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The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation

Year 2009, Volume: 1 Issue: 1, 34 - 41, 01.03.2009

Abstract

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

References

  • 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.
Year 2009, Volume: 1 Issue: 1, 34 - 41, 01.03.2009

Abstract

References

  • 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.
There are 18 citations in total.

Details

Other ID JA65FU52KA
Journal Section Articles
Authors

A.h. Sofiyev This is me

M. Avcar This is me

P. Ozyigit This is me

S. Adigozel This is me

Publication Date March 1, 2009
Published in Issue Year 2009 Volume: 1 Issue: 1

Cite

APA Sofiyev, A., Avcar, M., Ozyigit, P., Adigozel, S. (2009). The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation. International Journal of Engineering and Applied Sciences, 1(1), 34-41.
AMA Sofiyev A, Avcar M, Ozyigit P, Adigozel S. The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation. IJEAS. March 2009;1(1):34-41.
Chicago Sofiyev, A.h., M. Avcar, P. Ozyigit, and S. Adigozel. “The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation”. International Journal of Engineering and Applied Sciences 1, no. 1 (March 2009): 34-41.
EndNote Sofiyev A, Avcar M, Ozyigit P, Adigozel S (March 1, 2009) The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation. International Journal of Engineering and Applied Sciences 1 1 34–41.
IEEE A. Sofiyev, M. Avcar, P. Ozyigit, and S. Adigozel, “The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation”, IJEAS, vol. 1, no. 1, pp. 34–41, 2009.
ISNAD Sofiyev, A.h. et al. “The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation”. International Journal of Engineering and Applied Sciences 1/1 (March 2009), 34-41.
JAMA Sofiyev A, Avcar M, Ozyigit P, Adigozel S. The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation. IJEAS. 2009;1:34–41.
MLA Sofiyev, A.h. et al. “The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation”. International Journal of Engineering and Applied Sciences, vol. 1, no. 1, 2009, pp. 34-41.
Vancouver Sofiyev A, Avcar M, Ozyigit P, Adigozel S. The Free Vibration of Non-Homogeneous Truncated Conical Shells on a Winkler Foundation. IJEAS. 2009;1(1):34-41.

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