Author(s)

  Kavita¹, Satish Kumar¹, Pragati Sharma²

¹Department of Mathematics, M. M. University, Mullana, India.
²Department of Mathematics, Haryana College of Technology & Management, Kaithal, India.

The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.

Vibration, Trapezoidal Plate, Taper Constants, Thermal Gradient, Aspect Ratio, Non-Homogeneity, Parabolically Thickness, Linearly Density

Kavita,  . , Kumar, S. and Sharma, P. (2016) Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions. Applied Mathematics, 7, 1283-1296. doi: 10.4236/am.2016.712113.