Coupled thermo-mechanical dynamics of rotating nano-beams with spatiotemporal nonlocality and higher-order memory-driven heat transfer

Purpose This study aims to advance the thermo-electro-mechanical modeling of rotating nanobeam resonators. The primary objective is to develop a comprehensive theoretical framework that accurately predicts the nanobeam’s dynamic response under combined rotational, thermal and magnetic influences, considering crucial size-dependent and memory effects. This study seeks to offer deeper insights for the optimal design of advanced micro-electromechanical systems and nano-electromechanical systems (MEMS/NEMS). Design/methodology/approach The study uses the Euler–Bernoulli beam theory, integrating a novel spatiotemporal nonlocal elasticity theory based on the Klein–Gordon (KG) model, which incorporates both internal length and time scales. For heat conduction, the Moore–Gibson–Thompson (MGT) theory with a higher-order memory-dependent derivative is used. Governing equations are derived using Laplace transformation, with the inverse transform performed through Zakian’s algorithm for enhanced accuracy. Findings Numerical simulations reveal the significant roles of rotation and size-dependent effects on the nanobeam’s dynamic behavior. Key findings highlight the substantial influence of delayed time parameters, various kernel types and applied magnetic fields on the coupled fields (displacement, temperature, bending moment). The study also demonstrates that increasing angular velocity suppresses deformation, while magnetic fields enhance displacement but reduce bending moment. Research limitations/implications This study is based on the Euler–Bernoulli beam theory, which inherently neglects shear deformation and rotational inertia effects, limiting its applicability to slender beams. Practical implications The findings are crucial for the design and optimization of advanced MEMS/NEMS. This includes applications, such as micro-gyroscopes, high-frequency sensors, actuators and resonators, where accurate thermal, magnetic and mechanical coupling is essential at the nanoscale. The insights support enhanced structural stability, thermal control and stress management in smart nanoengineering systems. Originality/value This manuscript presents a novel and unified theoretical framework by uniquely integrating spatiotemporal nonlocal elasticity (KG type) with the MGT thermoelasticity theory incorporating higher-order memory-dependent derivatives. It offers a more physically realistic model for rotating nanobeams under coupled thermomechanical and magnetic fields, advancing beyond existing literature by considering combined size-dependent and memory effects.