Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress

Weiss, Mathieu; Chenia, Mahmoud; Savadkoohi, Alireza Ture; Lamarque, Claude‐Henri; Vaurigaud, Bastien; Hammouda, Abdelaziz

doi:10.1007/s11071-015-2314-8

Cited by 15 publications

(9 citation statements)

References 31 publications

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“…The choice of parameters scaling is governed by their physical range. The Slow Invariant Manifold (SIM) of the system can be obtained by treating the system (2) analytically after introducing the following Manevitch's complex variables [22,25]:…”

Section: Considered Model and Classical Treatmentmentioning

confidence: 99%

“…For prestressed systems, e.g. the systems in gravitational fields, in addition to first harmonics, constant terms of Fourier series should be taken into account as well [24][25][26]. The aim of the current paper is to include the third harmonics (in addition to the first ones) for a better prediction of the principle coupled system behaviors.…”

Section: Introductionmentioning

confidence: 99%

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Extended complexification method to study nonlinear passive control

et al. 2019

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The present research work aims to design a passive vibration control based on nonlinear energy pumping. An extended asymptotic approach is introduced based on the invariant manifold approach for the case of 1:1 resonance. It consists in introducing an extended form of Manevitch's complex variables, taking into consideration higher harmonics, enabling the detection of the invariant manifold of the system at fast time scale. At the slow time scale, equilibrium points and singularities are identified analytically in order to predict periodic regimes and strongly modulated responses. The example of a passive shunt loudspeaker using a nonlinear absorber is studied. Unlike classical investigations, the first and third harmonics are taken into consideration. It is demonstrated that the presence of the third harmonic improves the approximations of the results. Different cases are considered, where the obtained analytical results are in good agreement with those obtained via direct numerical integration of the principal system of equations.

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Section: Considered Model and Classical Treatmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended complexification method to study nonlinear passive control

et al. 2019

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“…-Depending on the condition of the system, complex variables of Manevitch (for systems without pre-stress) [33] or their extended versions (for pre-stressed systems) [23,28] are applied (i 2 = −1):…”

Section: A Two Dof System With Internal Variables In the Main Dofmentioning

confidence: 99%

“…In order to simplify, let us assume that A = I d . Complex variables of Manevitch [33] or their extended versions [23,28] are applied to system variables:…”

Section: Complexifications and Using The Galerkin Techniquementioning

confidence: 99%

“…Meanwhile, some research works have been studied which consider nonsmooth main oscillator and coupled nonsmooth or cubic NES. For instance, following coupled oscillators have been studied: a main oscillator with piecewise linear, Dahl-type and hardening elasto-plastic behaviors which are coupled nonsmooth NES [26][27][28]; a main oscillator with hysteresis behavior of Bouc-Wen type and a NES with general nonlinear potential function [29]; a main structure with single or several Saint-Venant elements [30] in parallel and a NES with cubic or general potential functions [31,32]. In this paper, we present a general methodology for studying the time multi-scale responses of main oscillators with general behaviors (nonlinear, nosmooth, ...) and coupled NES with general potentials (smooth, nonsmooth,...).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the 1:1 resonant energy exchanges between coupled oscillators with rheologies

Savadkoohi¹,

Lamarque²,

Weiss³

et al. 2016

Nonlinear Dyn

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The paper is composed of three main parts: the first part presents a two degrees of freedom coupled oscillators with rheology. One of the oscillators is intended to be the main structure and the second one is a nonlinear energy sink. The rheology of the system is represented via a set of internal variables that are governed by either differential inclusions or differential equations or direct algebraic relations between system variables. A step by step methodology is explained to trace system behaviors around a 1 : 1 resonance at different time scales. Invariant of the system at fast time scale is detected while possible periodic and strongly modulated regimes around its invariant are traced at slow time scales. The second part of the paper considers a set of several degrees of freedom main oscillators which are coupled to several nonlinear energy sinks. The overall system can house several rheologies. Explained methodology of the first part is expanded to this general case for tracing system responses at different time scales around 1 : 1 resonances. The third part of the paper presents two practical examples: The proposed methodology is used to detect invariants of systems and their equilibrium and singular points. This methodology provides some tools for designing equilibrium and singular points, i.e. periodic and strongly modulated regimes which lead to the design of nonlinear energy sinks for passively controlling and/or energy harvesting of the main oscillators.

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Design of a nonlinear absorber for a 2 degrees of freedom pendulum and experimental validation

Hurel

Savadkoohi

Lamarque

2021

Structural Contr & Hlth

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A nonlinear energy sink is designed to control the oscillations of a 2 degreesof-freedom pendulum under the following types of excitations: horizontal and vertical base displacements and initial energy. Coupled nonlinear governing system equations are treated with the multiple-scale methods with different assumptions depending on applied loads. Fast and slow system dynamics are revealed leading to detection of different possible dynamical regimes. The choice of the design parameters of the nonlinear energy sink is discussed, and a tuning method is proposed. The efficiency of the control is validated by an experimental study: a physical model of the pendulum is excited by the shake table. The response of the system shows that the nonlinear energy sink is able to control the main system.

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Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress

Cited by 15 publications

References 31 publications

Extended complexification method to study nonlinear passive control

Extended complexification method to study nonlinear passive control

Analysis of the 1:1 resonant energy exchanges between coupled oscillators with rheologies

Design of a nonlinear absorber for a 2 degrees of freedom pendulum and experimental validation

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