In this paper, thermoelastic damping in a nano-beam is studied employing the type III of Green-Naghdi (GN) theory (with energy dissipation). The nano-beam is considered as a beamtype of NEMS (nano-electro-mechanical systems). A nonlocal Euler–Bernoulli beam model is established based on the theory of nonlocal elasticity and the small scale effect is taken into consideration in the former theory. A hybrid numerical method based on the Galerkin finite element formulation and Newmark finite difference method is used to solve the derived governing equations. The presented formulations are valid for both types II and III of GN theory of generalized coupled thermoelasticity in NEMS and MEMS (micro-electro-mechanical systems). The obtained results for type II of GN theory (without energy dissipation) are validated by the existing analytical results in the literature to verify the presented method and results. To show the effects of thermoelastic damping on dynamic behaviors of thermoelastic field in NEMS, the type III of GN theory is investigated in the paper. The responses of nano-beam resonator in lateral deflection, temperature and stress fields considering simply supported conditions are obtained and shown as functions of length and time. Also, the effect of different loading parameters on the transient thermoelastic behaviors is studied in both types II and III in GN theory. The corresponding dynamic properties are presented, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant.

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