Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method

The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear temperature distribution in the thickness direction. The parabolic variation in thickness along the radial direction is controlled by a taper constant. The plate material is graded in the transverse direction and its mechanical properties are temperature-dependent. The thermal environment over the top and bottom surfaces of the plate is assumed to be uniform. Hamilton's principle has been used in obtaining the governing differential equations for thermo-elastic equilibrium and axisymmetric motion for such a plate model employing Kirchhoff plate theory. Numerical results for thermal displacements and natural frequencies of clamped and simply supported plates have been obtained using MATLAB. The effect of the taper constant, volume fraction index, and temperature difference on the vibration characteristics has been analyzed for the lowest three modes of vibration. A study in which the plate material has temperature-independent properties has also been performed. The accuracy of the present technique is verified by comparing the results with those available in the literature.

Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution

The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness inx-direction subjected to linear temperature distribution inx-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.

FREE VIBRATIONS OF NON-HOMOGENEOUS TAPERED SQUARE PLATE WITH BI-DIRECTIONAL TEMPERATURE VARIATIONS

An analysis is presented to the study the free vibrations of non- homogeneous clamped square plate with bidirectional temperature variations. It is assumed that thickness of the plate varies exponentially in one direction. Nonhomogeneity of plate material is assumed to arise due to parabolic variation of density along x-direction. Rayleigh-Ritz technique on the basis of classical plate theory is applied to solve the fourth order differential equation of motion. Numerical values of frequency are calculated with the help of Mathematica (Software) and are presented in tabular and graphical forms for different values of thermal gradient, taper constant and non-homogeneity constant.