Extracting the Coupled Dynamics in Thin-Walled Beams from Numerical Data Bases
Authors: Mohammad A. Bani-Khaled
In this work we use the Discrete Proper Orthogonal Decomposition transform to characterize the properties of coupled dynamics in thin-walled beams by exploiting numerical simulations obtained from finite element simulations. The outcomes of the will improve our understanding of the linear and nonlinear coupled behavior of thin-walled beams structures. Thin-walled beams have widespread usage in modern engineering application in both large scale structures (aeronautical structures), as well as in nano-structures (nano-tubes). Therefore, detailed knowledge in regard to the properties of coupled vibrations and buckling in these structures are of great interest in the research community. Due to the geometric complexity in the overall structure and in particular in the cross-sections it is necessary to involve computational mechanics to numerically simulate the dynamics. In using numerical computational techniques, it is not necessary to over simplify a model in order to solve the equations of motions. Computational dynamics methods produce databases of controlled resolution in time and space. These numerical databases contain information on the properties of the coupled dynamics. In order to extract the system dynamic properties and strength of coupling among the various fields of the motion, processing techniques are required. Time- Proper Orthogonal Decomposition transform is a powerful tool for processing databases for the dynamics. It will be used to study the coupled dynamics of thin-walled basic structures. These structures are ideal to form a basis for a systematic study of coupled dynamics in structures of complex geometry.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1128038Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 746
 Banerjee, J., R., Guo, S., Howson, W., P., 1997: Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping. Journal Computers and Structures, 59, 613-621.
 Bathe, K., 1995: Finite Element Procedures. Prentice Hall.
 Bishop, R. E., Johnson, D., 1979: The mechanics of vibrations. Cambridge University Press.
 Dokumaci, E. 1987: An exact solution for coupled bending and torsional vibrations of uniform beams having single cross-section symmetry. Journal of Sound And Vibration, 119, 443-449.
 Friberg, P., O., 1993: Coupled vibration of beams, an exact dynamic element stiffness matrix. International Journal of Numerical Methods in Engineering, 19, 479-493.
 Georgiou, I. T., and Schwartz, I.B., 1999,”Dynamics of Large Scale Coupled Structural/Mechanical System: A Singular Perturbation/Proper Orthogonal Decomposition Approach”, J. Appl. Math. (SIAM), Vol.59, No.4, pp. 1178-1207.
 Georgiou, I. T., Bani-Khaled, M. A., 2004: Identifying the shapes of coupled vibrations and deriving reduced order models for nonlinear shafts: a Finite Element-Proper Orthogonal Decomposition Approach. ASME International Mechanical Engineering Congress & Exposition Anaheim, California.
 Georgiou, I.T., Advanced Proper Orthogonal Decomposition Tools: Using Reduced Order Models to Identify Normal Modes of Vibration and Slow Invariant Manifolds in the Dynamics of Planar Nonlinear Rods. Nonlinear Dynamics, August, Volume 41, Issue 1-3, pp 69-110, 2005
 Georgiou, I. T. and Sansour, J., 1998 ,”Analyzing the Finite Element Dynamics of Nonlinear In-plane Rod by the Method of Proper Orthogonal Decomposition,” Computational Mechanics, New Trends and Applications, S.Idelsohn, E.Onate, and E. Dvorkin, eds., CIMNE, Barcelona, Spain.
 Jun, Li., Wanyou, Li., Rongying, S., Hongxing, H., 2004: Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli-Euler beams, Mechanics Research Communications. 31, 697-711.
 Tanaka, M., Bercin, A., N., 1999: Free vibration solution for uniform beams of nonsymmetrical cross-section using Mathematica. Journal Computers And Structures. 71, 1-8.
 Vlasov, V., Z., 1961: Thin-walled elastic beams, National Science Foundation and Department of Commerce.