Saeidreza Mohebpour

The nonlinear free vibrations and stability of pipes conveying fluid constructed of Functionally Graded Carbon Nano-Tube Reinforced Composite (FG-CNTRC) materials are studied in this paper. The material properties of FGCNTRC are supposed to be graded within the thickness direction and estimated by the modified rule of mixtures. The equations of motion of the system are derived using the extended Hamilton’s principle for open systems based on Timoshenko beam theory. To consider nonlinear effects, large deformations-small strains hypothesis is adopted by applying the von K´arm´an geometric nonlinear theory. The nonlinear free vibration and the fluid flow effects in the pipe system are investigated numerically, employing the super convergent finite element method to discretize nonlinear coupled partial differential equations. This is a powerful method to accurately predict steady state response of a dynamical system. The Newmark and Newton-Raphson methods are also applied to solve the resulted set of ordinary nonlinear differential equations. The applicability of the proposed mathematical approach is then be studied through several numerical investigations with different parameters including nanotube volume fraction, mass ratio, CNT distributions, fluid velocity and pipe geometry.