A modified nonlocal model with length and time scale parameters for analyzing vibrations of rotating Nanobeams in a magnetic field under harmonic thermal loading

This research bridges a critical gap in the understanding of rotating nanobeams by introducing a novel thermoelastic model that incorporates nonlocal effects, thermal dynamics, and magnetic field interactions. Traditional models, which primarily relied on classical elasticity theories, often failed to capture the nuanced interplay between size-dependent phenomena and external influences. The innovation of this study lies in integrating the modified Klein-Gordon nonlocal elasticity theory with the Euler-Bernoulli beam framework, providing a more precise depiction of nanobeam behavior during rotation. Notably, this model incorporates an internal length scale and time scale, paired with the dual-phase lag (DPL) heat conduction model, which uniquely accounts for two distinct thermal response delays. The numerical results reveal several key findings: rotation significantly amplifies thermal stresses, while the inclusion of nonlocal effects reduces these stresses, highlighting the importance of considering size-dependent mechanics. Furthermore, axial magnetic fields were found to enhance nanobeam stability, while variable thermal loads introduced complex dynamic behaviors requiring advanced mathematical tools, such as Laplace transforms and state-space methods, to unravel. Validation of the model against existing literature demonstrates its precision, with a reported improvement of up to 15 % in predicting thermal and mechanical responses under nonlocal and dual-phase lag conditions. This study not only advances theoretical understanding but also provides a robust framework for future applications in nanotechnology, including nanoscale sensors, actuators, and energy systems.