Analytical solution of a vibrational problem for visco-elastic plate with Kelvin type boundary conditions

Ashish Kumar Sharma1 , Manoj Kumar Dhiman2 , Silky Bensal3

1, 2, 3Department of Mathematics, IEC University, Baddi, H.P., India

1Corresponding author

Journal of Vibroengineering, Vol. 21, Issue 6, 2019, p. 1510-1518.
Received 23 December 2017; received in revised form 28 December 2018; accepted 10 January 2019; published 30 September 2019

Copyright © 2019 Ashish Kumar Sharma, et al. 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.
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Within this time of science and technology, tapered plates with different geometry conditions are used as a for the construction of wings and blades of aeronautical as well as engineering structures. The main aim of current work is to analyze the vibration of rectangular structure tapered plate with thermal effect variation along x and y axis. Rayleigh-Ritz method is use for judgment the solution of frequency equation. Now for several values of thermal gradient, aspect ratio and taper constant are considered to calculate structural parameters such as logarithmic decrement, time period and deflection.

Keywords: visco-elastic, thickness, frequency, vibration, thermal effect.


  1. Laura P. A. A., Grossi R. O., Carneiro G. I. 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, Issue 4, 1979, p. 499-505. [Publisher]
  2. Gupta A. K., Khanna A. Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions. Journal of Sound and Vibration, Vol. 301, 2007, p. 450-457. [Publisher]
  3. Gupta A. K., Khanna A. Vibration of clamped visco-elastic rectangular plate with parabolic thickness variations. Shock and Vibration, Vol. 15, Issue 6, 2008, p. 713-723. [Publisher]
  4. Gupta A. K., Khanna A., Gupta D. V. Free vibration of clamped visco-elastic rectangular plate having bi-direction exponentially thickness variations. Journal of Theoretical and Applied Mechanics, Vol. 47, Issue 2, 2009, p. 457-471. [CrossRef]
  5. Lal R., Dhanpati Effect of non-homogeneity on vibration of orthotropic rectangular plates of varying thickness resting on Pasternak foundation. Journal of Vibration and Acoustic, Vol. 131, Issue 1, 2009, p. 011007. [Publisher]
  6. Khanna A., Kaur N. Effect of thermal gradient on natural frequencies of tapered rectangular plate. Journal of Math Analysis, Vol. 7, Issue 16, 2013, p. 755-761. [Publisher]
  7. Khanna A., Kaur N. Vibration of non-homogeneous plate subject to thermal gradient. Journal of Low Frequency Noise, Vibration and Active Control, Vol. 33, Issue 1, 2014, p. 13-26. [Publisher]
  8. Khanna A., Kaur N. Effect of thermal gradient on vibration of non-uniform visco-elastic rectangular plate. Journal of the Institution of Engineers India Series, Vol. 97, Issue 2, 2015, p. 141-148. [Publisher]
  9. Avalos D. R., Laura P. A. A. Transverse vibrations of a simply supported plate of generalized anisotropy with an oblique cut. Journal of Sound and Vibration, Vol. 258, Issue 2, 2002, p. 773-776. [Publisher]
  10. Gupta A. K., Singhal P. Thermal effect on free vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness. Applied Mathematics, Vol. 1, Issue 6, 2010, p. 456-463. [Publisher]