期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2012.0037
关键词
group theory; symmetry; structural mechanics; vibration; natural frequency; mode
资金
- National Research Foundation of South Africa
Group theory has been used to study various problems in physics and chemistry for many years. Relatively recently, applications have emerged in engineering, where problems of the vibration, bifurcation and stability of systems exhibiting symmetry have been studied. From an engineering perspective, the main attraction of group-theoretic methods has been their potential to reduce computational effort in the analysis of large-scale problems. In this paper, we focus on vibration problems in structural mechanics and reveal some of the insights and qualitative benefits that group theory affords. These include an appreciation of all the possible symmetries of modes of vibration, the prediction of the number of modes of a given symmetry type, the identification of modes associated with the same frequencies, the prediction of nodal lines and stationary points of a vibrating system, and the untangling of clustered frequencies.
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