Abstract
In the nanoscale beam, the effect of the coupling between temperature and strain rate becomes domineering. In the present study, a generalized solution for the vibration of gold nano-beam resonator induced by ramp type heating is developed in the context of the Green and Naghdi model of generalized thermoelasticity. The solution takes into account the above effect. State-space and Laplace transform methods are used to determine the lateral vibration, temperature, displacement, stress and strain energy of the beam. A numerical example of gold nano-beam in femtoseconds scale has been calculated to illustrate the effect of the ramping time parameter on all the studied fields.