STATE-SPACE APPROACH TO VIBRATION OF GOLD NANO-BEAM INDUCED BY RAMP TYPE HEATING WITHOUT ENERGY DISSIPATION IN FEMTOSECONDS SCALE

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.