Determining the Advanced Frequency of Composited Functionally Graded Material Plates Using Third-Order Shear Deformation Theory and Nonlinear Varied Shear Coefficients

The shear effect is usually considered in the numerical calculation of thick composited FGM plates. The characteristics that have the greatest effect on thickness are displacement type, shear correction coefficient, material property and temperature. For the advanced frequency study of thick composited functionally graded material (FGM) plates, it is interesting to consider the extra effects of the nonlinear coefficient c1 term of the third-order shear deformation theory (TSDT) of displacement on the calculation of varied shear correction coefficients. The values of nonlinear shear correction coefficients are usually functions of c1, the power-law exponent parameter and environment temperature. Numerical frequency computations are calculated using a simple homogeneous equation, and are investigated using TSDT and the nonlinear shear correction coefficient for thick composited FGM plates. Results for natural frequencies are found via the functions of length-to-thickness ratio, the power-law exponent parameter, c1 and environment temperature. This novel study in advanced frequency aims to determine the effects of the TSDT and nonlinear shear correction on thick FGM plates under free vibration.