Journal of Applied Science and Engineering

Published by Tamkang University Press


Impact Factor



Anupam Khanna This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Ashish Kumar Sharma2

1Department of Mathematics, Maharishi Markandeshwar University (Mullana), Ambala, Haryana, India
2Department of Mathematics, Manav Bharti University, Solan, H. P., India


Received: January 10, 2012
Accepted: June 27, 2012
Publication Date: June 1, 2013

Download Citation: ||  


In the modern technology, the plates of variable thickness are widely used in engineering applications i.e. nuclear reactor, aeronautical field, naval structure, submarine etc. In this paper, effect of thermal gradient on vibration of square plate of varying thickness is studied. Thermal effect and thickness of plate vary bi-parabolic i.e. parabolic in x-direction and parabolic in y-direction. Rayleigh Ritz technique is used to calculate the fundamental frequencies. The frequencies corresponding to the first two modes of vibrations are obtained for a square plate for different values of taper constant and thermal gradient. Results are presented in Table and Graphical form.

Keywords: Vibration, Frequencies, Square Plate, Vibration, Thermal Gradient


  1. [1] Gupta, A. K. and Khanna, A., “Thermal Effect on Vibrations of Parallelogram Plate of Linearly Varying Thickness,” Advanced Studies of Theoretical Physics, Vol. 4, No. 17, pp 817826 (2010).
  2. [2] Gupta, A. K. and Khanna, A., “Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations,” Journal Shock and Vibration, Vol. 15, No. 6, pp. 713723 (2008).
  3. [3] Gupta, A. K. and Khanna, A., “Free Vibration of Clamped Visco-Elastic Rectangular Plate Having BiDirection Exponentially Thickness Variations,” Journal of Theoretical and Applied Mechanics, Vol. 47, No. 2, pp. 457471 (2009).
  4. [4] Gupta, A. K. and Khanna, A., “Vibration of ViscoElastic Rectangular Plate with Linearly Thickness Variations in Both Directions,” J. Sound and Vibration, Vol. 301, pp. 450457 (2007). doi: 10.1016/j.jsv. 2006.01.074
  5. [5] Khanna, A. and Sharma, A. K., “Study of Free Vibration of Visco-Elastic Square Plate of Variable Thickness with Thermal Effect,” Innovative System Design and Engineering, U.S.A. Vol. 2. No. 4 (2011).
  6. [6] Khanna, A. and Sharma, A. K., “Vibration Analysis of Visco-Elastic Square Plate of Variable Thickness with Thermal Gradient,” International Journal of Engineering and Applied Sciences, Turkey, Vol. 3, No. 4, pp. 16 (2011).
  7. [7] Gupta, A. K. and Kumar, L., “Thermal Effect on Vibration of Non-Homogenous Visco-Elastic Rectangular Plate of Linear Varying Thickness,” Meccanica, Vol. 43, pp. 4754 (2008). doi: 10.1007/s11012-007- 9093-3
  8. [8] Lal, R., “Transverse Vibrations of Orthotropic NonUniform Rectangular Plates with Continuously Varying Density,” Indian J. Pure Appl. Math., Vol. 34, No. 4, pp. 587606 (2003).
  9. [9] Leissa, A. W., Vibration of Plates, NASA SP, Vol. 160 (1969).
  10. [10] Leissa, A. W., “The Free Vibration of Rectangular Plates,” Journal of Sound and Vibration, Vol. 31, pp. 257293 (1973). doi: 10.1016/S0022-460X(73)80371-2
  11. [11] Li, W. L., “Vibration Analysis of Rectangular Plates with General Elastic Boundary Supports,” Journal of Sound and Vibration, Vol. 273, pp. 619635 (2004). doi: 10.1016/S0022-460X(03)00562-5
  12. [12] Lee, H. P., Lim, S. P. and Chow, S. I., “Free Vibration of Composite Rectangular Plates with Rectangular Cutouts,” Composite Structures, Vol. 8, No. 1, pp. 6381 (1987). doi: 10.1016/0263-8223(87)90016-X
  13. [13] Tomar, J. S. and Gupta, A. K., “Thermal Effect on Frequencies of an Orthotrophic Rectangular Plate of Linearly Varying Thickness,” Journal of Sound and Vibration, Vol. 90, No. 3, pp. 325331 (1983). doi: 10.1016/0022-460X(83)90715-0
  14. [14] Tomar, J. S. and Gupta, A. K., “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. 257262 (1985). doi: 10.1016/0022-460X(85)90389-X
  15. [15] Khanna, A. and Sharma, A. K., “Vibration Characteristics of Non-Homogeneous Visco-Elastic Square Plate,” Advances in Physics Theories and Applications, Vol. 2 (2011).
  16. [16] Kumar, S., Some Vibration Problems of Visco-Elastic Plate of Variable Thickness in Two Directions, Ph. D. Thesis, C. C. S. University, Meerut, U. P., INDIA (2005).