模态分析与动态子结构方法新进展

综述在模态分析与动态子结构 方法研究的一些最新进展.首先回顾经典的位移展开定理和模态叠加原理.为了加速 经典方法的收敛速度、提高计算效率, 进一步介绍两个新的结构位移展开定理(采用 固定界面模态的位移展开新定理, 给出采用低阶固定界面模态的高精度位移展开式; 采用混合模态的位移展开新定理, 给出采用低阶混合模态表示的高精度位移展开式) 和相应的动力学新解法.相应上述3个位移展开定理, 介绍采用解析推导的方法构造 出3类 动态精确子结构方法, 各种子结构模态综合法实质上都是它们的某种近似与变化形式, 从而 形成系统的动态子结构分析技术.上述介绍的模态分析与动态子结构方法新进展与经典模态分析技术一起形成 结构动力学分析技术的系统理论.

THE RESENT PROGRESSES ON MODAL ANALYSIS AND DYNAMIC SUB-STRUCTURE METHODS

The progresses on analytical modal analysis and dynamical sub-structure methods are reviewed in this paper. The classical displacement expansion theorem and the modal aggregation principle are discussed at the beginning of the paper. In order to accelerate the classical method's convergence rate and to improve the efficiency of the calculation, two new structure displacement expansion theorems are introduced. Corresponding to the above three displacements expansion theorems, three exact methods sub-structure are introduced. It is shown that all kinds of sub-structure methods can be regarded as the variations of the above exact methods. Therefore, systematical analytical sub-structure techniques can be constructed based on these three theorems. It can be summarized as follows: The exact dynamic sub-structure method using the free interface mode can be derived from the free interface modal displacement expansion theorem, hence high precision free interface modal synthesis methods ca,n be developed. The exact dynamic sub-structure method using the fixed mode can be derived from the fixed modal displacement expansion theorem, hence high precision fixed interface modal synthesis methods can be developed. The exact dynamic sub-structure method using the mixed mode can be interface derived from the mixed modal displacement expansion theorem, hence high precision mixed modal synthesis methods can be developed. These modal analysis techniques, dynamic sub-structure methods and the classical structural dynamics analysis techniques form a complete theory for the analysis of structural dynamics.