Vibrational behavior of thermoelastic rotating nanobeams with variable thermal properties based on memory-dependent derivative of heat conduction model

The current work presents a theoretical framework to analyze the nonlocal thermoelastic model with a general kernel function for memory-based derivatives by incorporating two-time delays. The introduced model aims at studying the thermomechanical response of rotating size-dependent nanobeams. The nonlocal elasticity theory and the generalized heat conduction model with phase delays are utilized to formulate the problem. In the proposed model, the thermal conductivity is expected to vary linearly with temperature and the system is excited by a variable harmonic heat source by considering the time-dependent exponential decaying load. To this end, the semi-analytical solutions for the transverse and axial displacements, thermodynamic temperature and bending moment are examined using the Laplace transform method. The effects of the nonlocal parameter and various loading conditions are also investigated and discussed. Finally, it is demonstrated that how the linear variation of thermal conductivity could affect the performance of the considered system.