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Gupta, A.K., Kumar, M., Kumar, S. and Khanna, A.‘Thermal effect on vibration of parallelogram plate of bi-directional linearly varying thickness, Applied Mathematics (2011), 2(1), 33-38(USA).

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Article

Effect of Thermal Gradient on Vibration of Non-Homogeneous Parallelogram Plate of Linearly Varying Thickness in Both Directions

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

2Department of Mathematics, Maharaja Agarsain Institute of Technology, Ghaziabad, U.P., India

3Department of Mathematics, College of Engineering Roorkee, Roorkee, U.A., India


Journal of Mathematical Sciences and Applications. 2013, Vol. 1 No. 3, 43-49
DOI: 10.12691/jmsa-1-3-2
Copyright © 2013 Science and Education Publishing

Cite this paper:
Arun Kumar Gupta, Kumud Rana, Dharma Veer Gupta. Effect of Thermal Gradient on Vibration of Non-Homogeneous Parallelogram Plate of Linearly Varying Thickness in Both Directions. Journal of Mathematical Sciences and Applications. 2013; 1(3):43-49. doi: 10.12691/jmsa-1-3-2.

Correspondence to: Arun  Kumar Gupta, Department of Mathematics, M.S. College, Saharanpur, U.P., India. Email: gupta_arunnitin@yahoo.co.in

Abstract

The paper presented here is to study the effect of thermal gradient on vibration of non-homogeneous parallelogram plate of linearly varying thickness in both directions. Thermal induced vibration of non-homogeneous parallelogram plate has been taken as one dimensional temperature distribution in linear from only. For non-homogeneity of the plate material, density is assumed to vary linearly. Using the method of separation of variables; the governing differential equation is solved. An approximate but, quite convenient frequency equation is derived by Rayleigh-Ritz technique with two terms deflection function. The frequencies corresponding to the first two modes of vibration has been computed for a clamped parallelogram plate for different values of non -homogeneity constant, aspect ratio, thermal constant, thickness variation constant and skew angle.

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