Thermo-elastic Damping in Nano-beam Resonators Based on Nonlocal Theory

In this article, thermo-elastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. To this end, governing equation ofmotion of the beam is obtained from stress–strain relationship of the nonlocal elasticity model and alsogoverning equations of thermo-elastic damping are established using two dimensional non-Fourier heat conduction. Free vibration of the nano-beam resonators is analyzed using Galerkin reduced order model formulation for the first mode of vibration. In the present investigation a clamped-clampednano-beam with isothermal boundary conditions at both ends is studied. This nonlocal model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The obtained results are compared with the numerical results of the classical thermo-elastic models.Thermo-elastic damping effects on the damping ratio are studied for the various nano-beam thicknesses and ambient temperatures. In addition, the study includes computations for different values of nonlocal theory parameter. The results show that with increasing the amount of nonlocal parameterand also with decreasing the length of the nano-beam, difference between the results of classical andnonlocal theory increases

Keywords:

Thermo-elastic Damping , Nano-beam Resonator , Nonlocal Theory of Elasticity