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

• The study utilizes the dual-phase-lag (DPL) thermoelasticity model, which accounts for the finite speed of thermal wave propagation and delays in heat flux and temperature gradients, providing a more accurate representation of nanoscale beam dynamics. • By integrating nonlocal elasticity theory, the research addresses the critical size-dependent effects that are essential when analyzing nanoscale structures, making the findings relevant for advanced engineering applications. • The governing coupled partial differential equations are solved in the Laplace domain, allowing for a simplified analysis. The results are numerically inverted to obtain deflection, temperature, and other field variables in the physical domain. • The research explores specific scenarios derived from the general model, revealing distinct behaviors of nanoscale beams under various conditions, which enhances the understanding of their dynamic response. • The insights gained from this study are applicable to materials science and the design of nanoscale systems, paving the way for innovative engineering solutions in fields such as nanotechnology and structural engineering. 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.