Application of TW-DQ method to nonlinear free vibration analysis of FG carbon nanotube-reinforced composite quadrilateral plates

In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels.

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Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Cylindrical Panels

International Journal of Materials Science and Engineering ◽

10.12720/ijmse.1.1.36-40 ◽

2013 ◽

pp. 36-40 ◽

Cited By ~ 3

Author(s):

Z. X. Lei ◽

J. L. Yu ◽

K. M. Liew

Keyword(s):

Carbon Nanotube ◽

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Reinforced Composite ◽

Cylindrical Panels

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Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach

Journal of Vibration and Control ◽

10.1177/1077546316659172 ◽

2016 ◽

Vol 24 (6) ◽

pp. 1123-1144 ◽

Cited By ~ 27

Author(s):

R Ansari ◽

J Torabi ◽

M Faghih Shojaei

Keyword(s):

Carbon Nanotube ◽

Free Vibration ◽

Vibration Analysis ◽

Cylindrical Shells ◽

Free Vibration Analysis ◽

Energy Functional ◽

Functionally Graded ◽

Differential Quadrature ◽

Annular Plates ◽

Reinforced Composite

Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature method and periodic differential operators in axial and circumferential directions, respectively, the discretized form of the energy functional is derived. Based on Hamilton’s principle and using the VDQ method, the reduced forms of mass and stiffness matrices are obtained. The comparison and convergence studies of the present numerical method are first performed and then various numerical results are presented. It is found that the volume fractions and functionally grading of carbon nanotubes play important roles in the vibrational characteristics of FG-CNTRC cylindrical, conical shells and annular plates.

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Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes

Journal of Vibration and Control ◽

10.1177/1077546319847836 ◽

2019 ◽

Vol 25 (14) ◽

pp. 2063-2078 ◽

Cited By ~ 10

Author(s):

Mahsa Heidari ◽

Hadi Arvin

Keyword(s):

Carbon Nanotubes ◽

Carbon Nanotube ◽

Free Vibration ◽

Direct Method ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Timoshenko Beams ◽

Nonlinear Free Vibration ◽

Reinforced Composite ◽

Linear And Nonlinear

In this paper, the linear and nonlinear free vibrations of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes are presented. The formulation is based on the assumptions of Timoshenko beam theory in addition to consideration of the nonlinear von Karman strain–displacement relationship. The effective material properties of carbon nanotube reinforced composites are determined employing the Mori–Tanaka micromechanics model and the extended mixture rule. For the carbon nanotube reinforced composite beams, uniform distribution and four types of functionally graded distribution patterns of single-walled carbon nanotube reinforcements are considered. A differential transform method is applied on the nondimensionalized equations of motion to release the flapping modeshapes and the associated natural frequencies. The direct method of multiple scales is implemented to derive the effective nonlinearity and the corresponding nonlinear natural frequency. The accuracy of the present outcomes is validated by the comparison with the results given in the literature. The numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fractions, distribution types of the carbon nanotubes, and rotation speed on linear and nonlinear free vibration characteristics of carbon nanotube reinforced composite beam. The results demonstrate the important role of carbon nanotube distribution profile on linear and nonlinear free vibration features.

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