基于测量试验数据修正有限元模型质量矩阵

摘要

For problem of correcting mass matrix of finite element model of undamped structural sys-tems ,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 ap-proximation 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 .Numeri-cal results show that the proposed methods are efficient .%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.