Analytical Solution of Thermoelastic Damping in a Nanoscale Beam using the Fractional Order Theory of Thermoelasticity

In this paper, we study the generalized thermoelastic vibration of a bounded nano-beam resonator under fractional order theory of thermoelasticity. The theory of generalized thermoelasticity with one relaxation time can be established in the limit as the special cases of the present model. The effect of fractional parameter is investigated on the nano-beam resonator for beams with clamped ends. Analytical expressions for the deflection, temperature change, frequency shift, and thermoelastic damping have been derived for the beam. The effect of the fractional parameter on the variation of frequency shifts and thermoelastic damping is analyzed graphically.