Mathematical modeling of concrete pipes reinforced with CNTs conveying fluid for vibration and stability analyses

In this study, vibration and stability of concrete pipes reinforced with carbon nanotubes (CNTs) conveying fluid are presented. Due to the existence of CNTs, the structure is subjected to magnetic field. The radial fore induced with fluid is calculated using Navier-Stokes equations. Characteristics of the equivalent composite are determined using Mori-Tanaka model. The concrete pipe is simulated with classical cylindrical shell model. Employing energy method and Hamilton\'s principal, the motion equations are derived. Frequency and critical fluid velocity of structure are obtained analytically based on Navier method for simply supported boundary conditions at both ends of the pipe. The effects of fluid, volume percent of CNTs, magnetic field and geometrical parameters are shown on the frequency and critical fluid velocity of system. Results show that with increasing volume percent of CNTs, the frequency and critical fluid velocity of concrete pipe are increased.