Periodic orbits of a conservative 2-DOF vibro-impact system by piecewise continuation: bifurcations and fractals

Tao, Hongcheng; Gibert, James M.

doi:10.1007/s11071-018-04734-4

Cited by 42 publications

(9 citation statements)

References 32 publications

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“…The NSA of a simple one-dimensional cantilever bar has recently attracted experimental interest [12] and has already been investigated analytically and numerically in semi-discrete and continuous settings in space [1,9,10,15,[17][18][19]22]. In the continuous framework, modes consisting of piecewise-linear solutions in space and time have been shown to exist [18,21,22].…”

Section: Contentsmentioning

confidence: 99%

D’Alembert function for exact non-smooth modal analysis of the bar in unilateral contact

Urman

Legrand

Junca

2021

Nonlinear Analysis: Hybrid Systems

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Section: Contentsmentioning

confidence: 99%

D’Alembert function for exact non-smooth modal analysis of the bar in unilateral contact

Urman

Legrand

Junca

2021

Nonlinear Analysis: Hybrid Systems

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“…In addition, the efficiency of SSVI NES was found to be improved with proper selection and optimization of the impact coefficient of restitution [111]. The periodic orbits at NNMs on the FEPs and the TET mechanisms have been thoroughly studied in [103,104,112] for linear oscillators attached to the symmetric DSVI NES. The FEP backbones and several symmetrical and unsymmetrical resonance subharmonic branches have been obtained for the SDOF linear system in [103] and the 3-DOF linear system in [104] when they were attached to the SSVI NES.…”

Section: Rotary Nessmentioning

confidence: 99%

“…In addition, different TET mechanisms between the linear system and the SSVI NES were analyzed. In [112], a detailed FEP analysis using the piecewise numerical continuation method has been also performed with a SDOF system attached with SSVI NES.…”

Section: Rotary Nessmentioning

confidence: 99%

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

2022

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Dynamical and structural systems are susceptible to sudden excitations and loadings such as wind gusts, blasts, earthquakes, and others which may cause destructive vibration amplitudes and lead to catastrophic impact on human lives and economy. Therefore, various vibration absorbers of linear and nonlinear coupling dynamics have been widely studied in plenty of publications where some have been applied in real-world practical applications. Firstly, the tuned-mass-damper (TMD), the first well-known linear vibration absorber that has been well-studied in the literature and applied with various structural and dynamical systems, is discussed. The linear vibration absorbers such as TMDs are widely used in real-life small- and large-scale structures due to their robust performance in vibration suppression of the low natural frequency structural modes. However, the TMD performs efficiently at narrowband frequency range where its performance is deteriorated by any changes in the frequency content in the structure and the TMD itself. Therefore, the targeted-energy-transfer mechanism which is found to be achieved by nonlinear energy sinks (NESs) has ignited the interest in passive nonlinear vibration suppression. Unlike TMDs, the NESs are dynamical vibration absorbers that achieve vibration suppression for wide range of frequency-energy levels. Given the very rapid growth in this field and the extensive research studies supporting the robustness of the NESs, this paper presents the different types of NESs and their applications with main emphasis on the rotary-based and impact-based NESs since they are of high impact in the literature due to their strong nonlinear dynamical behavior and robust targeted energy transfer.

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“…The FEPs of Hamiltonian versions of linear systems attached to NESs with odd-power stiffness coupling have been generated in several publications using analytical and numerical methods [1][2][3][4][5][43][44][45][46][47][48]. Similarly, FEPs of linear systems attached to rotating NES were obtained in [22,23] and systems attached to vibro-impact and piecewise NESs in [49][50][51][52][53]. In these sets of publications, fundamental backbone curves of 1:1 inphase and antiphase resonances were obtained.…”

Section: Introductionmentioning

confidence: 99%

Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator

AL-Shudeifat

Saeed

2021

Nonlinear Dyn

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The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been has been employed for vibration mitigation in many primary small-and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as Bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency-energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in-and out of-phase backbone branches, especially at low energy levels. The wavelet transform is imposed into the FEP for variety of initial conditions and damping content and it is found that the FEP has backbone branches at low energy levels associated with the oscillation of the bistable attachments about one of its stable equilibrium positions where passage through the unstable equilibrium position does not occur.

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Periodic orbits of a conservative 2-DOF vibro-impact system by piecewise continuation: bifurcations and fractals

Cited by 42 publications

References 32 publications

D’Alembert function for exact non-smooth modal analysis of the bar in unilateral contact

D’Alembert function for exact non-smooth modal analysis of the bar in unilateral contact

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator

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