Coupled effects of nano-size, stretching, and slip boundary conditions on nonlinear vibrations of nano-tube conveying fluid by the homotopy analysis method

• Formulating and analyzing nonlinear vibration of CNT conveying fluid.
• Coupling nonlocal model and stretching effect for CNT conveying fluid.
• Using the homotopy analysis method for nonlinear solution of fluid conveying pipe.
• Modeling the slip boundary condition by utilizing Knudsen number.
• Observing divergence instability in doubly-clamped CNT conveying fluid.

In this paper, natural frequency and nonlinear response of carbon nano-tube (CNT) conveying fluid based on the coupling of nonlocal theory and von Karman's stretching have been obtained. The homotopy analysis method (HAM) has been used for solving nonlinear differential equation of system and convergence region of approach presented. Effects of mid-plane stretching, nonlocal parameter and their coupling in the model have been investigated. It has been concluded that stretching effect is significant only for higher-amplitude initial excitations and lower beam aspect ratios. Moreover, by including the slip boundary condition, the effect of nano-size flow has been revealed in the nonlinear vibration model. We have concluded that small-size effects of nano-tube and nano-flow have impressed critical velocity of fluid significantly specially for gas fluid. Analytical results obtained from HAM solution show satisfactory agreement with numerical solutions such as Runge–Kutta. Having an analytical approach, we have been able to investigate the unbounded growth of amplitude of vibrations for flow velocities near the critical value. Moreover, by employing the second-order approximation of Galerkin's method, the estimated natural frequency of the first mode is verified. The obtained results would indicate that the effects of higher mode on the first natural frequency are negligible for the doubly-clamped CNT.

The nonlinear response and natural frequency of system, obtained by HAM are remarkably impressed by critical flow velocity of divergence, Knudsen number, and nonlocal parameters.Figure optionsDownload as PowerPoint slide