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

Charlemagne, S.; Lamarque, Claude‐Henri; Savadkoohi, Alireza Ture

doi:10.1007/s00707-017-1867-7

Cited by 15 publications

(14 citation statements)

References 45 publications

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“…2. A procedure to obtain this for other type of NES configurations and stiffness characteristics is found in [13,34,35]. First, the compound system's dynamics are analyzed on two time scales, where the fast time the stability of the SIM branches and the slow time will yield the same expression as ( 14) and dynamics on the SIM.…”

Section: Sim Dynamics and Stabilitymentioning

confidence: 99%

“…Either the complexity of the NES is increased by adding degrees-of-freedom (DOF)/additional mechanisms, or other stiffness characteristics are proposed. In the first line of thought, works have investigated 2DOF series NESs [12], a chain of NESs [13], or a conventional NES featuring an additional pendulum [14]. A complex mechanism was added to a conventional NES in [15] where two masses oscillated with a constant frequency on top of the NES.…”

Section: Introductionmentioning

confidence: 99%

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The periodically extended stiffness nonlinear energy sink

Dekemele

Habib

Loccufier

2022

Mechanical Systems and Signal Processing

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Conventional nonlinear energy sinks (NES) are considered to be a more robust alternative to linear vibration absorbers such as the tuned-mass-damper (TMD). While the conventional NES has a larger efficient frequency bandwidth than the TMD, it is only really efficient for a small energy range. This implies a deterioration of the NES's mitigation properties if the primary system's amplitude varies. To overcome this issue, other researchers resort to increasing the complexity of the NES by adding degrees-of-freedom. Here, another line of thought is presented, by proposing an unconventional stiffness characteristic. To increase the energy bandwidth the NES in this paper features a non-smooth, periodically extended stiffness characteristic. This NES is attached to an uncertain primary system and its performance is compared with that of the conventional NES and of the TMD by deriving the slow invariant manifolds (SIMs) in transient 1:1 resonance. The SIMs are curves that relate the vibration amplitudes of the primary system and the NES, and serve as an easy and computationally efficient tool to analyze performance. The research in this paper will prove that the newly proposed NES can be both robust regarding energy and frequency uncertainty, by considering the novel periodically extended stiffness characteristic.

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Section: Sim Dynamics and Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The periodically extended stiffness nonlinear energy sink

Dekemele

Habib

Loccufier

2022

Mechanical Systems and Signal Processing

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“…Currently, most investigations in this area are mainly concentrated on the vibration absorption of cubic oscillators. In this regard, NESs with two and multiple degrees-of-freedom, which can be seemed as reduced oscillator chains, have been used to suppress vibrations of impulsively and harmonically excited linear primary systems [26][27][28][29], aeroelastic instability of a rigid wing with structural nonlinearities [30], and responses of a six-story structure subjected to a shock-type loading [31]. Considering the limitations of the vibration absorber structure, equal-weight cubic oscillators are usually used (at least the weight of the oscillators are close).…”

Section: Introductionmentioning

confidence: 99%

Cross-scale energy transfer of chaotic oscillator chain in stiffness-dominated range

et al. 2022

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The investigations on the dynamics of hierarchical oscillator chains provide basic theories for the elds of acoustic metamaterial and passive guidance of energy ow. In the present study, the characteristics of stiffness-dominated energy transfer of a reduced cross-scale oscillator chain that generates chaotic vibrations are studied. The semi-analytical solutions are obtained by the complexi cation-averaging method and the least-square method for thoroughly searching the branches of responses. Then the energy transfer patterns of the oscillator chain are analyzed based on Runge-Kutta method. Moreover, chaotic responses are determined using the displacements and Lyapunov exponents of the system. The average energy and normalized energy ux are de ned to evaluate the energy distribution in each oscillator and the energy transfer between oscillators, respectively. The semi-analytical results show that the oscillator chain produces complex unstable branches of response around the resonance frequency of the linear oscillator. It is found that the detached higher branches of response of the chain are similar to that of a system consisting of one linear oscillator and one cubic oscillator. When chaotic responses occur, the energy transfer patterns that re ected by average energy and normalized energy ux are similar in the same branch of response for different excitation frequencies. However, energy transfer patterns in different branches of response are quite different even at the same excitation frequency, and the higher branch generates the lower energy transfer. Furthermore, analyses of the input energy and the scale between cubic oscillators demonstrate that variations of the two parameters slightly affect the normalized energy ux.

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“…Such a phenomenon is called a soliton in the case of a propagating wave and of a breather for a stationary wave [6,7]. Therefore, nonlinear chains appear as promising candidates on which to build a vibratory or acoustic control [8,9]. The vibratory energy can be localized in order to be dissipated or on the contrary scattered to be transferred to another frequency domain.…”

Section: Introductionmentioning

confidence: 99%