally. Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equation of motion are analyzed using the method of multiple scales in the case of 1 : 1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit Strongly Modulated Response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR response regimes. A good agreement between theoretical and experimental results is observed.

scholarly journals Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Harmonic Excitation ◽  
Mass Ratio ◽  
Electrodynamic Shaker ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Good Agreement

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. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.

Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing: Account of Detuning

2007 ◽  
Author(s):  
Y. Starosvetsky ◽  
O. V. Gendelman
Keyword(s):  
Averaging Method ◽  
Nonlinear Energy Sink ◽  
Linear Oscillator ◽  
External Forcing ◽  
Frequency Detuning ◽  
Main Resonance ◽  
Periodic Forcing ◽  
Local Bifurcations ◽  
Energy Sink ◽  
Nonlinear Energy

Dynamical system under investigation in the current work is comprised of harmonically forced linear oscillator with attached nonlinear energy sink. External forcing frequency detuning near the main resonance (1:1) is included in the system investigation. The detailed study of the periodic and quasi-periodic regimes is done in the work via (adaptive) averaging method. Local bifurcations of the periodic regimes are revealed and fully described in the space of system parameters (amplitude of excitation, damping, frequency detuning). Various possibilities of coexistence of the response regimes are predicted analytically and demonstrated numerically. Among those is a coexistence of two distinct periodic regimes together with strongly modulated response (SMR). All findings of the simplified analytic model are verified numerically and considerable agreement is observed.

scholarly journals Tracking modal interactions in nonlinear energy sink dynamics via high-dimensional invariant manifold

2020 ◽  
Author(s):  
Giuseppe Habib ◽  
Francesco Romeo
Keyword(s):  
Invariant Manifold ◽  
Mutual Effect ◽  
Nonlinear Energy Sink ◽  
High Amplitude ◽  
High Dimensional ◽  
Primary System ◽  
Modal Interactions ◽  
Transient Regimes ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract A nonlinear energy sink (NES), conceived to mitigate the vibrations of a multi-degree-of-freedom host mechanical system, is considered. The high-dimensional slow invariant manifold (SIM) describing the high-amplitude slow dynamics of the system is derived and exploited to interpret its transient regimes caused by impulsive excitation. It is shown that algebraic expressions derived from the SIM formulation enable to identify the so-called interaction points, providing the conditions in which two modes of the primary system interact and share energy through the nonlinear absorber. Moreover, the mutual effect of differently activated host system modes on the NES energy dissipation mechanism is discussed. Through sections of the multidimensional SIM, modal interaction triggering resonance capture cascades (RCC) can be effectively explained. The dissipation capabilities are eventually assessed in order to evaluate the efficiency of the RCC regime.

Sign in / Sign up

Export Citation Format

Share Document