谐和与随机噪声联合作用下的粘弹系统

基金项目: 国家自然科学基金资助项目(10072049)

Visco-Elastic Systems Under Both Deterministic Harmonic and Random Excitation

1.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2.
Department of Applied Mathematics, Foshan University, Foshan, Guangdong 528000, China;
3.
Institute of Vibration Engineering, Northwestern Polytechnical University,Xi'an 710072, China

摘要: 研究了粘弹系统在谐和与随机噪声联合作用下的响应和稳定性问题.用谐波平衡法和随机平均法分析了系统在确定性谐和激励和随机激励联合作用下的响应,讨论了粘弹项、随机扰动项对系统响应的影响.结果表明,在一定条件下,系统具有两个均方响应值和跳跃现象.数值模拟表明,谐波平衡法与随机平均法相结合的研究方法是有效的.
- 粘弹系统 /
- 谐波平衡法 /
- 随机平均法
Abstract: The response of visco-elastic system to combined deterministic harmonic and random excitation was investigated. The method of harmonic balance and the method of stochastic averaging were used to determine the response of the system. The theoretical analysis was verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increase, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exist.
- visco-elastic system /
- method of harmonic balance /
- method of stochastic averaging

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