Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input

Jing, Xingjian; Lang, Zi–Qiang

doi:10.1007/s11071-009-9493-0

Cited by 73 publications

(40 citation statements)

References 25 publications

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“…However, nonlinear damping is known to be significant at least in some cases. For example, the effect of nonlinear damping for the case of strictly dissipative force, being proportional to the velocity to the nth power, on the response and bifurcations of driven Duffing [55][56][57][58] and other types of nonlinear oscillators [45,57,[59][60][61] has been studied extensively. Also, nonlinear damping plays an important role in parametrically excited mechanical resonators [42,62] where without it, solutions will grow without bound [45,63].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear damping in a micromechanical oscillator

et al. 2011

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Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beamstring with a linear Voigt-Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account forall the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.

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Section: Introductionmentioning

confidence: 99%

Nonlinear damping in a micromechanical oscillator

et al. 2011

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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 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%

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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“…Should speed be multiplied by n times, the dissipated power would increase n 2 times. In addition, non-linear effects are usually present in the system [15].…”

Section: Magnetic Dampersmentioning

confidence: 99%