Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism

Yang, Jian; Xiong, Yeping; Xing, Jing Tang

doi:10.1016/j.jsv.2012.08.010

Cited by 155 publications

(74 citation statements)

References 31 publications

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“…The rest is nonlinear and negative stiffness configured by the linear spring [22]. Here, one should note that the total pendulum system is not as simple as above description.…”

Section: System Modelmentioning

confidence: 95%

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Chen

2015

Nonlinear Dyn

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A compressed air generator hang under vehicle is simplified as a suspension mass connected to a vertical spring and two horizontal springs. It is configured generally as a geometrical negative stiffness to reduce dynamic stiffness. The periodic motion, chaotic motion and bifurcation of the compressed air generator model are investigated using the incremental harmonic balance method in combination with arc length continuation technique. The stability and bifurcation route are also distinguished with Floquet theory. The system exhibits a period doubling bifurcation route to chaos in different regions of excitation frequency. The stiffness ratio of the vertical spring and the horizontal spring has a significant influence on the dynamic response. When the vertical stiffness is close to the stiffness at horizontal direction, resonance occurs with the emergence of the chaotic motion. The dynamic response of the vibration system can be improved by reducing the stiffness in the horizontal direction to increase the stiffness ratio. L. Yuanping Key Lab of Disaster Forecast and Control in Engineering, Ministry of Education of the People'

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“…The rest is nonlinear and negative stiffness configured by the linear spring [22]. Here, one should note that the total pendulum system is not as simple as above description.…”

Section: System Modelmentioning

confidence: 95%

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Chen

2015

Nonlinear Dyn

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“…Then, the other parameters can be calculated according to Table 1. And the parameters for the DVA proposed in this paper can be calculated according to (31) and (32). Based on the fourth-order Runge-Kutta method, the response of the primary system without DVA and with different DVAs can be obtained.…”

Section: The Response Of the Primary System To Random Excitationmentioning

confidence: 99%

“…In 2013, Acar and Yilmaz [30] studied a new adaptively passive DVA with a negative stiffness mechanism analytically and experimentally and found that it could suppress the amplitude of the system by appropriately adjusting the parameters. Yang et al [31] investigated a nonlinear vibration isolation system with a negative stiffness mechanism. Zhu et al [32] invented a kind of negative stiffness system used in gravity compensation for tiny vibration machines.…”

Section: Introductionmentioning

confidence: 99%

Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness

Shen

Wang

Yang

et al. 2016

Mathematical Problems in Engineering

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A new type of dynamic vibration absorber (DVA) with negative stiffness is studied in detail. At first, the analytical solution of the system is obtained based on the established differential motion equation. Three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimum tuning ratio and optimum stiffness ratio of DVA are obtained by adjusting the three fixed points to the same height according to the fixed-point theory. Then, the optimum damping ratio is formulated by minimizing the maximum value of the amplitude-frequency curves according to ∞ optimization principle. According to the characteristics of negative stiffness element, the optimum negative stiffness ratio is also established and it could still keep the system stable. In the end, the comparison between the analytical and the numerical solutions verifies the correctness of the analytical solution. The comparisons with three other traditional DVAs under the harmonic and random excitations show that the presented DVA performs better in vibration absorption. This result could provide theoretical basis for optimum parameters design of similar DVAs.

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“…More than one mode could be decayed by this damped mount. Later, many literatures concerned the usage of power flow in quantifying the nonlinear vibration isolation with flexible base [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Power Flow in a Two‐Stage Nonlinear Vibration Isolation System with High‐Static‐Low‐Dynamic Stiffness

Shao

Ding

2018

Shock and Vibration

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The manuscript concerns the power flow characterization in a two-stage nonlinear vibration isolator comprising three springs, which are configured so that each stage of the system has a high-static-low-dynamic stiffness. To demonstrate the distinction of evaluation for vibration isolation using power flow, force transmissibility is used for comparison. The dynamic behavior of the isolator subject to harmonic excitation, however, is of interest here. The harmonic balance method (HBM) could be used to analyze the frequency response curve (FRC) of the strong nonlinear vibration system. A suggested stability analysis to distinguish the stable and the unstable HBM solutions is described. Increasing both upper and lower nonlinear stiffness could bend the first resonant peak to the left. The isolation range in the power and the force transmissibility plot could be extended to the lower frequencies when the nonlinear stiffness is increased, but the rate of roll-off for the power transmissibility is twice the rate for the force transmissibility at each horizontal stiffness setting. An explanation for this phenomenon is given in the paper.

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Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism

Cited by 155 publications

References 31 publications

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness

Power Flow in a Two‐Stage Nonlinear Vibration Isolation System with High‐Static‐Low‐Dynamic Stiffness

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