确定性周期与随机激励联合作用下非线性系统非平稳响应的统计线性化方法

作者：Kong Fan; Han Ren-Jie; Zhang Yuan-Jin

来源：Journal of Vibration Engineering, 2022, 35(3): 625-634.

DOI：10.16385/j.cnki.issn.1004-4523.2022.03.012

• Combined excitation
• Monte Carlo simulation
• Non-linear systems
• Non-stationary response
• Runge-Kutta method
• Statistical linearization

A non-stationary statistical linearization method is proposed for determining the stochastic response of non-linear single-degree-of-freedom systems, subjected to the combined periodic and non-stationary stochastic excitation. Specifically, assuming the system response as a sum of a periodic and of a zero-mean stochastic component, leads two equivalent coupled differential equations, governing the deterministic and the stochastic component, respectively. The derived stochastic sub-equation under non-stationary zero-mean stochastic excitation is cast into an equivalent linear equation, by resorting to the non-stationary statistical linearization method. The related Lyapunov equation governing the second moment of the linear stochastic response, and the deterministic sub-equation governing the periodic response, are solved simultaneously using standard numerical algorithms. Pertinent Monte Carlo simulation demonstrates the applicability and accuracy of the proposed semi-analytical method. ? 2022, Editorial Board of Journal of Vibration Engineering. All right reserved.

• 单位
  武汉理工大学; 合肥工业大学