Abstract
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.
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