In this article, size-dependent modeling and analysis of thermoelastic coupling effect on the oscillations of Timoshenko nanobeams are carried out. Small-scale effect on the nanostructure and heat conduction is taken into account with the aid of nonlocal strain gradient theory (NSGT) together with dual-phase-lag (DPL) heat conduction model. In order to illustrate the influence of nonclassical scale parameters on the coefficients of governing equations, the normalized forms of size-dependent equations of motion and heat conduction are established by definition of some dimensionless parameters. These coupled differential equations are then solved in the Laplace domain to attain the analytical thermoelastic responses of a simply supported Timoshenko nanobeam subjected to a dynamic load. Through several numerical examples, a detailed parametric study is performed to illuminate the decisive role of nonlocal, strain gradient and phase lag parameters in thermoelastic behavior of Timoshenko nanobeams. Furthermore, comparing the results corresponding to various relative magnitudes of nonlocal and strain gradient length scale parameters confirms the potential of NSGT for covering both hardening and softening characteristic of nanoscale structures.

在本文中，进行了尺寸相关建模和热弹性耦合效应对 Timoshenko 纳米梁振荡的分析。借助非局部应变梯度理论 (NSGT) 和双相滞后 (DPL) 热传导模型，考虑了对纳米结构和热传导的小尺度影响。为了说明非经典尺度参数对控制方程系数的影响，通过定义一些无量纲参数，建立了尺寸相关的运动方程和热传导方程的归一化形式。然后在拉普拉斯域中求解这些耦合的微分方程，以获得承受动态载荷的简支 Timoshenko 纳米梁的解析热弹性响应。通过几个数值例子，进行了详细的参数研究，以阐明非局部、应变梯度和相位滞后参数在 Timoshenko 纳米梁的热弹性行为中的决定性作用。此外，比较与非局部和应变梯度长度尺度参数的各种相对大小相对应的结果，证实了 NSGT 覆盖纳米结构硬化和软化特性的潜力。