Science and Education Publishing Journal of Mathematical Sciences and Applications 1 3 2013 12 06 Effect of Thermal Gradient on Vibration of Non-Homogeneous Parallelogram Plate of Linearly Varying Thickness in Both Directions 43 49 EN Arun Kumar Gupta Department of Mathematics, M.S. College, Saharanpur, U.P., India Kumud Rana Dharma Veer Gupta JMSA2013132 10.12691/jmsa-1-3-2 2013 11 06 2013 11 23 2013 12 06 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.