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Abstract
In this paper, vibration analysis of a thin circular disc interacting with a fluid in cylindrical container is carried out. It has been done systematically by carrying our mathematical modeling and subsequently validated by ANSYS software. The author has first determined natural frequencies and mode shapes for a thin circular disc alone and then for fluid contained by a cylindrical vessel alone. The author had then found natural frequencies and mode shapes for coupled case of thin circular disc interacting with a fluid contained by the cylindrical container. The same had been validated by ANSYS software. It is found that natural frequencies of coupled vibrations are different than that of the frequency of disc or fluid taken separately. In order to study the correct failure pattern of the coupled vibration system, it, thus, becomes a necessity to study coupled vibration analysis
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References
- Warburton, G. B., "Vibration of Rectangular Plates", Proc Instn Mech Engrs, 168, 1954, pp. 371-381.
- Bokil, V. B. and Shirahatti, U. S., "A Technique for the Modal Analysis of Sound-structural Interaction Problems", Journal of Sound and Vibrations, 173 (1), 1994, pp. 23-41.
- Scarpa, F., "Parametric Sensitivity Analysis of a Coupled Structural-acoustic Systems", Journal of Vibration and Acoustics, 122(2), 2000, pp. 109-115.
- Maity, D. and Bhattacharyya, S. K., "A Parametric Study on Fluid-structure Interaction Problems", Journal of Sound and Vibrations, 263, 2003, pp.917-935.
- Gorman, D.J. and Ding, W., "The superpositionGalerkin Method for Free Vibration Analysis of Rectangular Plates", Journal of Sound and Vibration", 194(2), 1996, pp.187-198.
- Airey, J.R., "The Vibrations of Circular Plates and their Relation to Bessel Functions", Institute of Physics, London, Proc. Phy. Soc. London, 23, 1911, pp.225-232.
- Amabili, M., "Shell-plate Interaction in the Free Vibrations of Circular Cylindrical Tanks Partially Filled with a Liquid: The Artificial Spring Method", Journal of Sound and Vibrations, 199(3), 1997, pp.431-452.
- Lee,W.K., Yeo,M.H. and Samoilenko, S.B., "The Effect of the Number of Nodal Diameters on Nonlinear Interactions in two Asymmetric Vibration modes of a Circular Plate", Journal of Sound and Vibrations, 268, 2003, pp.1013-1023.
- Kalnins, A. and Dym, C.L., "Vibration: Beams, Plates and Shells", 60-88, Dowden, Hutchingson and Ross Inc, 1976.
- Watson, G. N., "A Treatise on the Theory of Bessel Functions by Cambridge Mathematical Library, Cambridge University Press, 1996.
- Hoffman, J. D. and Zucrow, M.J, "Gas Dynamics Vol. II, Multidimensional Flow", John Wiley and
- Sons, 1977.
- Fahy, F. J., "Foundations of Engineering Acoustics", Academic Press (Elsevier), 2003.
- Pellicano, F., Amabili, M. and Vakakikis, A.F., "Non Linear Vibrations And Multiple Resonances of Fluid
- Filled, Circular Shells Part-1: Equations of Motion and Numerical Methods", Journal of Vibration and
- Acoustics, 122(4), 2000.
- ANSYS Users’ Manual, ANSYS Inc. Ltd, Ver. 10, 2005.
References
Warburton, G. B., "Vibration of Rectangular Plates", Proc Instn Mech Engrs, 168, 1954, pp. 371-381.
Bokil, V. B. and Shirahatti, U. S., "A Technique for the Modal Analysis of Sound-structural Interaction Problems", Journal of Sound and Vibrations, 173 (1), 1994, pp. 23-41.
Scarpa, F., "Parametric Sensitivity Analysis of a Coupled Structural-acoustic Systems", Journal of Vibration and Acoustics, 122(2), 2000, pp. 109-115.
Maity, D. and Bhattacharyya, S. K., "A Parametric Study on Fluid-structure Interaction Problems", Journal of Sound and Vibrations, 263, 2003, pp.917-935.
Gorman, D.J. and Ding, W., "The superpositionGalerkin Method for Free Vibration Analysis of Rectangular Plates", Journal of Sound and Vibration", 194(2), 1996, pp.187-198.
Airey, J.R., "The Vibrations of Circular Plates and their Relation to Bessel Functions", Institute of Physics, London, Proc. Phy. Soc. London, 23, 1911, pp.225-232.
Amabili, M., "Shell-plate Interaction in the Free Vibrations of Circular Cylindrical Tanks Partially Filled with a Liquid: The Artificial Spring Method", Journal of Sound and Vibrations, 199(3), 1997, pp.431-452.
Lee,W.K., Yeo,M.H. and Samoilenko, S.B., "The Effect of the Number of Nodal Diameters on Nonlinear Interactions in two Asymmetric Vibration modes of a Circular Plate", Journal of Sound and Vibrations, 268, 2003, pp.1013-1023.
Kalnins, A. and Dym, C.L., "Vibration: Beams, Plates and Shells", 60-88, Dowden, Hutchingson and Ross Inc, 1976.
Watson, G. N., "A Treatise on the Theory of Bessel Functions by Cambridge Mathematical Library, Cambridge University Press, 1996.
Hoffman, J. D. and Zucrow, M.J, "Gas Dynamics Vol. II, Multidimensional Flow", John Wiley and
Sons, 1977.
Fahy, F. J., "Foundations of Engineering Acoustics", Academic Press (Elsevier), 2003.
Pellicano, F., Amabili, M. and Vakakikis, A.F., "Non Linear Vibrations And Multiple Resonances of Fluid
Filled, Circular Shells Part-1: Equations of Motion and Numerical Methods", Journal of Vibration and
Acoustics, 122(4), 2000.
ANSYS Users’ Manual, ANSYS Inc. Ltd, Ver. 10, 2005.