Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

doi:10.1088/1674-1056/28/1/010203

中国物理B ›› 2019, Vol. 28 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/28/1/010203

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

Deli Wang(王德莉), Wei Xu(徐伟), Xudong Gu(谷旭东)

1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2018-06-29 修回日期:2018-11-13 出版日期:2019-01-05 发布日期:2019-01-05
通讯作者: Wei Xu E-mail:weixu@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11872305 and 11872307) and the Excellent Doctorate Cultivating Foundation of Northwestern Polytechnical University, China.

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

Deli Wang(王德莉)¹, Wei Xu(徐伟)¹, Xudong Gu(谷旭东)²

1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2018-06-29 Revised:2018-11-13 Online:2019-01-05 Published:2019-01-05
Contact: Wei Xu E-mail:weixu@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11872305 and 11872307) and the Excellent Doctorate Cultivating Foundation of Northwestern Polytechnical University, China.

摘要/Abstract

摘要：

The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact (VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope (SAEE) is adopted to seek the stationary probability density functions (PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo (MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.

关键词: viscoelastic system, right unilateral nonzero offset barrier impacts, stochastic averaging of energy envelope (SAEE), stochastic P-bifurcation

Abstract:

Key words: viscoelastic system, right unilateral nonzero offset barrier impacts, stochastic averaging of energy envelope (SAEE), stochastic P-bifurcation

中图分类号: (Probability theory)

02.50.Cw

02.50.Ng (Distribution theory and Monte Carlo studies) 05.10.Gg (Stochastic analysis methods) 05.40.Ca (Noise)

王德莉, 徐伟, 谷旭东. Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts[J]. 中国物理B, 2019, 28(1): 10203-010203.

Deli Wang(王德莉), Wei Xu(徐伟), Xudong Gu(谷旭东). Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts[J]. Chin. Phys. B, 2019, 28(1): 10203-010203.

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Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

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