Thermoelastic damping analysis in micro-beam resonators considering nonlocal strain gradient based on dual-phase-lag model

•TED is first established in nonlocal strain gradient theory with dual-phase-lag model.•The equations with scale effects on TED are solved by complex frequency method.•The effects of scale parameters and material properties on TED are examined.•Both stiffness hardening and softening effects are captured.•The present method is useful to evaluate TED in nanomechanical resonators. Thermoelastic damping (TED), as a main source of intrinsic energy dissipation, is crucial to the design of the micro/nano-devices and -systems with higher quality factor (Q-factor). However, the classical analysis model of TED fails in micro/nano-scale due to the influence of small-scale effect. The present article focuses on investigating the influence of scale effect on the TED of micro-beam resonators by considering stress nonlocal and higher-order strain gradient effects. Firstly, the governing differential equations are formulated by employing the nonlocal strain gradient theory (NSG) in conjunction with the dual-phase-lag (DPL) heat conduction model. According to the assumption of vibration mode and the boundary conditions, the size-dependent Q-factor expression of TED is derived by the complex frequency method. Finally, the influences of various parameters on the TED of micro-beam resonators, such as nonlocal parameter, length scale coefficient, slenderness ratio and material type, are discussed in detail. And then, the analysis results are compared with the TED of classical thermal-mechanical model. This article provides a novel theoretical analysis model of the TED in micro/nano-meter scale field, which has practical significance in the design of high-efficiency devices and systems.