摘要
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 onto the complex frequency plane. The formation of a branch point in the parameter Space is the foundation of explaining localization and veering phenomena. By the 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..
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 onto the complex frequency plane. The formation of a branch point in the parameter Space is the foundation of explaining localization and veering phenomena. By the 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..
基金
This work was partially supported by the NNSFC and the ASFC.
