Abstract
The present research presents a new advanced mathematical model based on memory-dependent generalized thermoelasticity with time delays to investigate the thermoelastic vibrations of rotating nanobeams with variable thermal conductivity. In contrast to the traditional derivative, it turns out that the memory-dependent derivative of physical processes, which represents the average total rate of change over a period of time, depends on the previous states. Furthermore, the influence of size on the dynamic responses to thermoelastic vibrations in nanobeams is taken into account. The silicon nanobeam was heated with a non-Gaussian laser beam, which caused vibrations due to the thermo-elastic damping effect. The problem has been treated analytically in the transformed field with the help of the Laplace transform and numerically inverted using a suitable numerical approach based on the Fourier series expansion method. The significance of the memory-dependent derivative elements (kernel functions, time delay) as well as the effects of changing the thermal conductivity, angular velocity of rotation, and nonlocal parameters on the behavior of the studied fields were analyzed. According to the results, it was shown that the function of the nucleus in its various forms, as well as the time delay, has a significant influence on the memory-dependent heat wave propagation. In the presence of a memory-dependent derivative, statistically significant differences in physical quantities for distinct models were detected.