## 1 Introduction  
There are some investigations of shear deformation effects in composited plates. In 2020, [PERSON] and [PERSON] [1] used various displacement theories, e.g., third-order shear deformation theory (TSDT), first-order shear deformation theory (FSDT), etc., to study laminated magnetostrictive plates; in their research, the numerical dynamic results of vibration suppression are presented. There are some dynamical investigations of thermal vibrations in the temperature environment. In 2020, [PERSON] et al. [2] used an experimental test for hypersonic vehicles to investigate the vibration of lightweight ceramic insulating material in extremely thermal conditions. In 2020, [PERSON] and [PERSON] [3] applied a three-dimensional (3D) nonlinear variable thermo-viscoelastic numerical theory to investigate the dynamic stress and time response of vibration in thick functionally graded material (FGM) rotating annular plates undergoing temperature rises. In 2020, [PERSON] et al. [4] presented the numerical analysis of a 3D integrated package to investigate the fatigue of through-silicon-via copper (TSV-Cu) structures under thermal and vibration coupled loads. In 2019, [PERSON] et al. [5] used FSDT in a numerical approach to investigate the flutter and vibration of stiffened FGM plates under different temperature conditions. In 2019, [PERSON] et al. [6] used two versions of Euler-Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) in a numerical approach to study the thermal vibration behaviors of rotating FGM micro-beams. In 2016, [PERSON] et al. [7] used FSDT in a numerical approach to calculate the dynamic and vibration for piezoelectric FGM plates under different temperature conditions. In 2006, [PERSON] and [PERSON] [8] used higher-order shear deformation theory (HSDT) in a numerical approach to investigate the time response of piezoelectric FGM plates under different temperature conditions. In 2004, [PERSON] and [PERSON] [9] used HSDT in a numerical approach to investigate the time response of FGM plates under different temperature conditions.  
The generalized differential quadrature (GDQ) method has been applied for FGM plates. In 2019, [PERSON] [10] studied the dynamic responses of thick FGM plates by using the TSDT effect and fully homogeneous equation under different temperature conditions. The simply modified factor of shear correction was used without considering the nonlinear terms of TSDT. In 2014, [PERSON] [11] studied the dynamic responses of Terfenol-D FGM plates by considering the FSDT effect and the simply modified factor of shear correction under different temperature conditions. In 2012, [PERSON] [12] presented the dynamic responses for Terfenol-D FGM plates by using the FSDT effect and constant value of shear correction equal to 5/6 under rapid heating. It is interesting to further study the dynamic responses of stresses and deflection in the TSDT approach of GDQ computations, and the advanced nonlinear varied-modified coefficient of shear correction for thick FGM plates under different temperature condition. The parametric effects of temperature and power law index of FGM on the dynamic responses of stress and deflection are investigated for thick FGM plates.  
This paper will proceed as follows. Firstly, the advanced nonlinear varied-modified coefficient of shear correction including the coefficient term \(z^{3}\) of TSDT is presented. Secondly, the dynamic responses of stresses and deflection in GDQ computation are presented. Finally, the parametric effects of temperature and power law index of FGM on the dynamic responses of stress and deflection are presented.