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

Abstract

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by using, two dimensional non-Fourier heat conduction with one relaxation time based on continuum theory frame. 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-clamped nano-beam with isothermal boundary conditions at both ends is studied. This nonlocal nano-beam 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 thermoelastic models. Thermoelastic damping effects on the damping ratio are studied for the various nano-beam thicknesses and ambient temperatures. In addition to, the study includes computations for different values of nonlocal theory parameter. The results show that with increasing the amount of nonlocal parameter and also with decreasing the length of the nano-beam, difference of the results of classical and nonlocal theory increases.