• Steel and Composite Structures
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• 제46권4호
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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.

• Steel and Composite Structures
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• 제28권5호
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free.

• Wind and Structures
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• 제25권2호
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• pp.131-156
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• 2017

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin-Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton's principle is utilized for deriving the motion equations where the size effects are considered based on Eringen's nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

• Steel and Composite Structures
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• 제42권2호
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• pp.243-256
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• 2022

A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1-continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.

• Computers and Concrete
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• 제26권3호
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• pp.213-226
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• 2020

The present study covenants with the static and free vibration behavior of nanocomposite sandwich plates reinforced by carbon nanotubes resting on Pasternak elastic foundation. Uniformly distributed (UD-CNT) and functionally graded (FG-CNT) distributions of aligned carbon nanotube are considered for two types of sandwich plates such as, the face sheet reinforced and homogeneous core and the homogeneous face sheet and reinforced core. Based on the first shear deformation theory (FSDT), the Hamilton's principle is employed to derive the mathematical models. The obtained solutions are numerically validated by comparison with some available cases in the literature. The elastic foundation model is assumed as one parameter Winkler - Pasternak foundation. A parametric study is conducted to study the effects of aspect ratios, foundation parameters, carbon nanotube volume fraction, types of reinforcement, core-to-face sheet thickness ratio and types of loads acting on the bending and free vibration analyses. It is explicitly shown that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

• Steel and Composite Structures
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• 제37권2호
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• pp.253-258
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• 2020

Vibration response in a sandwich plate with a nanocompiste core covered by magnetic layer is presented. The core is armed by functionalyy graded-carbon nanotubes (FG-CNTs) where the Mori-Tanaka law is utilized assuming agglomeration effects. The structure plate is located on elastic medium simulated by Pasternak model. The governing equations are derived based on Mindlin theory and Hamilton's principle. Utilizing diffrential quadrature method (DQM), the frequency of the structure is calculated and the effects of magnetic layer, volume percent and agglomeration of CNTs, elastic medium and geometrical parameters of structure are shown on the frequency of system. Results indicate that with considering magnetic layer, the frequency of structure is increased.

• Advances in nano research
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• 제5권2호
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• pp.69-97
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• 2017

In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

• Steel and Composite Structures
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• 제28권3호
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• pp.381-388
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• 2018

In this paper, forced vibration of micro cylindrical shell reinforced by functionally graded carbon nanotubes (FG-CNTs) is presented. The structure is subjected to transverse harmonic load and modeled by beam model. The size effects are considered based on strain gradient theory containing three small scale parameters. The mixture rule is used for obtaining the effective material properties of the structure. Based on sinusoidal shear deformation theory of beam, energy method and Hamilton's principle, the motion equations are derived. Applying differential quadrature method (DQM) and Newmark method, the frequency curves of the structure are plotted. The effect of different parameters including, CNTs volume percent and distribution type, boundary conditions, size effect and length to thickness ratio on the frequency curves of the structure is studied. Numerical results indicate that the dynamic deflection of the FGX-CNT-reinforced cylindrical is lower with respect to other type of CNT distribution.

• Steel and Composite Structures
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• 제44권2호
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• Structural Engineering and Mechanics
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• 제64권4호
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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.