Vibration Studies of Circular Cylindrical Shells Using Self-Organizing Maps (SOM) Approach and Multivariate Analysis

Abstract

Network and multivariate approach are employed to research the free vibration of circular cylindrical shells in present work. An analytical procedure is developed for finding the frequencies and vibration modes of circular cylindrical shells with shear diaphragm boundary conditions, based on Flugge’s classic thin shell theory. Many design samples could be obtained with the help of design of experiment technique. The information behind these design samples can be investigated by the self-organizing map (SOM) approach. SOM is a tool for data mining. It can map high-dimensional data to two-dimensional plots. When the dataset is large, the clustering of samples is needed then. The clustering of samples can be obtained by combining SOM and traditional multivariate approach, such as hierarchical and partitive techniques. The samples in different clusters would have their own characteristics. The dimension-reduction approaches are used for finding the structure of data set. The variable significance of each cluster is examined based on standard deviation. A classification method, LVQ, is also used for finding discrimination rules of vibration modes. The rules from LVQ are compared with traditional decision-tree approach.