M Sheikhlou - Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili
Gh Rezazadeh - Mechanical Engineering Department, Urmia University, Urmia, Iran.
H Azimloo - Mechanical Engineering Department, Urmia University, Urmia, Iran.
R Shabani - Mechanical Engineering Department, Urmia University, Urmia, Iran.

Thermo-elastic damping (TED) is a source of dissipation in micro/nano-scale resonators and recognized as a dominant loss mechanism at room temperature. Predicting TED is crucial in the design of high quality factor micro/nano-electromechanical systems (MEMS/NEMS) resonators. Experimental results revealed that the size effects are significant in the mechanical behavior of these structures when thedimensions become small and comparable to molecular distances. In this paper, the size-dependent TED of beam-resonators has been investigated on the basis of the nonlocal elasticity theory and Euler–Bernoulli beam theory. The governing equations of coupled thermoelastic problems have been derived for transverse vibration of a thin beam. The Galerkin discretization method and complex-frequency approach have been used to study eigenvalue solution of TED of a beam resonator with both ends clamped and isothermal. As a validation, the obtained results when the nonlocal effect is not taken into account have been compared with benchmark analytic results available in the literature for a silicon nano-beam resonator and a very good agreement has been observed. Finally, numerical results addressing the significance of the nonlocal effect on the TED ratio of the beam resonators have been presented

Nonlocal elasticity theory, Euler–Bernoulli beam theory, Thermo-elastic damping, Nano-beam, Quality factor