基于不完全模态测量数据的粘性阻尼矩阵的修正

Updating Viscous Damping Matrix Based on Incomplete Complex Modal Measured Data

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,依据测量模态数据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 are certain errors between the prediction from the finite element model and the experimental results from the test model or an actual structure. Updating the existing structural dynamic model based on the measured modal data is very important in predicting the actual behaviors of the structure precisely. The analytical mass and stiffness matrices are assumed correct and only the viscous damping matrix needs to be updated in this paper. 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.