In this study, a nanoscale beam of transversely isotropic thermoelastic (TIT) medium with two temperature and with Green–Naghdi (GN) III theory of thermoelasticity for free vibrations with simply supported boundaries have been examined. Euler–Bernoulli (EB) beam theory is used to formulate a mathematical model of the nanoscale beam in a closed form. The lateral deflection, frequency shift, thermal moment and thermoelastic damping have been solved. A program in MATLAB software is developed to find the numerical values for different physical quantities. The lateral deflection, frequency shift, thermal moment and thermoelastic damping for the varying two temperature, different modes, frequency of time harmonic sources, thickness of nano-beam, and material medium of nano-beam has been represented graphically and discussed. The results for some particular cases have also been compared to some earlier work done.

在这项研究中，研究了具有两个温度的横向各向同性热弹性（TIT）介质的纳米级梁，并利用Green-Naghdi（GN）III热弹性理论对具有简单支撑边界的自由振动进行了研究。欧拉-伯努利（EB）束理论用于建立封闭形式的纳米级束的数学模型。解决了横向挠度，频移，热矩和热弹性阻尼。开发了MATLAB软件中的程序来查找不同物理量的数值。用图形表示了变化的两个温度，不同模式，时间谐波源的频率，纳米束的厚度以及纳米束的材料介质的横向挠度，频移，热矩和热弹性阻尼。