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Journal of Mathematics
Volume 2013 (2013), Article ID 721868, 6 pages
http://dx.doi.org/10.1155/2013/721868
Research Article

An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate

1Department of Mathematics, Maharishi Markandeshwar University, Mullana, Haryana, Ambala 133203, India
2Department of Mathematics, KIIT College of Engineering, Haryana, Gurgaon 122001, India

Received 10 January 2013; Accepted 21 April 2013

Academic Editor: Harold Benson

Copyright © 2013 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. P. A. A. Laura, R. O. Grossi, and G. I. Carneiro, “Transverse vibrations of rectangular plates with thickness varying in two directions and with edges elastically restrained against rotation,” Journal of Sound and Vibration, vol. 63, no. 4, pp. 499–505, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. A. W. Leissa, “studies in plate vibration 1981–1985 part II, complicating effects,” The Shock and Vibration Digest, vol. 19, no. 3, pp. 10–24, 1987. View at Google Scholar · View at Scopus
  3. A. K. Gupta, T. Johri, and R. P. Vats, “Thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi-directional parabolically varying thickness,” in Proceedings of the International Conference on World Congress on Engineering and Computer Science, pp. 784–787, San Diego, Calif, USA, 2007.
  4. A. K. Gupta, A. Khanna, and D. V. Gupta, “Free vibration of clamped visco-elastic rectangular plate having bi-direction exponentially thickness variations,” Journal of Theoretical and Applied Mechanics, vol. 47, no. 2, pp. 457–471, 2009. View at Google Scholar · View at Scopus
  5. 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, pp. 267–277, 1973. View at Google Scholar · View at Zentralblatt MATH
  6. S. Kumar, Effect of thermal gradient on some vibration problems of orthotropic visco-elastic plates of variable thickness [Ph.D. thesis], Chaudhary Charan Singh University, Meerut, India, 2003.
  7. R. Lal and Dhanpati, “Effect of nonhomogeneity on vibration of orthotropic rectangular plates of varying thickness resting on pasternak foundation,” Journal of Vibration and Acoustics, Transactions of the ASME, vol. 131, no. 1, Article ID 011007, 9 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Singh and V. Saxena, “Transverse vibration of a rectangular plate with bidirectional thickness variation,” Journal of Sound and Vibration, vol. 198, no. 1, pp. 51–65, 1996. View at Publisher · View at Google Scholar · View at Scopus
  9. J. S. Tomar and A. K. Gupta, “Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness,” Journal of Sound and Vibration, vol. 90, no. 3, pp. 325–331, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. 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
  11. W. L. Li, “Vibration analysis of rectangular plates with general elastic boundary supports,” Journal of Sound and Vibration, vol. 273, no. 3, pp. 619–635, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. 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
  13. A. W. Leissa, “Vibration of plate. NASA,” SP-160, 1969.