Vibration Analysis of Nano-Beam with Consideration of Surface Effects and Damage Effects

Abstract

On the basis of Euler-Bernoulli beam theory, surface elastic theory, the strain equivalent assumption and modiffed couple stress theory, the nonlinear governing equations of the nano-beam are derived. In addition, the Galerkin method and the Harmonic Balance Method are adopted so as to give a solution to the equations. In the example, the effects of nano-beam length, nano-beam thickness, damage factor and surface efect to curves of amplitude-frequency response of the nano-beam are discussed. The results show that damage effects should be taken into consideration and the frequency can be controlled by load and structure size of nano-beam.

Keywords

• damage
• geometric nonlinearity
• surface energy
• nano-beam