Nonlinear vibration of fluid-conveying double-walled carbon nanotubes under random material property

In this study, one performs the stochastic dynamic analysis of nonlinear vibration of the fluid-conveying double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. Based on the Hamilton’s principle, the nonlinear governing equations of the fluid-conveying DWCNTs are derived. In order to truly describe the random material properties of the DWCNTs, the Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position. By adopting 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 one uses 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 calculated. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies for both cases of coupling between longitudinal displacement and transverse displacement and uncoupling between them. However, the coefficients of variation of the amplitude of the displacement remain almost constant and stay within certain range with respect to the frequency. The calculated stochastic dynamic response plays an important role in estimating the structural reliability of the DWCNTs.