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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。
On the basis of analyzing the weighted orthogonality of the vibration mode matrix with respect to the mass and stiffness matrix, the minimum correction of the physical parameters of the system is identified by using the vibration frequency and mode shape data. The Lagrange multiplier method is used to solve the error of mass and stiffness matrix The weight norm is the minimum optimization problem, the method to calculate the physical parameters of vibrating system based on the measured modal parameters is proposed, and the expressions of the physical parameters identification are deduced under the condition of complete and incomplete experimental modal parameters. An iterative algorithm is given and modal tests and numerical analysis are carried out on a 4 DOF system. The analysis results show that the stiffness matrix and the mass matrix are very close to the true values, and the maximum errors are 0.086% and 0.34% respectively. Therefore, the proposed method has high reliability.