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本文基于模态综合超单元法和模态加速度叠加法的原理,提出了一种求解大型复杂结构动态响应的新方法。利用固定对接主模态,可使结构的副自由度全部精确地缩聚掉,大大降低求解方程的阶数。然后利用模态综合超单元法求结构系统的动态特性,最后用模态加速度叠加法求出有阻尼多自由度结构系统的动态响应值。关于结构系统阻尼如何确定,我们提出了一个新的思想。该思想以子结构为出发点。子结构的阻尼阵与子结构的刚度阵和质量阵成正比,其比例系数由试验或者以往积累的经验所确定。然后利用固定对接技术,将各子结构装配起来,就得到了整个结构系统的阻尼阵。这种处理方法的优点是明显的,因为子结构与整个结构系统相比,其阻尼是比较容易精确地确定的。应用以上提出的方法,与应用有限元技术求结构系统的整体解相比,CUP时间可大大节省,计算效率大为提高,並且具有很高的精度。又因为本文提出的方法是基于动态子结构法,所以大型复杂结构系统的动态响应计算可望在微机上进行。
Based on the principle of modal synthesis superelement method and modal acceleration superposition method, this paper proposes a new method to solve the dynamic response of large-scale complex structures. By using the fixed butt joint main mode, all the degrees of sub-degrees of freedom of the structure can be accurately condensed, and the order of the solution equation is greatly reduced. Then using the modal synthetic superelement method to find the dynamic characteristics of the structural system, and finally using the modal acceleration superposition method to obtain the dynamic response value of the damping multi-degree-of-freedom structural system. With regard to how the structural system damping is determined, we propose a new idea. The idea starts with a substructure. The damping matrix of the substructure is proportional to the stiffness matrix and the mass matrix of the substructure, and its proportionality coefficient is determined by experiments or previous accumulated experience. Then using the fixed docking technique to assemble the substructures, the damping array of the entire structural system is obtained. The advantages of this method of treatment are obvious, because the damping of the substructure compared to the entire structural system is relatively easy to determine accurately. Applying the method proposed above, compared with using the finite element technique to find the overall solution of the structural system, the CUP time can be greatly saved, the computational efficiency is greatly improved, and it has a high accuracy. Because the method proposed in this paper is based on the dynamic substructure method, the dynamic response calculation of large-scale and complex structural systems is expected to be performed on the microcomputer.