The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation
In this work, free vibration of non-homogeneous truncated conical shells on a Winkler foundation is studied. After formed the fundamental relations and governing equations, the dimensionless frequency parameter of the non-homogeneous isotropic truncated conical shell with or without an elastic foundation are found. Finally, effects of variations of the shell characteristics, non-homogeneity and the Winkler foundation on minimum values of the dimensionless frequency parameter have been studied. The results are compared with other works in open literature
Keywords:
Conical shells, elastic foundation, non-homogeneity, free vibration,
___
- Pasternak, P.L., On a New Method of Analysis of an Elastic Foundation by Means of two Foundation Constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture. Moscow, USSR, 1954. (in Russian)
- Bajenov V.A. The Bending of the Cylindrical Shells in an Elastic Medium, Kiev: Visha Shkola, (in Russian), 1975.
- Sun, B. and Huang, Y., The exact solution for the general bending problems of conical shells on the elastic foundation. Appl.Math.Mech.Engl.Ed.9, 5, 455-469,1988.
- Paliwal, D.N., Pandey, R.K. and Nath, T., Free vibration of circular cylindrical shell on Winkler and Pasternak foundation. Int. J. Press. Vessel. Piping, 69, 79-89, 1996.
- Amabili, M. and Dalpiaz, G., Free vibration of cylindrical shells with non-axisymmetric mass distribution on elastic bed, Meccanica 32, 71–84, 1997.
- Ng, T.Y. and Lam, K.Y. Free vibrations analysis of rotating circular cylindrical shells on an elastic foundation. J. Vibration and Acoustics, 122, 85-89, 2000.
- Civalek, O., Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods. Int. J. Pressure Vessels and Piping, 82, 470-479, 2005.
- Tj H.G., Mikami, T., Kanie, S., Sato M., Free vibrations of fluid-filled cylindrical shells on elastic foundations. Thin-Walled Structures, 43, 11, 1746-1762, 2005
- Lomakin, V.A., The Elasticity Theory of Non-homogeneous Materials, Nauka, Moscow, (in Russian) 1976.
- 0. Awrejcewicz, J., Krysko, V.A., Kutsemako, A.N., Free vibrations of doubly curved in-plane non-homogeneous shells. J. Sound and Vibration 225 (4) 701-722 1999.
- 1. Lal, R., Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness: A spline technique. J. Sound and Vibration, 306, 203-214.
- 2. Sofiyev, A.H., Karaca, Z., The vibration and stability of laminated non-homogeneous orthotropic conical shells subjected to external pressure. Europen J. MechanicsA/Solids, 28,2, 317-328, 2009.
- 3. Tomar, J., Gupta, D. and Kumar, V., Natural frequencies of a linearly tapered nonhomogeneous isotropic elastic circular plate resting on an elastic foundation. J. Sound and Vibration, 111,1-8,1986.
- 4. Sofiyev, A.H., Keskin, S.N. and Sofiyev Al. H., Effects of elastic foundation on the vibration of laminated non-homogeneous orthotropic circular cylindrical shells. J. Shock and Vibration, 11, 89-101, 2004.
- 5. Sheng, G.G., Wang, X., Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium. J. Reinforced Plastics and Composites, 27, 2, 117-134, 2008.
- 6. Irie, T., Yamada, G., Tanaka, K., Natural frequencies of truncated conical shells. J. Sound and Vibration, 92, 3, 447-453, 1984.
- 7. Agamirov, VL. Dynamic Problems of Nonlinear Shells Theory, Moscow: Nauka, (in Russian) 1990.
- 8. Liew, K.M., Ng, T.Y., Zhao, X., Free vibration analysis of conical shells via the element- free kp-Ritz method. J. Sound and Vibration, 281, 627-645, 2005.
- Başlangıç: 2009
- Yayıncı: Akdeniz Üniversitesi