• Steel and Composite Structures
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• v.46 no.4
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• pp.553-563
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• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.515-526
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• 2017

Dynamic response of functionally graded Carbon nanotubes (FG-CNT) reinforced pipes conveying viscous fluid under accelerated moving load is presented. The mixture rule is used for obtaining the material properties of nano-composite pipe. The radial force induced by viscous fluid is calculated by Navier-Stokes equation. The material properties of pipe are considered temperature-dependent. The structure is simulated by Reddy higher-order shear deformation shell theory and the corresponding motion equations are derived by Hamilton's principal. Differential quadrature (DQ) method and the Integral Quadrature (IQ) are applied for analogizing the motion equations and then the Newmark time integration scheme is used for obtaining the dynamic response of structure. The effects of different parameters such as boundary conditions, geometrical parameters, velocity and acceleration of moving load, CNT volume percent and distribution type are shown on the dynamic response of pipe. Results indicate that increasing CNTs leads to decrease in transient deflection of structure. In accelerated motion of the moving load, the maximum displacement is occurred later with respect to decelerated motion of moving load.

• Wind and Structures
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• v.24 no.3
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• pp.267-285
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• 2017

This paper addresses vibration and instability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying viscous fluid. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Flugge shell model is applied for mathematical modeling of structure. Based on energy method and Hamilton's principal, the motion equations are derived. Differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as volume percent of CNTs, elastic medium, boundary condition and geometrical parameters are discussed.

• Wind and Structures
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• v.30 no.2
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• pp.133-140
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• 2020

In this paper, critical fluid velocity and frequency of laminated pipe conveying fluid are presented. Each layer of the pipe is reinforced by functionally graded carbon nanotubes (FG-CNTs). The internal fluid is assumed turbulent and the induced forces are calculated by momentum equations. The pipe is resting on viscoelastic foundation with spring, shear and damping constants. The motion equations are derived based on classical shell theory and energy method. Differential quadrature method (DQM) is used for solution and obtaining the critical fluid velocity. The effects of volume percent and distribution of CNT, boundary condition, lamina layer number, length to radius ration of pipe, viscoelastic medium and fluid velocity are shown on the critical fluid velocity. Results show that with increasing the lamina layer number, the critical fluid velocity increases.

• Advances in concrete construction
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• v.9 no.1
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• pp.103-113
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• 2020

This paper deal with the critical fluid velocity response of nanocomposite pipe conveying fluid based on numerical method. The pressure of fluid is obtained based on perturbation method. The motion equations are derived based on classical shell theory, energy method and Hamilton's principle. The shell is reinforced by nanoparticles and the distribution of them are functionally graded (FG). The mixture rule is applied for obtaining the equivalent material properties of the structure. Differential quadrature method (DQM) is utilized for solution of the motion equations in order to obtain the critical fluid velocity. The effects of different parameters such asCNT nanoparticles volume percent, boundary conditions, thickness to radius ratios, length to radius ratios and internal fluid are presented on the critical fluid velocity response structure. The results show that with increasing the CNT nanoparticles, the critical fluid velocity is increased. In addition, FGX distribution of nanoparticles is the best choice for reinforcement.