随机杜芬振子动力响应的摄动解  

Perturbation Solution for Dynamic Response of a Stochastic Duffing Oscillator

作　　者：高志远 GAO Zhi-yuan(Department of Civil and Traffic Engineering,Yellow River Conservancy Technical Institute,Kaifeng 475004,China)

机构地区：[1]黄河水利职业技术学院土木与交通工程学院,开封475004

出　　处：《建材世界》2025年第2期66-69,共4页The World of Building Materials

摘　　要：论文使用随机摄动法求解含有不确定性参数的非线性杜芬振子在外部激励下的动力响应。考虑实际运动过程中杜芬振子弹性模量k的随机性,建立随机杜芬振子的运动平衡方程,通过摄动法计算方程的解并进行统计分析,与蒙特卡洛模拟法(10000次样本)结果进行对比。数值算例表明,二阶摄动法有较高的计算精度,同时相较于蒙特卡洛模拟法其计算效率显著提高。This study utilizes a stochastic perturbation approach to investigate the dynamic behavior of a nonlinear Duffing oscillator with uncertain parameters under external excitation.The randomness of the elasticity modulus k of the oscillator is taken into account,leading to the derivation of the governing equation of motion for the system.The perturbation method is employed to obtain the solution,followed by a statistical analysis.The results are subsequently compared with those derived from Monte Carlo simulations(10000 samples).Numerical simulations indicate that the second-order perturbation method yields accurate results.Additionally,it significantly reduces the computational time compared to the Monte Carlo approach.

关 键 词：杜芬振子 随机变量 蒙特卡洛 摄动法 

分 类 号：O322[理学—一般力学与力学基础]