单层网壳结构动力稳定性分析方法

本文系统分析了单层网壳结构动力稳定性的研究方法。论证了对于在复杂荷载作用下非线性、多自由度复杂结构的动力稳定性问题,基于严格数学定义的Lyapunov运动稳定性理论目前尚不能提供有效的判别准则。通过理论分析和计算指出“刚度矩阵的正定与负定”不足以判定结构是否动力失稳。提出了动力响应全过程曲线的概念,并以此曲线为基础结合结构的时程响应曲线来判定网壳结构的动力稳定性。通过对不同类型荷载、不同计算条件下的网壳结构的弹性和弹塑性动力稳定性的分析,验证了本文所提判别方法的合理性。

Analysis method of dynamic stability of single-layer reticulated domes

Some research methods of dynamic stability of single layer reticulated domes are discussed. Theoretical investigation is made using the Lyapunov dynamic stability theory, and it has been found that the dynamic instability could not be fully characterized by the negative tangent stiffness of MDOF system. The negative tangent stiffness is not a sufficient condition for the judgment of dynamic instability. It is difficult to research dynamic stability of single layer reticulated domes under earthquake actions by the Lyapunov dynamic stability theory. Thus, a practical method for researching dynamic stability of single layer reticulated domes is presented. A panoramic dynamic response curve is set up for dynamic stability research that can be utilized with time history response curves of structure together. The method is verified by elastic and plastic dynamic stability analysis of some prototype reticulated domes with various kinds of loading conditions.