Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics
Full Article - Open Access.
DYNAMIC BEHAVIOR OF FRAMED STRUCTURES WITH AN ELASTIC INTERNAL HINGE
The study of the dynamic properties of framed structures is extremely important in the field of structural engineering. In this paper the first natural frequencies of transverse vibration of frames are determined. The elastic structural system consists of a beam supported by a column. The presence of an internal hinge located in different positions of the beam is considered. The hinge is elastically restrained against rotation and translation. Attention is given to the way in which supports are modeled. It is known that ideal supports used in many structural models do not fit exactly with the real supports. Here the column is considered not rigidly connected to the foundation. The displacement of the component elements are assumed to be described by the theory of Euler-Bernoulli. The governing equations of the system, together with the boundary and compatibility conditions are obtained using the technique of variational calculus. Applying the method of separation of variables, the exact values of the natural frequencies of the model are obtained. Results are given for different cases, which arise from combining different magnitudes in the internal elastic hinge. These results are compared with those obtained using the finite element method, and in particular cases they are also compared with values available in the literature. Finally, an experimental device allows verifying the procedure.
Palavras-chave: Vibration, Frame, Modal shapes, Elastically supported, Hinge.,
-  Laura P A. A., Valerga de Greco, B. H., Filipich C. A., “In-plane vibrations of frames carrying concentrated masses”. Journal of Sound and Vibration,. 17(3), 447–458, 1987.
-  Warburton, G.B., “The Dynamical Behaviour of Structures”. (2nd edition), Pergamon Press Ltd., Oxford, 1976.
-  Blevins R., “Formulas for Natural Frequency and Mode Shape”, Krieger Melbourne, FL, 199
-  Clough R. W., Penzien J. “Dynamics of Structures”. McGraw!Hill New York. 1975.
-  Timoshenko S., Young D.H., “Vibration Problems in Engineering”. Van Nostrand, Princeton, New York, 1956. .
-  Karnosky I. A., Lebed O. I., “Free vibrations of beam and frames”. McGraw-Hill. New York, 2004
-  Lin H.P., Ro, J. “Vibration analysis of planar serial-frame structures”, Journal of Sound and Vibration 262, 1113-1131, 2003.
-  Wu J.J., “Use of the elastic-and-rigid-combined beam element for dynamic analysis of a two-dimensional frame with arbitrarily distributed rigid beam segments”. Applied Mathematical Modelling 35, 1240–1251, 2011.
-  Mei C., “Wave control of vibrations in multi-story planar frame structures based on classical vibration theories”. Journal of Sound and Vibration, 330, 5530–5544, 2011.
-  Filipich C.P., Laura P. A. A., “In-plane vibrations of portal frames with end supports elastically restrained against rotation and translation”. Journal of Sound and Vibration. 117, 467-476, 1987.
-  H. Bang, “Analytical solution for dynamic analysis of a flexible L-shaped structure”. Journal of Guidance, Control and Dynamics, 19 (1), 248–250, 1996.
-  Gürgöze M., “Comment on ‘Analytical solution for dynamic analysis of a flexible Lshaped structure’”. Journal of Guidance, Control and Dynamics, 21 (2), 359, 1998.
-  Oguamanam D.C.D., Hasen J.S., Heppler G. R., “Vibration of arbitrarily oriented twomember open frame with tip mass”. Journal of Sound and Vibration. 209; 651-669,1998.
-  Heppler G. R., Oguamanam D.C.D., Hasen J.S., “Vibration of a two-member open frame”. Journal of Sound and Vibration. 263, 299-317, 2003.
-  Albarracín C. M., Grossi R. O., “Vibrations of elastically restrained frames”, Journal of Sound and Vibration. 285, 467-476, 2005.
-  Lee H. P., Ng T. Y., “In-plane vibrations of planar frame structures”. Journal of Sound and Vibration, 172, 420-427, 1994.
-  Wang, C.Y., Wang, C.M., “Vibrations of a beam with an internal hinge”. International Journal of Structural Stability and Dynamics. 1, 163-167, 2001.
-  Lee Y.Y., Wang C.M., Kitipornchai S., “Vibration of Timoshenko beams with internal hinge”. Journal of engineering Mechanics. 129, 293-301, 2003.
-  Chang, T.P., Lin, G.L., Chang, E., “Vibrations analysis of a beam with an internal hinge subjected to a random moving oscillator”. International Journal of Solid and Structures. 43, 6398-6412, 2006.
-  Grossi, R.O., Quintana, M. V., The transition conditions in the dynamics of elastically restrained beams”. Journal of Sound and Vibration, 316, 274-297, 2008.
-  Quintana V., Raffo J. L., Grossi R. O., “Eigenfrequencies of generally restrained Timoshenko beam with an internal hinge”. Mecánica Computacional XXIX, 2499-2516, 2010.
-  Chondros, T.G., Dimarogonas, A.D. y Yao, J., “A continuous cracked beam vibration theory”. Journal of Sound and Vibration, 215, 17-34, 1998.
-  Wolfram MATHEMATICA 8 software. Version 8000. Copyright 1988-2010.
-  ALGOR software. Version 23.01. 2009.
Ratazzi, A. R.; Bambill, D. V.; Rossit, C. A.; "DYNAMIC BEHAVIOR OF FRAMED STRUCTURES WITH AN ELASTIC INTERNAL HINGE", p. 4483-4498 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1].
São Paulo: Blucher,
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19921
últimos 30 dias | último ano | desde a publicação