Gauss白噪声激励下分数阶导数系统的非平稳响应  

Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation

作　　者：李伟 赵俊锋[2] 李瑞红[1] N.特里索维奇 

机构地区：[1]西安电子科技大学数学与统计学院,西安710071 [2]西北工业大学理学院应用数学系,西安710072 [3]贝尔格莱德大学机械工程学院力学系

出　　处：《应用数学和力学》2014年第1期63-70,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11302157;11202155);中央高校基本科研业务费专项资金(K5051370008);中国与塞尔维亚科技合作项目(2-14)~~

摘　　要：研究了Gauss(高斯)白噪声激励下具有分数阶导数阻尼的非线性随机动力系统的非平稳响应.应用等价线性化方法将非线性系统转化为等价的线性系统,之后采用随机平均法获得系统响应满足的FPK(Fokker-Planck-Kolmogorov)方程,其中分数阶导数近似为一个周期函数.使用Galerkin方法求解FPK方程进而得到系统的近似非平稳响应.数值结果验证了方法的正确性和有效性.Non-stationary response of a nonlinear stochastically dynamical system with frac- tional derivative damping under Gaussian white-noise excitation was investigated. Based on the equivalent linearization method, the orial nonlinear system was converted to a linear system with respect to the vibration amplitude and phase, then the stochastic averaging method was applied to obtain the FPK equation, in which the fractional derivative was approximated by a periodic function. The approximate non-stationary response of the FPK equation was derived with Galerkin method. Numerical results verify the efficiency and correction of the proposed method.

关 键 词：非平稳响应 分数阶导数 随机平均法 GALERKIN方法 

分 类 号：O324[理学—一般力学与力学基础]