Table of Contents
Journal of Structures
Volume 2014 (2014), Article ID 642926, 6 pages
http://dx.doi.org/10.1155/2014/642926
Research Article

Thermal Effect on Vibration of Tapered Rectangular Plate

1Department of Mathematics, Maharishi Markandeshwar University, Ambala, Haryana 133203, India
2Department of Mathematics, Northern India Engineering College, New Delhi 110053, India

Received 23 January 2014; Revised 24 May 2014; Accepted 23 June 2014; Published 8 July 2014

Academic Editor: Lucio Nobile

Copyright © 2014 Anupam Khanna and Ashish Singhal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. W. Leissa, “Vibration of plates,” Tech. Rep. SP-160, NASA, 1969. View at Google Scholar
  2. A. W. Leissa, “The free vibration of rectangular plates,” Journal of Sound and Vibration, vol. 31, no. 3, pp. 257–293, 1973. View at Google Scholar
  3. R. K. Jain and S. R. Soni, “Free vibrations of rectangular plates of parabolically varying thickness,” Indian Journal of Pure and Applied Mathematics, vol. 4, no. 3, pp. 267–277, 1973. View at Google Scholar
  4. J. S. Tomar and A. K. Gupta, “Effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions,” Journal of Sound and Vibration, vol. 98, no. 2, pp. 257–262, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. A. W. Leissa, “Recent studies in plate vibration 1981–1985 part II: complicating effects,” Shock and Vibration Digest, vol. 19, no. 3, pp. 10–24, 1987. View at Google Scholar · View at Scopus
  6. B. Singh and S. Chakraverty, “Transverse vibration of circular and elliptical plates with variable thickness,” Indian Journal of Pure Applied Mathematics, vol. 22, no. 9, pp. 787–803, 1991. View at Google Scholar
  7. J. N. Sharma and D. Chand, “Vibrations in a transversely isotropic plate due to suddenly punched hole,” Indian Journal of Pure and Applied Mathematics, vol. 27, no. 2, pp. 217–226, 1996. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. A. W. Leissa, “The historical bases of the Rayleigh and Ritz methods,” Journal of Sound and Vibration, vol. 287, no. 4-5, pp. 961–978, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Chakraverty, R. Jindal, and V. K. Agarwal, “Flexural vibrations of non-homogeneous elliptic plates,” Indian Journal of Engineering and Materials Sciences, vol. 12, no. 6, pp. 521–528, 2005. View at Google Scholar · View at Scopus
  10. A. K. Gupta and A. Khanna, “Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions,” Journal of Sound and Vibration, vol. 301, no. 3-5, pp. 450–457, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. A. K. Gupta and A. Khanna, “Vibration of clamped visco-elastic rectangular plate with parabolic thickness variations,” Shock and Vibration, vol. 15, no. 6, pp. 713–723, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Lal, Y. Kumar, and U. S. Gupta, “Transverse vibrations of non-homogeneous rectangular plates of uniform thickness using boundary characteristic orthogonal polynomials,” International Journal of Applied Mathematics and Mechanics, vol. 6, no. 14, pp. 93–109, 2009. View at Google Scholar
  13. A. Khanna, N. Kaur, and A. K. Sharma, “Effect of varying poisson ratio on thermally induced vibrations of non-homogeneous rectangular plate,” Indian Journal of Science and Technology, vol. 5, no. 9, pp. 3263–3267, 2012. View at Google Scholar · View at Scopus
  14. A. K. Gupta and L. Kumar, “Thermal effect on vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness,” Meccanica, vol. 43, no. 1, pp. 47–54, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. A. Khanna and A. K. Sharma, “Natural vibration of visco-elastic plate of varying thickness with thermal effect,” Journal of Applied Science and Engineering, vol. 16, no. 2, pp. 135–140, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Khanna and P. Arora, “Effect of sinusoidal thickness variation on vibrations of non-homogeneous parallelogram plate with bi-linearly temperature variations,” Indian Journal of Science and Technology, vol. 6, no. 9, pp. 5228–5234, 2013. View at Google Scholar
  17. A. Kumar Gupta, V. Panwar, and R. P. Vats, “Vibrations of non-homogeneous rectangular plate of variable thickness in both directions with thermal gradient effect,” International Journal of Applied Mathematics and Mechanics, vol. 6, no. 16, pp. 19–37, 2010. View at Google Scholar