Study the Effect of Thermal Gradient on Transverse Vibration of Non-Homogeneous Orthotropic Trapezoidal Plate of Parabolically Varying Thickness

Abstract

The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. The non homogeneity of the plate is characterized by taking linear variation of the Young's modulus and parabolically variation of the density of the material. The non homogeneity is assumed to arise due to the variation in the density of the plate material and it is taken as parabolically. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the transverse vibrations of orthotropic trapezoidal plates, are derived with boundary condition clamped-simply supported-clamped-simply supported. Frequencies corresponding to first two modes of vibration are calculated for the trapezoidal plate for various combinations of the parameters of the non-homogeneity, thermal gradient, taper constant and for different values of the aspect ratios and shown by figures. All The results presented here are entirely new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that cases the results have been compared with those found in the existing literatures and are in excellent agreement.

The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. The non homogeneity of the plate is characterized by taking linear variation of the Young's modulus and parabolically variation of the density of the material. The non homogeneity is assumed to arise due to the variation in the density of the plate material and it is taken as parabolically. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the transverse vibrations of orthotropic trapezoidal plates, are derived with boundary condition clamped-simply supported-clamped-simply supported. Frequencies corresponding to first two modes of vibration are calculated for the trapezoidal plate for various combinations of the parameters of the non-homogeneity, thermal gradient, taper constant and for different values of the aspect ratios and shown by figures. All The results presented here are entirely new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that cases the results have been compared with those found in the existing literatures and are in excellent agreement.

Keywords

Thermal Gradient, Vibration, Orthotropic Trapezoidal Plate, Parabolically Thickness, Non-Homogeneity

Thermal Gradient, Vibration, Orthotropic Trapezoidal Plate, Parabolically Thickness, Non-Homogeneity

Cite this paper

nullA. Gupta and S. Sharma, "Study the Effect of Thermal Gradient on Transverse Vibration of Non-Homogeneous Orthotropic Trapezoidal Plate of Parabolically Varying Thickness,"*Applied Mathematics*, Vol. 2 No. 1, 2011, pp. 1-10. doi: 10.4236/am.2011.21001.

nullA. Gupta and S. Sharma, "Study the Effect of Thermal Gradient on Transverse Vibration of Non-Homogeneous Orthotropic Trapezoidal Plate of Parabolically Varying Thickness,"

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