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Abstract
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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.
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