Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

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.

Download Full-text

An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions

Scientific Reports ◽

10.1038/s41598-017-12596-w ◽

2017 ◽

Vol 7 (1) ◽

Cited By ~ 15

Author(s):

Zeyu Shi ◽

Xiongliang Yao ◽

Fuzhen Pang ◽

Qingshan Wang

Keyword(s):

Exact Solution ◽

Carbon Nanotube ◽

Free Vibration ◽

Boundary Conditions ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Composite Beams ◽

Functionally Graded ◽

Arbitrary Boundary ◽

Reinforced Composite

Download Full-text

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

International Journal of Computational Methods ◽

10.1142/s0219876218501335 ◽

2019 ◽

Vol 17 (03) ◽

pp. 1850133 ◽

Cited By ~ 3

Author(s):

T. Truong-Thi ◽

T. Vo-Duy ◽

V. Ho-Huu ◽

T. Nguyen-Thoi

Keyword(s):

Carbon Nanotubes ◽

Carbon Nanotube ◽

Free Vibration ◽

Numerical Solutions ◽

Composite Plates ◽

Functionally Graded ◽

Triangular Element ◽

Reinforced Composite ◽

Strain Smoothing ◽

Discrete Shear Gap

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

Download Full-text