Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (2) : 324-336     https://doi.org/10.1007/s11709-018-0466-6
 RESEARCH ARTICLE
Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method
T. VO-DUY1,2, V. HO-HUU1,2, T. NGUYEN-THOI1,2()
1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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 Abstract In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied. Corresponding Author(s): T. NGUYEN-THOI Just Accepted Date: 30 January 2018   Online First Date: 29 March 2018    Issue Date: 12 March 2019
 Cite this article: T. VO-DUY,V. HO-HUU,T. NGUYEN-THOI. Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method[J]. Front. Struct. Civ. Eng., 2019, 13(2): 324-336. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-018-0466-6 http://journal.hep.com.cn/fsce/EN/Y2019/V13/I2/324
 Tab.1 Fig.1  Sketch of a laminated composite beam Tab.2  Material parameters of a FG-CNTRC beam Tab.3  Comparison of dimensionless frequency parameters, $ω‾=ω L2 h ρmEm$ of FG-CNTRC beams for $V CNT*$ = 0.12 and 0.17 Tab.4  Comparison of dimensionless frequency parameters, $ω‾=ω L2 h ρmEm$ of FG-CNTRC beams for $VCNT *$ = 0.28 Tab.5  Comparison of dimensionless frequency parameter $ω‾=ω L2 h ρE11$ of four-layered angle-ply [q/–q/–q/q] beams Tab.6  First three dimensionless frequencies of cross-ply [0°/90°] FG-CNTRC beams Tab.7  First three dimensionless frequencies of a cross-ply [0°/90°/0°] FG-CNTRC beams Tab.8  First three dimensionless frequencies of four-layered angle-ply [q/–q/–q/q] FG-X beam Tab.9  First three dimensionless frequencies of four-layered angle-ply [q/–q/–q/q] UD-CNTRC beam Tab.10  First three dimensionless frequencies of four-layered angle-ply [q/–q/–q/q] FG-V beam Tab.11  First three dimensionless frequencies of four-layered angle-ply [q/–q/–q/q] FG-O beam Fig.2  The first dimensionless frequency of angle-ply [q/–q/–q/q] FG-X beam with boundary condition of CC Fig.3  The first dimensionless frequency of the angle-ply [45°/–45°/–45°/45°] FG-CNTRC beam with various distributions and boundary conditions for the case of $VCNT *$ = 0.17 Fig.4  The first dimensionless frequency of angle-ply [45°/–45°/–45°/45°] FG-X beam with boundary condition of CC versus various length-to-thickness ratios Tab.12  First three dimensionless frequencies of a beam with various numbers of layers Fig.5  First dimensionless frequencies of the clamped-clamped FG-CNTRC beams with various numbers of layers for the case of $VCNT *$ = 0.12 Tab.13  First three dimensionless frequencies of laminated FG-CNTRC beams with various distributions of layers