《剩余质量阵和剩余刚度阵的近似计算方法》

在模态综合法中，剩余质量阵和剩余刚度阵的计算通常依赖于子结构的质量阵和刚度阵，由于几乎不可能通过实验方法得到子结构的质量阵和刚度阵，因此很难将实验数据应用于理论模态综合法中。针对这一困难，通过分析剩余质量阵和刚度阵的表达式，推导出它们的近似计算公式，这一近似计算公式中不含质量阵和刚度阵，亦即不需要事先知道质量阵和刚度阵就可以计算剩余质量阵和剩余刚度阵，从而回避实验辨识质量阵和刚度阵这一极具挑战的动力学反问题，克服实验模态综合法应用中的困难。数值计算表明，所提的剩余质量阵和剩余刚度阵的近似计算方法切实可行，且模态综合结果具有较高的精度。

An Approximated Method for Calculating Residual Mass Matrix and Residual Stiffness Matrix

A difficulty encountered when using theoretical component mode synthesis method with purely experimental data is that mass matrix and stiffness matrix are necessary in order to take the residual inertia relief attachment modes into account. Yet the mass matrix and stiffness matrix of a substructure are not always available from an experimental approach. To overcome this difficulty, the approximated expressions for the residual mass matrix and residual stiffness matrix are proposed in which the mass matrix and stiffness matrix are not needed. An improved CMS formulation is then developed for the case when taking the experimental data into account. It is based on the same formulation normally used when using analytical data. However, no need exists anymore to have the mass matrix and stiffness matrix of the substructures at the same time accounting for the residual inertia relief attachment modes. The accuracy and efficiency of the proposed CMS method are proved by a numerical example.