Nonlinear vibration and dynamic response of nano composite conical tube by conveying fluid flow

Abstract

Modeling of tubes containing fluid flow is widely used in the study of heat exchangers, nuclear reactors, micro and nano tools, etc. This system is structurally simple but very complex in terms of dynamic behavior and vibrations. In this paper, an analytical relationship for nonlinear vibrations of self-excitation of a nanocomposite conical tube containing fluid flow is extracted, one end of which is free and the other side is fixed and is under gravitational force. The base material is assumed to be 1200 series aluminum, which is reinforced with carbon nanotubes. The Hamiltonian equations are obtained, assuming the Euler–Bernoulli beam theory and the use of the Galerkin method, dissected the partial derivative equations into Ordinary Differential Equations (ODE), then solved by MATLAB coding and investigated the effect of various parameters on system behavior. As the fluid velocity increases, the amplitude of the vibration increases and the nonlinear effects of the system increase, so more modes are needed to converge the responses. In a conical tube, the βT coefficient increases with increasing inner diameter along the tube and the system becomes more stable. Increasing the length of the pipe makes the opening conical pipe more stable and the closing conical pipe more unstable. The change in length has no effect on the stability of the cylindrical tube.