• Smart Structures and Systems
• /
• v.26 no.2
• /
• pp.185-193
• /
• 2020

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

• Steel and Composite Structures
• /
• v.50 no.2
• /
• pp.135-148
• /
• 2024

This paper analytically investigates the free vibration analysis of functionally graded-carbon nanotube reinforced composite (FG-CNTRC) plates by dynamic stiffness method (DSM). The properties of CNTRC are determined with the extended rule of mixture. The governing differential equations of motion based on the first-order shear deformation theory of CNTRC plate are derived using Hamilton's principle. The FG-CNTRC plates are studied for a uniform and two different distributions of carbon nanotubes (CNTs). The accuracy and performance of the DSM are compared with the results obtained from closed closed-form and semi-analytical solution methods in previous studies. In this study, the effects of boundary condition, distribution type of CNTs, plate aspect ratio, plate length to thickness ratio, and different values of CNTs volume fraction on the natural frequencies of the FG-CNTRC plates are investigated. Finally, various natural frequencies of the plates in different conditions are provided as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.

• Steel and Composite Structures
• /
• v.47 no.1
• /
• pp.1-17
• /
• 2023

This paper deals with the free vibration behavior of rotating composite beams reinforced with carbon nanotubes (CNTs) under uniform thermal loads. The temperature-dependent beam material is assumed to be a mixture of single-walled carbon nanotubes (SWCNTs) in an isotropic matrix and five different functionally graded (FG) distributions of CNTs are considered according to the variation along the thickness, namely the UD-uniform, FG-O, FG-V, FG-Λ and FG-X distributions where FG-V and FG-Λ are unsymmetrical patterns. Considering the Timoshenko beam theory (TBT), a new finite element formulation of functionally graded carbon nanotube reinforced composite (FGCNTRC) beam is created for the first time. And the effects of several essential parameters including rotational speed, hub radius, effective material properties, slenderness ratio, boundary conditions, thermal force and moments due to temperature variation are considered in the formulation. By implementing different boundary conditions, some new results of both symmetric and non-symmetrical distribution patterns are presented in tables and figures to be used as benchmark for further validation. In addition, as an alternative advanced composite application for rotating systems exposed to thermal load, the positive effects of CNT addition in improving the dynamic performance of the system have been observed and the results are presented in several tables and figures.

• Steel and Composite Structures
• /
• v.25 no.2
• /
• pp.141-155
• /
• 2017

This paper presents an investigation into the magneto-thermo-mechanical vibration and damping of a viscoelastic functionally graded-carbon nanotubes (FG-CNTs)-reinforced curved microbeam based on Timoshenko beam and strain gradient theories. The structure is surrounded by a viscoelastic medium which is simulated with spring, damper and shear elements. The effective temperature-dependent material properties of the CNTs-reinforced composite beam are obtained using the extended rule of mixture. The structure is assumed to be subjected to a longitudinal magnetic field. The governing equations of motion are derived using Hamilton's principle and solved by employing differential quadrature method (DQM). The effect of various parameter like volume percent and distribution type of CNTs, temperature change, magnetic field, boundary conditions, material length scale parameter, central angle, viscoelastic medium and structural damping on the vibration and damping behaviors of the nanocomposite curved microbeam is examined. The results show that with increasing volume percent of CNTs and considering magnetic field, material length scale parameter and viscoelastic medium, the frequency of the system increases and critically damped situation occurs at higher values of damper constant. In addition, the structure with FGX distribution type of CNTs has the highest stiffness. It is also observed that increasing temperature, structural damping and central angle of curved microbeam decreases the frequency of the system.

• Steel and Composite Structures
• /
• v.42 no.1
• /
• pp.23-32
• /
• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Steel and Composite Structures
• /
• v.44 no.4
• /
• pp.451-471
• /
• 2022

In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite-Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FG-CNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-X-CNTRC beam is the highest, followed by UD and FG-O.

• Steel and Composite Structures
• /
• v.36 no.6
• /
• pp.643-656
• /
• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Structural Engineering and Mechanics
• /
• v.64 no.3
• /
• pp.381-390
• /
• 2017

Present paper deals with the large amplitude flexural vibration of carbon nanotube reinforced composite (CNTRC) plates. Distribution of CNTs as reinforcements may be uniform or functionally graded (FG). The equivalent material properties of the composite media are obtained according to a refined rule of mixtures which contains efficiency parameters. To account for the large deformations, von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity is included into the formulation. The matrix representation of the governing equations is obtained according to the Ritz method where the basic shape functions are written in terms of the Chebyshev polynomials. Time dependency of the problem is eliminated by means of the Galerkin method and the resulting nonlinear eigenvalue problem is solved employing a direct displacement control approach. Results are obtained for completely clamped and completely simply supported plates. Results are first validated for the especial cases of FG-CNTRC and cross-ply laminated plates. Afterwards, parametric studies are given for FG-CNTRC plates with different boundary conditions. It is shown that, nonlinear frequencies are highly dependent to the volume fraction and dispersion profiles of CNTs. Furthermore, mode redistribution is observed in both simply supported and clamped FG-CNTRC plates.

• Steel and Composite Structures
• /
• v.23 no.6
• /
• pp.623-631
• /
• 2017

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.

• Advances in nano research
• /
• v.16 no.5
• /
• pp.445-458
• /
• 2024

The objective of this paper is to present free vibration and static stability analyses of rotating composite beams reinforced with carbon nanotubes (CNTs) under uniform thermal loads. Beam structural equations and CNT-reinforced composite (CNTRC) beam formulations are derived based on Timoshenko beam theory (TBT). The temperature-dependent properties of the beam material, such as the elastic modulus, shear modulus, and material density, are assumed to vary over the thickness according to the rule of mixture. The beam material is modeled as a mixture of single-walled carbon nanotubes (SWCNTs) in an isotropic matrix. The SWCNTs are aligned and distributed in the isotropic matrix with different patterns of reinforcement, namely the UD (uniform), FG-O, FG-V, FG- Λ and FG-X distributions, where FG-V and FG- Λ are asymmetric patterns. Numerical examples are presented to illustrate the effects of several essential parameters, including the rotational speed, hub radius, effective material properties, slenderness ratio, boundary conditions, thermal force, and moments due to temperature variation. To the best of the authors' knowledge, this study represents the first attempt at the finite element modeling of rotating CNTRC Timoshenko beams under a thermal environment. The results are presented in tables and figures for both symmetric and asymmetric distribution patterns, and can be used as benchmarks for further validation.