Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator

In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in the beam are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping and frequency shift.