Dynamical behavior of a mechanical system including Saint-Venant component coupled to a non-linear energy sink

Weiss, Mathieu; Savadkoohi, Alireza Ture; Gendelman, Oleg; Lamarque, Claude‐Henri

doi:10.1016/j.ijnonlinmec.2014.03.002

Cited by 23 publications

(8 citation statements)

References 24 publications

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“…Other system with non-regular nonlinearities and introduction of perturbation in the main system have been also investigated in [6,7].…”

Section: System Equationsmentioning

confidence: 99%

“…Then multiple scales are introduced in derivatives with fast time ߬ 0 = ߬ and ߬ ݆ = ߝ ݆ ߬ for j=1, 2,.. slow time scales. As exposed in [2,5,6,7] there is a nonlinear relation between ܰ 1 and ܰ 2 if we consider ߬ 0 → ∞, i.e. to analyse fixed points of the system.…”

Section: Nes Design Calculationsmentioning

confidence: 99%

“…If initial condition is such as N 1 < (N 2-, N 1+ ) the system will directly reach the stable branch on the left until static equilibrium. It has been exposed in [5,6,7,9] that the first behaviour when the dynamic of the system bifurcates is more efficient for vibration control. As a result the invariant manifold and its local maximum (ܰ 2− , ܰ 1+ ) can be used for design purpose.…”

Section: Nes Design Calculationsmentioning

confidence: 99%

See 2 more Smart Citations

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Weiss

Vaurigaud

Savadkoohi

et al. 2015

MATEC Web of Conferences

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Abstract. This work deals with the design and experiment of a cubic nonlinear energy sink (NES) for horizontal vibration mitigation of a bridge cable. Modal analysis of horizontal linear modes of the cable is experimentally performed using accelerometers and displacement sensors. A theoretical simplified 2-dof model of the coupled cable-NES system is used to analytically design the NES by mean of multi-time scale systems behaviours and detection its invariant manifold, equilibrium and singular points which stand for periodic and strongly modulated regimes, respectively. Numerical integration is used to confirm the efficiency of the designed NES for the system under step release excitation. Then, the prototype system is built using geometrical cubic nonlinearity as the potential of the NES. Efficiency of the prototype system for mitigation of horizontal vibrations of the cable under for step release and forced excitations is experimentally demonstrated.

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“…Other system with non-regular nonlinearities and introduction of perturbation in the main system have been also investigated in [6,7].…”

Section: System Equationsmentioning

confidence: 99%

Section: Nes Design Calculationsmentioning

confidence: 99%

Section: Nes Design Calculationsmentioning

confidence: 99%

See 1 more Smart Citation

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Weiss

Vaurigaud

Savadkoohi

et al. 2015

MATEC Web of Conferences

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“…Numerous works investigate the dynamics of two degree-of-freedom systems where a nonlinear oscillator called as nonlinear energy sink (NES) is used to localize vibratory energy of a main structure [1][2][3][4], among which some consider a linear main system and a NES with a cubic restoring force [5][6][7][8][9], leading to applications in various fields such as aerospace [10] or acoustical [11] engineering. Other types of nonlinearities of the NES have been studied as well, e.g., non-polynomial NES [12], vibro-impact NES [13] or piece-wise linear NES with timevarying mass [14], while some works focus on vibratory energy mitigation of nonlinear main systems such as hysteretic oscillators [15,16]. The aforementioned theoretical studies have been validated by experimental investigations.…”

Section: Introductionmentioning

confidence: 99%

Vibratory control of a linear system by addition of a chain of nonlinear oscillators

2017

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An N -degree-of-freedom model consisting of a single-degree-of-freedom linear system coupled to a chain of (N − 1) light nonlinear oscillators is studied. The connection between the chain and the singledegree-of-freedom system is supposed to be linear. Time multi-scale system behaviors at fast and slow time scales are investigated and lead to the detection of the slow invariant manifold and equilibrium and singular points. These points correspond to periodic regimes and strongly modulated responses, respectively. These analytical developments are used to provide evidence of transfer of vibratory energy of the main system to the chain in the form of localized modes during periodic regimes and extreme energy exchanges between modes when the overall structure faces singularities. Furthermore, analytical predictions at slow time scale and nonlinear normal modes of the system are compared with numerical results obtained from direct time integration of the system equations, showing a good agreement between them. Finally, we present a procedure showing how these analytical developments can be used to study a system where the main structure is replaced by a multi-degree-of-freedom linear system, by projecting its dynamics on one of its modes.

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“…vibro-impact and non-polynomial nonlinearities, non-smooth potential function with constant or time-dependent mass [44][45][46][47][48][49][50]. There have been some research works that consider nonlinear main structural system to be controlled by cubic or non-smooth NES; in detail: a main oscillator with piece-wise linear and also Dahl-type behavior and a coupled nonsmooth NES [51,52]; the main system with hysteresis behavior of Bouc-Wen type and a NES with general nonlinear potential function [53]; the main structure with single or several Saint-Venant elements [54] in parallel and a NES with cubic or general potential function [55,56]. The current paper is a summary of our two previous research works which deals with the localization of vibratory energy of: (i) vertical main structural systems by a nonsmooth NES [48] and (ii) main structural systems with a set of parallel Saint-Venant elements by a NES with general potential function [56].…”

Section: Introductionmentioning

confidence: 99%

Localization of Vibratory Energy of Main Linear/Nonlinear Structural Systems by Nonlinear Energy Sink

Lamarque

Savadkoohi

2015

Springer Proceedings in Physics

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Two systems are considered: the system I is composed of a main linear structure which is coupled to a nonsmooth nonlinear energy sink. Here, effects of the gravity forces are not neglected. The system II consists of a main structure with a set of parallel Saint-Venant elements that is attached to a nonlinear energy sink with general odd nonlinear potential function. Time multi-scale energy exchanges between two oscillators is detected; in detail: the invariant manifold of the system at fast time scale is traced while detected equilibrium and singular points at slow time scale give us envision about system behavior(s) at pseudo-steady-state regime(s). All of detected behaviors provide us design tools for tuning necessary parameters of nonlinear energy sink for the localization of vibratory energy of main structural systems.

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Dynamical behavior of a mechanical system including Saint-Venant component coupled to a non-linear energy sink

Cited by 23 publications

References 24 publications

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Vibratory control of a linear system by addition of a chain of nonlinear oscillators

Localization of Vibratory Energy of Main Linear/Nonlinear Structural Systems by Nonlinear Energy Sink

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