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Meccanica

, Volume 43, Issue 4, pp 449–458 | Cite as

Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions

  • A. K. Gupta
  • Harvinder Kaur
Article

Abstract

The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique. The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.

Keywords

Thermal gradient Vibration Rectangular plate Thickness variation Visco-elastic mechanics 

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References

  1. 1.
    Laura PAA, Grossi RO, Carneiro GI (1979) Transverse vibrations of rectangular plates with thickness varying in two directions and with edges elastically restrained against rotation. J Sound Vib 63(4):499–505 MATHCrossRefADSGoogle Scholar
  2. 2.
    Singh B, Saxena V (1996) Transverse vibration of rectangular plate with bi-directional thickness variation. J Sound Vib 198(1):51–65 CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Sobotka Z (1978) Free vibration of visco-elastic orthotropic rectangular plates. Acta Tech CSAV 6:678–705 MathSciNetGoogle Scholar
  4. 4.
    Sharma RK (1977) Some vibration problems of orthotropic plates and shells. PhD thesis, University of Roorkee, Roorkee, India Google Scholar
  5. 5.
    Tomar JS, Gupta AK (1983) Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness. J Sound Vib 90(3):325–331 MATHCrossRefADSGoogle Scholar
  6. 6.
    Taylor RL Govindjee S (2002) Solution of clamped rectangular plate problems. Technical Report, UCB/SEMM, 09 Google Scholar
  7. 7.
    Young D (1950) Vibration of rectangular plates by the Ritz method. J Appl Mech Trans ASME 17(4):448–453 MATHGoogle Scholar
  8. 8.
    Rossi RE (1999) Transverse vibrations of thin, orthotropic rectangular plates with a rectangular cutouts with fixed boundaries. J Sound Vib 221(4):733–776 CrossRefADSGoogle Scholar
  9. 9.
    Tomar JS, Gupta AK (1985) Effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions. J Sound Vib 98(2):257–262 MATHCrossRefADSGoogle Scholar
  10. 10.
    Nowacki W (1962) Thermo elasticity. Pergamon Press, New York Google Scholar
  11. 11.
    Leissa AW (1969) Vibration of plates. NASA SP-160, US Govt. Printing office Google Scholar
  12. 12.
    Bhatanagar NS, Gupta AK (1988) Vibrations analysis of visco-elastic circular plate subjected to thermal gradient. Model Simul Control B 15(1):17–31 Google Scholar
  13. 13.
    Gupta AK, Khanna A (2007) Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions. J Sound Vib 301(207):450–457 CrossRefADSGoogle Scholar
  14. 14.
    Gupta AK, Johri T, Vats RP (2007) Thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi-directional parabolically varying thickness. In: Proceedings of international conference in world congress on engineering and computer science, San Francisco, USA, 24–26 October 2007, pp 784–787 Google Scholar
  15. 15.
    Gupta AK, Kumar A, Gupta DV (2007) Vibration of visco-elastic orthotropic parallelogram plate with linearly thickness variation. In: Proceedings of international conference in world congress on engineering and computer science, San Francisco, USA, 24–26 October 2007, pp 800–803 Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsM.S. CollegeSaharanpurIndia
  2. 2.Department of MathematicsGovt. CollegeHaryanaIndia

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