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

Arun Kumar Gupta^1, , Kumud Rana² and Dharma Veer Gupta³

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

Cite this paper:
Arun Kumar Gupta, Kumud Rana and 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

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.

Keywords:
thermal vibration non-homogeneous parallelogram plate linearlyvarying thickness

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