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结构动力学有限元模型的修正对于结构动特性、动响应乃至动强度的计算都具有重要意义。用矩阵型方法进行模型修正时,由于测试模态数目较少,导致修正过程中的方程欠定,很难求解出满意的修正结果,为此提出了一种新的有限元模型刚度矩阵和质量矩阵的求解方法。从数学的角度出发,以待修正模型的质量矩阵和刚度矩阵作为修正矩阵的估计,同时利用质量矩阵和刚度矩阵的稀疏性和对称性,得到具有较高精度的修正矩阵。以简单的梁和板为例,验证了该求解方法的可行性和有效性。
Modification of structural dynamics finite element model is of great significance to the calculation of dynamic characteristics, dynamic response and dynamic strength of structures. When the model is modified by the matrix method, a new finite element model stiffness matrix is proposed because of the small number of test modes, which leads to the underdetermined equation in the correction process and difficult to find the satisfactory correction results. Solution of quality matrix. From the mathematical point of view, the mass matrix and the stiffness matrix of the model to be corrected are used as the estimation of the correction matrix, and the correction matrix with higher accuracy is obtained by using the sparsity and symmetry of the mass matrix and the stiffness matrix. Taking a simple beam and plate as an example, the feasibility and effectiveness of this method are verified.