Study of thermal gradient effect on vibrations of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations

Here, thermal gradient effect on vibration of non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations is studied. The non-homogeneity is assumed to arise due to the variation in the density of the plate material. Rayleigh Ritz method is used to evaluate the fundamental frequencies and deflection function. The two-dimensional thickness variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Yet the method used for the solution of present problem provides an approximate solution but it is quite convenient and authentic one. A two-term deflection function is used. Frequency corresponding to first mode of vibration is calculated for clamped plate for different values of temperature gradient, taper constants and non-homogeneity constant. In special cases, comparisons have been made with results that are available in the literature.