基于建模误差位置识别的有限元模型修正方法

提出了一种修正有限元模型的方法。将模型修正分为两步，首先用矩阵型方法求出系统质量、刚度矩阵的误差矩阵，通过定义的误差百分比确定建模误差位置；然后针对建模误差比较大的单元（子结构）依据特征方程和固有振型对质量矩阵的加权正交条件建立参数修正方程组，方程求解采用奇异值分解法。算例表明它能有效地避免先前方法中参数修正的盲目性，修改结果物理意义明确，精度较好。

Modification of Finite Element Model Based on Identified Error Locations

A new method to modify the finite element model from incomplete modal data is presented. The process can be divided into two steps. First, the error matrices of structural system are figured out by matrix method, and the modeling errors can be located by defining percentage error. Then the equations of parameter modification for the elements (substructures) with more modeling errors are deduced according to characteristic equation and weighting orthogonality conditions of mode shapes to mass matrix. Those equations are solved by singular decomposition. Numerical examples show that the blindness of parameter modification in current methods is avoided, and the influences of errors of the test modal data, especially random errors of mode shapes, are depressed effectively.