Abstract
Purpose
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 Flügge’s classic thin shell theory.
Methods
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.
Results
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.
Similar content being viewed by others
References
Leissa AW (1993) Vibration of Shells (NASA SP 288). US Government Printing Office, Washington, D.C.
Chandra Mohan Rao BDV, Ramana Rao NV (2012) Free vibration analysis and optimization of cylindrical shells. Adv Vib Eng 11(3):325–336
Yang J, Fu Y, Li C (2007) Analysis of nonlinear vibration for axisymmetrical laminated cylindrical shells with delamination. Adv Vib Eng 6(4):281–292
Umadi Kiran M, Kamat SM, Badari Narayana K (2009) Free vibration and buckling characteristics of different cylindrical constructions—an analytical approach. Adv Vib Eng 8(1):41–58
Singh BN, Yadav D, Iyengar NGR (2002) Free vibration analysis of laminated cross-ply cylindrical panels with random material properties. Adv Vib Eng 1(3):285–296
Montgomery DC, Runger GC (2003) Applied statistics and probability for engineers. Wiley, New York, USA
Bouveyron C, Brunet-Saumard C (2014) Model-based clustering of high-dimensional data: a review. Comput Stat Data Anal 71(1):52–78
Battiti R, Brunato M (2013) The LION way: machine learning plus intelligent optimization. Lionsolver Inc, Los Angeles, USA
Hair JF, Black WC, Babin BJ (2010) Multivariate data analysis. Pearson Prentice Hall, Upper Saddle River, New York, USA
Johnson RA, Wichern DW (2007) Applied multivariate statistical analysis. Prentice Hall, Upper Saddle River, New York, USA
Nisbet R, Elder J, Miner C (2009) Handbook of statistical analysis and data mining applications, Elsevier Inc, London UK
Timm NH (2001) Applied multivariate analysis. Springer, New York, USA
Kohonen T (2001) Self-organizing maps. Springer, New York, USA
Lee JA, Verleysen M (2007). Nonlinear dimensionality reduction. Springer, New York, USA
Flügge (1973) Stresses in shells. Springer, Berlin
Guodao S, Yingcai W, Ronghua L, Shixia L (2013) A survey of visual analytics techniques and applications: state-of-the-art research and future challenges. J Comput Sci Technol 28(5):852–867
Kohonen T (2013) Essentials of the self-organizing map. Neural Netw 37(1):52–65
Vesanto J (2002) Data exploration process based on the self-organizing map. Helsinki University of Technology, Espoo
Polzlbauer G (2008) Advanced data exploration methods based on self-organizing maps. Vienna University of Technology, Vienna
Polzlbauer G, Dittenbach M, Rauber A (2006) Advanced visualization of self-organizing maps with vector fields. Neural Netw 19(6–7):911–922
Ultsch A, Siemon HP (1990) Kohonen’s self-organizing feature maps for exploratory data analysis. In: Proceedings of the International Neural Network Conference (INNC’90), Klumer
Polzlbauer G, Rauber A (2005) Graph projection techniques for self-organizing maps. In: European Symposium on Artificial Neural Networks
Ultsch A (2003) Maps for the visualization of high-dimensional data spaces. In: Proceedings of the Workshop on Self Organizing Maps
Ultsch A (2003) U*-Matrix: a tool to visualize clusters in high dimensional Data. University of Marburg, Marburg
Ultsch A (2005) U*C: self-organizied clustering with emergent feature maps. University of Marburg, Marburg
Pampalk E, Dixon S, Widmer G (2004) Exploring music collections by browsing different views. Comput Music J 28(2):49–60
Jain AK, Dubes RC (1988) Clustering algorithms. Prentice Hall, Upper Saddle River
Nanda SJ, Panda G (2014) A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm Evol Comput 16(1):1–18
Jolliffe IT (2002) Principal component analysis. Springer, New York, USA
Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(22):2319–2323
Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(22):2323–2326
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396
Borg I, Groenen PJF (2005) Modern multidimensional scaling, theory and applications, 2nd edn. Springer, New York, USA
Sammon JW (1969) A nonlinear mapping algorithm for data structure analysis. IEEE Trans Comput 18(5):401–409
Demartines P, Herault J (1995) CCA: curvilinear component analysis. In: 15th Workshop GRETSI
Vesanto J, Alhoniemi E (2000) Clustering of the self-organizing map. IEEE Trans Neural Netw 11(3):586–600
Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Recog Mach Intell 1(2):224–227
Bauer H, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans Neural 3(4):570–579
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhiqiang, W., Xuebin, L. & Lihua, H. Vibration Studies of Circular Cylindrical Shells Using Self-Organizing Maps (SOM) Approach and Multivariate Analysis. J. Vib. Eng. Technol. 6, 387–399 (2018). https://doi.org/10.1007/s42417-018-0052-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42417-018-0052-1