Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid

Abstract This paper investigates the effect of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force on the transverse vibration of the double-walled carbon nanotubes conveying fluid and the interaction between two types of nonlinearities. By using the Hamilton’s principle, the nonlinear governing equations of the double-walled carbon nanotubes conveying fluid are deduced. The effects of two types of nonlinearities on the coaxial and noncoaxial vibrations of the double-walled carbon nanotubes conveying fluid are discussed in numerical examples. The results show that the effect of geometric nonlinearity on the amplitude–frequency properties can be neglected if two types of nonlinearities are simultaneously considered. Compared with the uncoupling, the coupling between the longitudinal and transverse vibrations has little effect on the amplitude–frequency properties with considering two types of nonlinearities simultaneously. However, the coupling has significant effect on the amplitude–frequency properties with only considering the geometric nonlinearity.