随机参数弹性连杆在平稳随机激励下的动力可靠性分析

Dynamic Reliability Analysis of Elastic Linkage Mechanism with Stochastic Parameters under Stationary Random Excitation

研究随机参数弹性连杆机构在平稳随机激励下的动力响应分析。利用拓广的随机因子法,从求解系统固有频率的瑞利商公式出发,得出物理参数和几何参数均为随机变量的弹性连杆时变固有频率的均值和方差。从动力平稳随机响应在频域上的表达式出发,利用求解随机变量函数的矩法和数字特征的代数综合法,计算出随机参数弹性连杆机构在平稳随机激励下弹性位移和速度的均方值的均值、方差表达式,由动力可靠度的公式导出其动力可靠度的均值和方差的计算公式。通过算例,分析机构物理参数和几何尺寸的随机性对机构动力可靠度随机性的影响。

The stationary random vibration analysis of elastic linkage mechanism with random with random parameters are investigated.Based on the Rayleigh quotient formula,the expressions of the mean value and the variance of the time-variable natural frequencies of elastic linkage mechanism with random physical and geometrical parameters are educed using the generalized random factor method.From the expression of dynamic stationary random response of the frequency domain,the computational expressions of the mean value,variance and variation coefficient of the mean square value of elastic displacement and velocity responses under the stationary random excitation are developed by means of the random variable＇s functional moment method and the algebra synthesis method.And then the expressions of the mean value and the variance of system dynamic reliability are educed from the Poisson formula of calculating dynamic reliability.The influence of the random of mechanism physical and geometric dimensions parameters on the system dynamic reliability is analyzed through the examples,validating the feasibility of this method.