模态局部化及频率曲线转向现象研究的几何理论

根据复平面映射理论，详细讨论了结构振动系统的固有频率曲线在复平面的几何特点．研究表明，频率曲线重合和转向现象实际上可进行统一的几何描述．复参数平面中支点的形成是解释局部化现象和曲线转向现象的基础．利用近频摄动理论中的缩聚方法将系统降维，大大拓宽了这一几何方法的使用范围．计算实例验证了理论分析所得的结果．该文是对Ｍ．Ｓ，Ｔｒｉ－ａｎｔａｆｙｌｌｏｕ等近期工作的改进与推广．

A GEOMETRIC THEORYY IN INVESTIGATION ON MODE LOCALIZATION AND FREQUENCY LOCI VEERING PHENOMENA

According to the mapping theory in complex plane, the geometric features of eigen frequency loci of systems undergoing free vibrations are investigated. It is concluded that the phenomena of curve coalescence and veering can be described in a unified manner from the singularities of mapping from the complex parameter plane into the complex frequency plane. The formation of a branch point in the parameter space is the foundation of explaining localization and veering phenomena. By use of condensation to reduce the dimension of a system, the scope of application of the geometric theory is widely expanded. The theory is applied to examples to verify the validity of the proposed approach. The present work is an improvement and extension of recent work by M. S.Traintafyllou et al.