Physical parameter identification method of vibration system based on minimum correction value method
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摘要: 在分析振型矩阵关于质量和刚度矩阵加权正交性的基础上, 利用振动频率和振型数据识别系统物理参数的最小修正量, 借助Lagrange乘子法, 求解约束条件下的质量与刚度矩阵误差加权范数为最小的优化问题, 提出了以实测模态参数为基准的振系物理参数识别的计算方法, 推导了完整和非完整2种试验模态参数情形下的物理参数识别计算表达式, 给出了迭代算法, 并对4自由度系统进行了模态试验及数值分析。分析结果表明: 刚度矩阵和质量矩阵与真值非常接近, 最大误差分别为0.086%和0.34%, 因此, 提出的方法具有很高的可靠性。Abstract: Based on the orthogonality of the vibration modal matrix with respect to the mass and stiffness matrices for vibration system, the minimum correction values of physical parameters for vibration system were identified by vibration frequency and model.The optimization problem of vibration system with restrictions was solved by Lagrange multipler.A physical parameter identification method was proposed based on measured modal data.The formulae of physical parameter identification for holonomic and nonholonomic modal parameters were educed.An iterative arithmetic was given.The modal experiment and numerical analysis of a vibration system with 4 DOFs were carried out.Analysis result shows that the mass and stiffness matrices approach their real values, their maxmum errors are 0.34% and 0.086% respectively, so the method has high reliability.
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