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

作     者：王德莉 徐伟 谷旭东 Deli Wang;Wei Xu;Xudong Gu

作者机构：Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’an 710072China Department of Engineering MechanicsNorthwestern Polytechnical UniversityXi’an 710072China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2019年第28卷第1期

页      面：195-204页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11872305 and 11872307) the Excellent Doctorate Cultivating Foundation of Northwestern Polytechnical University,China 

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

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.