Vibration Responses of Rubber Tires With Fractional Damping Under Stochastic Excitation

FAN Yuan-qin; XU Wei; HAN Qun; YANG Yong-ge

doi:10.3879/j.issn.1000-0887.2014.12.005

Volume 35 Issue 12

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FAN Yuan-qin, XU Wei, HAN Qun, YANG Yong-ge. Vibration Responses of Rubber Tires With Fractional Damping Under Stochastic Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1330-1340. doi: 10.3879/j.issn.1000-0887.2014.12.005

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Vibration Responses of Rubber Tires With Fractional Damping Under Stochastic Excitation

doi: 10.3879/j.issn.1000-0887.2014.12.005

Department of Applied Mathematics, Northwestern Polytechnical University,Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11172233；11302169）

Received Date: 2014-05-13
Rev Recd Date: 2014-11-04
Publish Date: 2014-12-15

Abstract

Abstract

The vertical dynamic responses of rubber tires with fractional damping under the KanaiTajimi noise excitation were investigated with the stochastic averaging method. Firstly, the earthquake wave was approximated with the KanaiTajimi noise, and the differential equation for tire vibration was established through combination of the point contact model with the fractional derivative model. Then, the stochastic averaging method was used to solve the stationary probability density analytically. In turn, validity of the proposed method was verified against the MonteCarlo numerical simulation results. The probability density was applied to determine the mean values and variances of vibration displacements of the 2 kinds of tires made of polybutadiene and butyl B252 rubbers, respectively. The results show that the mean value and variance of vibration displacement increase with the rubber’s storage modulus and decrease with its dissipation modulus. That means, the lower the rubber’s storage modulus is or the higher its dissipation modulus is, the better the vibration damping effect of the resulting tire will be. The work provides a theoretical reference for the design and manufacture of rubber tires.
- fractional damping,
- rubber material,
- stochastic averaging method,
- viscoelastic material

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References(25)

References

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