Nonlinear thermal–mechanical vibration of flow-conveying double-walled carbon nanotubes subjected to random material property

The present study deals with the dynamic response variability of nonlinear thermal–mechanical vibration of the fluid-conveying double-walled carbon nanotubes (DWCNTs) by considering the effects of the temperature change, geometric nonlinearity and nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are derived based on the Hamilton’s principle and theory of thermal elasticity. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to position to actually describe the random material property of the DWCNTs. By utilizing the Monte Carlo simulation, the nonlinear coupled governing equations of the fluid-conveying DWCNTs become deterministic. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear coupled deterministic differential equations for many different sample functions. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations (SDs) of the amplitude of the displacement are calculated, meanwhile the effects of the temperature change and flow velocity on the statistical dynamic response of the DWCNTs are investigated. It is concluded that the mean value and SD of the amplitude of the displacement increase nonlinearly with the increase of the frequencies in both low and high temperatures. Furthermore, the mean value of the amplitude of the displacement for any fixed frequency decreases due to the temperature change in low temperature; on the contrary, it increases under the temperature change in high temperature.