Analyzing nanoscale beam dynamics under moving loads and thermal decay with a DPL Thermoelastic Framework

This innovative study develops a novel analytical framework to investigate the dynamics of nanoscale beams subjected to moving loads within an exponentially decaying thermal field that varies across both time and space. Utilizing the dual-phase-lag (DPL) thermoelasticity model, the research demonstrates originality by incorporating the finite speed of thermal wave propagation and addressing critical delays in heat flux and temperature gradients , key phenomena often overlooked in conventional thermoelastic models. Moreover, the study makes a noteworthy contribution by integrating nonlocal elasticity theory to account for size-dependent effects, an essential consideration for accurately modeling nanoscale structures. This innovative approach opens new avenues for advanced engineering applications in materials science and nanoscale system design. To simplify the analysis, the coupled partial differential equations governing the system are solved in the Laplace domain, with numerical inversion methods employed to obtain deflection, temperature, and other field variables in the physical domain. By examining specific cases derived from the general model, the study reveals distinctive behavioral patterns of nanoscale beams under varying conditions. This work not only delivers critical insights into the thermal and structural response of nanoscale systems but also underscores its transformative potential for advancing nanotechnology and materials engineering.