Nonlocal radiating thermoelastic nanobeams with the rotary inertia: damped waves under the Green–Naghdi II theory

We consider the problem of modeling thermoelastic nanobeams that dissipate thermal energy by radiation. The proposed study focuses on one-dimensional nanostructures whose mechanical behavior is described by a nonlocal elasticity theory and modeled through the Rayleigh beam theory, which includes the effects of rotary inertia. Thermal energy exchange with the environment is accounted for by employing an extended form of the Green Naghdi type II theory of thermoelasticity, which allows the modeling of radiative effects without resorting to classical Fourier diffusion. The coupled thermoelastic system is solved under wave-form assumptions, allowing for the emergence of damped wave phenomena induced by the radiating effects. The results highlight the differences between the Rayleigh and Euler Bernoulli formulations, especially in the local regime, and confirm the presence of dissipative behavior in terms of wave speed attenuation and damping over time. Although the model is linear, the structure of the dispersion relation reflects features typically associated with nonlinear responses, such as amplitude-dependent wave attenuation. This provides a foundation for future nonlinear extensions in thermomechanical nanobeams, in line with recent advances in nonlinear nanomechanics. The model may be suitable for applications in nanoengineering fields where temperature effects on mechanical response are non-negligible, such as nanosensors and thermomechanical actuators.