Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems

Lang, Zi–Qiang; Jing, Xingjian; Billings, S.A.; Tomlinson, G.R.; Peng, Z.K.

doi:10.1016/j.jsv.2009.01.001

Cited by 126 publications

(64 citation statements)

References 13 publications

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“…Early studies [1] showed that the implementation of nonlinear damping may bring improvements to the isolation performance of a lightly linear damped isolator by suppressing its resonance amplitude without degrading its high-frequency isolation efficiency. Recent rigorous theoretical works [2][3][4][5] also pointed out that the cubic nonlinear damping (denoted as the first type of nonlinear damping in this paper), i.e., f I d ∝ṙ 3 ( f I d is the damping force andṙ denotes the relative velocity), can suppress the resonance amplitude while keep the force transmissibility almost unchanged at low or high frequencies for a singledegree-of-freedom (SDOF) isolator. This concept was also extended to the study of multi-degree-of-freedom (MDOF) isolation problems by Peng [6] and Lang [7].…”

Section: Introductionmentioning

confidence: 88%

“…As the isolator subjected to harmonic excitation and considered with sufficient linear damping (e.g., with a linear modal damping of 0.1-0.3), the primary harmonic term can be assumed to dominate its steady-state response [25][26][27], i.e., r ≈ Im Re jϕ (3) where R denotes the complex response of the nonlinear secondary spring, ϕ denotes its generic angle and j is the imaginary unit.…”

Section: Description Of Nonlinear Zener Modelmentioning

confidence: 99%

“…As been discussed above, in order to simultaneously meet the requirements of low resonance amplitude and good isolation performance at high-frequency range, these scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] studied the lightly damped or even no damped linear isolators (already have good isolation efficiency at high frequencies) and added nonlinear damping elements to improve their poor resonance performances. While in this paper, we develop another novel way by presenting a sufficient damped isolator (naturally owns low resonance amplitude) and employ a nonlinear spring to reduce its vibration transmissibility at high frequencies without deteriorating its resonance performance.…”

Section: Introductionmentioning

confidence: 99%

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Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

2016

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In order to obtain an isolator with low resonance amplitude as well as good isolation performance at high frequencies, this paper explores the usage of nonlinear stiffness elements to improve the transmissibility efficiency of a sufficient linear damped vibration isolator featured with the Zener model. More specifically, we intend to improve its original poor highfrequency isolation performance and meanwhile maintain or even reduce its already low resonance amplitude by adding a nonlinear secondary spring into the isolator. Its isolation performances are evaluated under two input scenarios namely force transmissibility under force input and displacement transmissibility under base excitations, respectively. Thereafter, both analytical and numerical study is performed to compare the high-frequency transmissibility as well as resonance condition of the nonlinear isolator with its corresponding linear one. Results show that the introduction of nonlinear secondary spring in the Zener model can achieve an ideal improvement, i.e., reducing the transmissibility at high frequencies and meanwhile suppressing the resonance amplitude. It is also shown that both force and displacement transmissibility of the non-

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Section: Introductionmentioning

confidence: 88%

Section: Description Of Nonlinear Zener Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

2016

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“…If the damper is linear, there is a well-known trade-off between choosing a high damping coefficient, to control the response at resonance, and choosing a low damping coefficient, to reduce the vibration transmission well above resonance [37]. A number of methods of overcoming this problem have been suggested, including the use of cubic nonlinear dampers [38]. When driven one frequency at a time, cubic damping will produce a high equivalent linear damping value at resonance, when the response level is high, but a low equivalent linear damping value at excitation frequencies well above resonance, where the response level is low, as required.…”

Section: (B) Vibration Isolationmentioning

confidence: 99%

Nonlinear damping and quasi-linear modelling

Elliott

Tehrani

Langley

2015

Phil. Trans. R. Soc. A.

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The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a ‘quasi-linear’ model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the n th power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system’s response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea.

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“…For example, Peng and Lang [21] have derived a recursive algorithm to determine the structure of the OFRF for the system described by a nonlinear differential equation model. More recently, the OFRF based approach has been applied in the analysis and design of nonlinear vibration isolators [22][23][24]. For example, by using the OFRF, Lang et al [22] and Peng et al [23] have rigorously proved significant beneficial effects of nonlinear damping on vibration isolation systems.…”

Section: Introductionmentioning

confidence: 99%

Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

Zhu

Lang

2018

IEEE Trans. Contr. Syst. Technol.

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Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems

Cited by 126 publications

References 13 publications

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

Nonlinear damping and quasi-linear modelling

Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

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