基于测量试验数据修正有限元模型质量矩阵

对无阻尼结构系统有限元模型质量矩阵修正问题,以该矩阵修正量的F-范数为目标函数,并以待修正质量矩阵应具有的性质,如满足正交关系,对称性,半正定性和稀疏性作为约束条件,数学上形成带约束的矩阵最佳逼近问题。给出了问题有解的条件,基于循环投影方法,提出了求解矩阵最佳逼近问题的数值方法。数值结果说明了所给方法的有效性。

Mass Matrix Correction of Finite Element Model Using Measured Test Data

For problem of correcting mass matrix of finite element model of undamped structural systems, the desired mass matrix properties, including orthogonality relation, symmetry, positive semi definiteness and sparsity, are imposed as side constraints to form mathematically the optimal matrix approximation problems. The solvability conditions for the problems are presented. Based on the cyclic projection method, numerical methods are proposed for solving the matrix nearness problems. Numerical results show that the proposed methods are efficient.