Three-Dimensional Plate Dynamics in the Framework of Space-Fractional Generalized Thermoelasticity: Theory and Validation

Abstract

This work aims to study the dynamics of 3D plates under uniform and nonuniform temperature distributions in the framework of the space-fractional generalized thermoelasticity (S-FGT) approach. The quadratic eigenvalue problem is obtained, which means that the thermoelastic damping plays a meaningful role due to the plate’s thermal energy absorption. The plate’s complex frequency spectrum and mode shapes (free ends) under two different temperature distributions are considered for different values of the fractional continua order α and the length scale parameter l. For the first four frequencies, the fractional modes closest to the experimental results and the classical modes are presented with the absolute differences between them. For the nonuniform temperature distribution case, the mode shape analysis is performed assuming that modulus of elasticity, thermal expansion, and specific heat parameters are functions of the temperature. The primary outcomes of the paper can be stated as follows: 1) the S-FGT approach analysis gives more reliable results than the classical (local) theory; 2) the peak point of the out-of-plane mode amplitude is shifted toward the warmed zone; 3) a mode shifting is observed for the uniform temperature distribution in contrast to the nonuniform temperature distribution; 4) the fractional order derivative and length scale parameter depend on temperature, similar to other material properties such as elastic modulus, specific heat, and coefficients of thermal expansion; 5) a decrease in the fractional order is observed, while temperature increases for the fixed length scale parameter. These novelties indicate that the S-FGT approach establishes a new model for analyzing materials under heating, and the results may be beneficial for designing thermal structures.