Thermal Gradient Effect on Vibrations of Non-homogeneous Rectangular Plate having Continuously Parabolically Varying Thickness in both Directions

Abstract

This paper presents the effect of thermal gradient on vibrations of non-homogeneity of the material of plate structures on the vibration frequencies for continuously parabolically varying thickness in both directions. The non-homogeneity of the plate is characterized by taking linear temperature variations in the Young’s modulus and linear variation in density of the material. Vibrational behaviors of non-homogeneous rectangular plates of variable thickness having two opposite edges (y = 0 and b) simply supported and the other two edges (x = 0 and a) may be clamped have been analyzed on the basis of classical plate theory. Related tables are incorporated to show the effect of the thermal gradient on non-homogeneous materials having continuously parabolically varying thickness in both directions on the frequencies of the vibration of rectangular plates for different values of thermal gradient, tapers constant and non-homogeneity constant.

Keywords: Non-homogeneous, parabolically varying thickness, rectangular plate, thermal gradient, vibration, both directions.