Small Scale Effect on Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes with Uncertainty

Abstract

This paper investigates the statistical dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are studied by using the theory of nonlocal elasticity. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton's principle. The Young's modulus of elasticity of the DWCNTs is assumed as stochastic to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin's method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed; meanwhile the effects of small scale coefficients on the statistical dynamic response of the DWCNTs are investigated.