Vibration Computational of Visco-Elastic Plate with Sinusoidal Thickness Variation and Linearly Thermal effect in 2D

Authors

  • Subodh Kumar Sharma Associate Prof. & Head of Dept., Govt. P.G College, Ambala Cantt. Haryana, India
  • Ashish Kumar Sharma Research Scholar Dept. of Mathematics, Pacific University, Udaipur, Raj., India

Keywords:

Vibration, Frequency, Taper Constant, Thermal Effect, Plate.

Abstract

The attention of recent technology has been directed toward faster and larger, and therefore the
needs for more flexible and lighter structures are obvious. This trend has increased the practical importance
of dynamic analysis in addition to the classical static analysis, and the numerical evaluation of vibrational
characteristics of structural elements has become an important part of the design process. The free,
transverse vibration of isotropic square plate is investigated in the paper. The thickness of the plate is varying
sinusoidal linearly in 2D and temperature linearly in 2D:
Rayleigh-Ritz technique has been employed to obtain fundamental frequencies of first two modes. The effect
of structural parameters such as taper constants and thermal gradient with clamped boundary condition has
been taken. Numerical results thus obtained are shown graphically.

References

1. Khanna A, Ashish Kumar Sharma, “Natural Frequency of Viso-Elastic Square Plate with Thickness Variation”, Elixir Mech. Engg., Vol. 56, pp: 13264- 13267 (2013).
2. Khanna, A., Sharma, A. K., Singh, H. and Magotra, V. K., “Bi-parabolic thermal effect on vibration of viscoelastic square plate”, Journal of applied Mathematics and Bioinformatics, vol. 1(2), pp. 39-48 (2011).
3. A.K. Gupta and Anupam Khanna, “Thermal Effect on Vibrations of Parallelogram Plate of Linearly Varying Thickness”, Advanced Studies of Theoretical Physics, Vol.4 (17), pp: 817-826 (2010).
4. Gupta A.K., Johri T., Vats R.P., “Study of thermal gradient effect on vibrations of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations”, Meccanica, 45(3), pp: 393-400 (2010).
5. Gupta A.K., Kaur H., “Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions”, Meccanica, Vol. 43(4), 449-458 (2008).
6. 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( 3), pp: 450-457 (2007).
7. V.Pradeep and N. Ganesan, “Buckling and vibration of rectangular composite visco-elastic sandwich plates under thermal loads”, Composite Structure, Vol. 77(4), 419-429 (2007).

Published

2019-01-04