1∶1内共振对随机振动系统可靠性的影响  

THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM

作　　者：王浩宇[1] 吴勇军[1] 

机构地区：[1]上海交通大学工程力学系,上海200240

出　　处：《力学学报》2015年第5期807-813,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(11272201;11372271;11132007)~~

摘　　要：研究了二自由度耦合非线性随机振动系统在高斯白噪声激励下基于首次穿越模型的可靠性问题.在1∶1内共振情形,原始系统的运动方程经平均后化为一组关于慢变量的伊藤随机微分方程.建立了后向柯尔莫哥洛夫方程以及庞德辽金方程,在一定的边界条件和(或)初始条件下求解这两个偏微分方程,分别得到系统的条件可靠性函数以及平均首次穿越时间.进而建立了无内共振情形系统的后向柯尔莫哥洛夫方程与庞德辽金方程.将无内共振情形的结果与1∶1内共振情形的结果做比较,发现1∶1内共振能显著降低系统可靠性.用蒙特卡罗数值模拟验证了理论结果的有效性.Based on first-passage model, the reliability problem of two degrees-of-freedom random vibration system under Gaussian white noise excitations is studied analytically. In the case of 1 ： 1 internal resonance, the equations of motion of the original system are reduced to a set of Ito stochastic differential equations after averaging. The backward Kolmogorov equation and the Pontryagin equation, which determine the conditional reliability function and the mean first-passage time of the random vibration systems, are constructed under appropriate boundary and （or） initial conditions, respectively. To study the influence of the internal resonance on the reliability, the averaged It6 stochastic differential equations, the backward Kolmogorov equation and the Pontryagin equation in the case of non-internal resonance are also derived. Numerical solutions of high-dimensional backward Kolmogorov equation and Pontryagin equation are obtained. The results of resonant case and non-resonant case are compared. It is shown that 1 ： 1 internal resonance can greatly reduce the reliability. All the analytical results are validated by Monte Carlo digital simulation.

关 键 词：1:1内共振 平均法 可靠性函数 平均首次穿越时间 数值模拟 

分 类 号：O322[理学—一般力学与力学基础] O324[理学—力学]