This paper analyzes the thermoelastic dynamic behavior of simply supported viscoelastic nanobeams of fractional derivative type due to a dynamic strength load. The viscoelastic Kelvin–Voigt model with fractional derivative with Bernoulli–Euler beam theory is introduced. The generalized thermoelastic heat conduction model with a two-phase lag is also used. It is assumed that the beam is rotating at a uniform angular velocity and that the thermal conductivity varies linearly depending on the temperature. Due to a variable harmonic heat and retreating time-dependent load, the nanobeam is excited. The Laplace integral transformation technique is used as the solution method. The thermodynamic temperature, deflection function, bending moment, and displacement are numerically calculated. Results of fractional and integer viscoelastic material models are compared. In the studied system, the effect of the nonlocal parameter, viscosity and varying load on the solutions is shown, and the temperature-dependence of the thermal conductivity is analyzed.

中文翻译：

---

由于机械和热载荷而具有可变热导率的旋转纳米束的热粘弹性分数模型

本文分析了分数导数型简支粘弹性纳米梁在动态强度载荷作用下的热弹性动力学行为。介绍了基于伯努利-欧拉梁理论的具有分数导数的粘弹性Kelvin-Voigt模型。还使用了具有两相滞后的广义热弹性热传导模型。假设光束以均匀的角速度旋转，并且热导率随温度线性变化。由于可变的谐波热量和撤退的时间相关负载，纳米束被激发。采用拉普拉斯积分变换技术作为求解方法。热力学温度、挠度函数、弯矩和位移是通过数值计算的。比较了分数和整数粘弹性材料模型的结果。在所研究的系统中，显示了非局部参数、粘度和变化载荷对溶液的影响，并分析了热导率与温度的关系。