Analysing Nano Resonator dynamics influenced from an oscillating thermal load in the framework of two temperature A-B fractional model

This study investigates vibration phenomenon including thermocoupling effects in nanoscale resonators exposed to a fluctuating heat source. Mathematical model of the problem is established by employing the Atangana-Baleanu (A-B) fractional derivative within a two-temperature, three-phase-lag thermoelastic heat transfer model. The approach incorporates the non-singular Mittag-Leffler kernel associated with the A-B operator to account for memory-dependent effects, providing an enhanced representation of thermal and mechanical wave propagation in microscale systems. The governing equations for a clamped nano-resonator beam are solved analytically by using the Laplace transform technique, with numerical inversions carried out via the Riemann-sum approximation to determine the distributions of displacement, conductive and thermodynamic temperatures, and axial stress. Analysis of the significant parameters depicted through the graphical representations, highlights the crucial impacts of the A-B fractional parameter, two-temperature phenomena, and the angular frequency of the heat source on the thermophysical fields. The results align with trends observed in previous theoretical and computational studies, thereby confirming the model’s accuracy and its effectiveness in elucidating complex interactions within nanoscale resonators. These findings establish a solid foundation for optimizing the design and functionality of micro- and nano-electromechanical systems subjected to dynamic thermal loads.