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建立了考虑物理参数和几何参数均为随机变量的齿轮-转子扭转振动系统在随机荷载激励下的动力学方程.利用Newmark-β逐步积分法将此随机参数时变刚度系统的动力学方程转换为拟静力学控制方程.利用求解随机变量函数数字特征的矩法,导出了系统动态位移反应的均值和方差计算公式.通过算例得出了:系统的时变刚度对系统响应有冲击作用,系统的物理参数、几何参数和外荷载幅值的随机性对系统动力响应的影响不可忽略,其中几何参数的随机性对系统位移响应的随机性影响较大.
The dynamic equation of gear-rotor torsional vibration system under random load excitation considering both physical and geometrical parameters is established. By using Newmark-β step-by-step integration method, the dynamic equation of the system is transformed into Quasi-static control equations are derived by using the moment method for solving the numerical feature of random variable function. The formulas for calculating the mean and variance of the system dynamic displacement response are derived. The calculated results show that the time-varying stiffness of the system has an impact on the system response, The influence of the physical parameters, the geometric parameters and the randomness of the external load amplitude on the system dynamic response can not be ignored. The randomness of the geometric parameters has a great influence on the randomness of the system displacement response.