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应用拓广的随机因子法分析了物理参数和几何参数均为随机变量的齿轮-转子系统的时变固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同随机因子的矩阵之和的形式,再由求解系统固有频率的瑞利商公式出发,将系统频率展成部分频率分量之和的形式,利用求解随机函数数字特征的代数综合法求解系统固有频率的数字特征。通过算例分析了随机参数对系统固有频率的影响,并验证了方法的可行、有效和正确性。
The random variable method is used to analyze the time-dependent natural frequency of gear-rotor system whose physical parameters and geometric parameters are both random variables. The stiffness and mass matrices of the system are decomposed into the form of the sum of the matrices with the same random factor. Based on the Rayleigh quotient formula for solving the natural frequency of the system, the system frequency is developed into the form of the sum of the partial frequency components, Algebra Synthesis Method for Digital Feature of Function Solves Digital Feature of Natural Frequency of System. An example is given to analyze the influence of random parameters on the natural frequency of the system, and the feasibility, validity and correctness of the method are verified.