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B.P. Wang, S. Nomura, B.H. Dennis and K.L. Lawrence

Mechanical and Aerospace Engineering, University of Texas at Arlington, United States of America

doi:10.4203/ccp.108.244

B.P. Wang, S. Nomura, B.H. Dennis, K.L. Lawrence, "The Ritz Method for Beam Vibration Analysis Revisited", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 244, 2015. doi:10.4203/ccp.108.244

Keywords: beam vibration, Ritz method.

Summary

In this paper alternative procedures for beam vibration analysis by the Ritz method are presented. The objective is to find formulations that can be used for higher order models. The general procedures are implemented using two basis functions (monomial and poly-cosine). In addition, two approaches for imposing essential boundary conditions are studied: the null space approach ({c}-formulation) and the nodal displacement approach ({u}-formulation). The main findings are: (1) the performance of the monomial basis can be improved by the {u}-formulation, (2) the Poly-cosine basis function outperforms the monomial basis and very high order models can be used for both {c} and {u} formulations. These results are illustrated by numerical examples.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping Paper 244 The Ritz Method for Beam Vibration Analysis Revisited B.P. Wang, S. Nomura, B.H. Dennis and K.L. Lawrence Mechanical and Aerospace Engineering, University of Texas at Arlington, United States of America doi:10.4203/ccp.108.244 purchase the full-text of this paper Full Bibliographic Reference for this paper B.P. Wang, S. Nomura, B.H. Dennis, K.L. Lawrence, "The Ritz Method for Beam Vibration Analysis Revisited", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 244, 2015. doi:10.4203/ccp.108.244 Keywords: beam vibration, Ritz method. Summary In this paper alternative procedures for beam vibration analysis by the Ritz method are presented. The objective is to find formulations that can be used for higher order models. The general procedures are implemented using two basis functions (monomial and poly-cosine). In addition, two approaches for imposing essential boundary conditions are studied: the null space approach ({c}-formulation) and the nodal displacement approach ({u}-formulation). The main findings are: (1) the performance of the monomial basis can be improved by the {u}-formulation, (2) the Poly-cosine basis function outperforms the monomial basis and very high order models can be used for both {c} and {u} formulations. These results are illustrated by numerical examples. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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