Acta Mech https://doi.org/10.1007/s00707-018-2281-5 ORIGINAL PAPER S. Rashahmadi · S. A. Meguid Modeling size-dependent thermoelastic energy dissipation of graphene nanoresonators using nonlocal elasticity theory Received: 22 June 2018 / Revised: 7 August 2018 © Springer-Verlag GmbH Austria, part of Springer Nature 2018 Abstract Recent developments in nanostructured materials have led to the use of graphene sheets as resonators in advanced micro- and nanoelectromechanical systems. An important feature of micro- and nanoresonators is their ability to function with low power dissipation. The main intrinsic mechanism of energy loss in these advanced devices is thermoelastic damping (TED). In this article, we study TED effects in orthotropic graphene sheets of varied lengths operating at different temperatures using nonlocal elasticity theory. For this purpose, the fundamental thermoelastic relations are used to develop a system of coupled partial differential equations to describe the behavior of graphene nanoresonators. The orthotropic mechanical and thermal properties of graphene were taken into account in our model for zigzag and armchair chiralities operating at different temperatures. The free in-plane vibration of the graphene nanoresonator is analyzed using Galerkin method. Decidedly, we show that the developed system of equations is capable of describing the TED behavior of graphene nanoresonators along the two considered chiralities during thermoelastic vibration. Specifically, we examined the influence of size, chirality, and temperature upon thermoelastic damping, as measured by the so-called quality factor, of the graphene nanoresonator. Our results reveal that the nanoresonator experiences higher energy dissipation with increased temperature. They also reveal the dependence of the energy dissipation upon the size and chirality of the graphene sheet. 1 Introduction Recent advances in micro- and nanoelectromechanical systems (MEMS/NEMS) such as mechanical nanores- onators have attracted significant attention from the scientific community. Mechanical nanoresonators are one of the most significant components of MEMS/NEMS devices. They can sense very small quantities, such as mass and force, as a result of changes in their resonance response. The performance of MEMS/NEMS can be improved by using more efficient nanoresonators that make use of low density, high flexibility, and high-strength graphene sheet [1]. In fact, graphene sheets have been considered as very suitable candidates to replace silicon in the next-generation MEMS/NEMS [2]. In recent years, extensive efforts have been dedicated to design new classes of resonators with high sensitivity, fast response, and reduced energy consumption. Reducing the energy consumption of a resonator will lead to smaller energy source. Energy consumption becomes critical, when the number of nanoresonators in an electronic device is significant. These electronic devices will be subjected to thermoelastic effects and would thus suffer from thermoelastic damping (TED) effects. S. Rashahmadi · S. A. Meguid (B ) Mechanics and Aerospace Design Laboratory, University of Toronto, Toronto, ON M5S 3G8, Canada E-mail: meguid@mie.utoronto.ca S. Rashahmadi Department of Mechanical Engineering, Urmia University, Urmia, Iran