This study aims to examine the dynamics of 3D plates under uniform and non-uniform temperature distributions within the framework of the Fractional Generalized Thermoelasticity approach. The following crucial outcomes reflect the completeness of the proposed model:

•          The variations of natural frequencies and mode shapes versus temperature are compared with the experimental results of the NASA report. It is observed that these are both fundamental for identifying the fractional material properties and the thermal and elastic ones.

• The nonlocal approach using fractional calculus gives more consistent results with the experimental one than the classical local theory.

• In the model, the effects connected with thermoelastic damping result in the quadratic eigenvalue problem where complex frequencies and modes are obtained.

• The complex frequency spectrum and mode shapes of the 3D plate with free ends under two different temperature distributions are considered for different values of the fractional continua order   and the length scale parameter  .

• The fractional solution closest to the experimental results and the classical modes are compared for the first four frequencies. Moreover, the absolute differences between them are also presented with contour plots. 

• For the uniform temperature distribution, a mode shifting is observed between the modes corresponding to the 4th and 5th frequencies, while this is not kept for the non-uniform temperature distribution. 

• For the non-uniform temperature distribution, mode shape analysis is performed, assuming that elasticity modulus, thermal expansion, and specific heat parameters are functions of temperature.

• The frequencies close to the experimental values are obtained at smaller values of fractional order while temperature increases for the fixed length scale parameter. 

• It is observed that the peak point of the out-of-plane displacement is shifted toward the warm zone under the non-uniform temperature distribution. This investigation shows a good agreement with the experimental observations.

These novelties indicate that combining fractional mechanics and Generalized thermoelasticity can establish a more accurate model for complex materials under thermal loading.

https://doi.org/10.2514/1.J063310