结构动力模型修正中的一类矩阵反问题

AN MATRIX INVERSE PROBLEM IN STRUCTURAL DYNAMIC MODEL UPDATING

在实际工程中,由有限元模型得到的计算值与通过试验获得的测量值之间往往存在偏差,为了能够精确预测结构的动力响应,依据测量信息修正存在的动力模型是非常必要的．本文考虑用不完备复模态测量数据修正粘性阻尼矩阵的问题．在假定分析质量矩阵与分析刚度矩阵是精确的情况下,通过求解一个约束最优化问题,得到了满足特征方程的加权Frobenius范数意义下的最优对称非负定修正矩阵．

There is a gap between predictions resulting from finite element model （FEM） and experimental results of a testing moelel or actual structure. Updating the existing dynamic model based on modal measured data is very important in order to predict actual behaviors of the structure precisely via the structural dynamic model. In this paper, the analytical mass and stiffness matrices are assumed correct and only the viscous damping matrix needs to be updated. By solving a constrained optimization problem, the optimal corrected semi-positive definite damping matrix complied with the required eigenvalue equation is found under a weighted Frobenius norm sense.