Thermal Effect on Vibration of Orthotropic Rectangular Plate with Thickness Variation as Linearly & Parabolically in x- and y- Directions Respectively

Arun Kumar Gupta^1, and Subodh Kumar²

¹Department of Mathematics, M. S. College, Saharanpur, U.P., India

²Department of Mathematics, Govt.College, Ambala Cantt, Haryana, India

Cite this paper:
Arun Kumar Gupta and Subodh Kumar. Thermal Effect on Vibration of Orthotropic Rectangular Plate with Thickness Variation as Linearly & Parabolically in x- and y- Directions Respectively. Journal of Mathematical Sciences and Applications. 2013; 1(2):32-35. doi: 10.12691/jmsa-1-2-4

Abstract

The main objective of the present investigation is to study linear temperature behavior of orthotropic rectangular plate of bi-direction variable thickness. The thickness of the plate is considered as linearly in x-direction and parabolically in y-direction. Rayleigh-Ritz technique has been employed to obtain fundamental frequencies for the first two modes of vibrations. The effect of structural parameters such as taper constants and thermal gradient with c-c-c-c boundary condition has been taken. Numerical results thus obtained are shown graphically. Excellent agreement is noted when comparison is made with previous available experimental data.

Keywords:
thermal gradient vibration rectangular plate thickness variation linearly and parabolically

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References:

[1]	A. W. Leissa: Vibration of plates. NASA-SP-160, U.S. Govt. Printing Office, (1969).
[2]	P. A. A. Laura, R. H. Gutierrez: Vibration analysis on a rectangular plate subjected to a thermal gradient. J. Sound and Vibration, 72 (1980), 263.
[3]	Y. S. Yang: The vibrations of a circular plate with variable thickness. J. Sound and Vibration, 165 (1993), 178-184.
[4]	A. K. Gupta, A. Khanna: Vibration of clamped visco-elastic rectangular plate with parabolic thickness variations. Shock and Vibration, 15 (2008), 713-723.
[5]	Y. Shibaoka: On the transverse vibration of an elliptic plate with clamped edge. J. Phy. Soc. Japan, 11 (1956), 797-803.
[6]	A. K. Gupta, H. Kaur: Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions. Meccanica, 43 (2008), 449-458.
[7]	A. K. Gupta, S. Kumar: Thermal effect on vibration of orthotropic rectangular plate with parabolic thickness variations. Acta Technica, 55 (2010), 315-325.
[8]	W. Q. Chen, K. Y. Lee, H. J. Ding: On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plate. J. Sound and Vibration, 279 (2005), 237-251.
[9]	E. Pan, P. R. Heyliger: Free vibrations of simply supported and multilayered magneto-electro-elastic plates. J. Sound and Vibration, 252 (2002), 429-442.
[10]	S. Chakraverty, R. Jindal, V. K. Agarwal: Flexural vibrations of non-homogeneous elliptic plates. Indian J. Engineering and Materials Sciences, 12 (2005), 521-528.
[11]	J.S. Tomar and A.K.Gupta: Effect of thermal gradient on frequencies of orthotropic rectangular plate whose thickness varies in two directions, J.Sound and Vibration, 98(1985), 257-262.
[12]	J.S. Tomar and A.K.Gupta: Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness, J.Sound and Vibration,90(1983), 325-331.
[13]	J.S. Tomar and A.K.Gupta: Effect of exponential temperature variation on frequencies of an orthotropic rectangular plate of exponentially varying thickness, Proceeding of the workshop on computer application in continuum mechanics, March 11-13(1988), Deptt. of Math. U.O.R, Roorkee, 183-188.
[14]	A.K. Gupta and A.Khanna: Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, J. Sound and Vibration, 301(2007), 450-457.
[15]	A.K.Gupta and H.Kaur: Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plate with linearly thickness variation in both directions, Meccanica, 43(2008), 449-458.
[16]	A.K.Gupta, A. Kumar and Y.K.Gupta : Vibration of visco-elastic parallelogram plate with parabolic thickness variation, Applied Mathematics, 1(2010), 128-136.
[17]	A.K. Gupta and P. Singhal: Effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness, Applied Mathematics, 1(2010), 326-333.