Free vibration, bending and buckling of a FG-CNT reinforced composite beam Comparative analysis with hybrid laminated composite beam

Puneet Kumar*, J. Srinivas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose – The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications. Design/methodology/approach – In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code. Findings – First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios. Originality/value – A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.

Original languageEnglish
Pages (from-to)590-611
Number of pages22
JournalMultidiscipline Modeling in Materials and Structures
Issue number4
StatePublished - 9 Nov 2017
Externally publishedYes


  • Distribution profile
  • Finite element modeling
  • Laminated hybrid composite beam
  • Ritz approximation
  • Volume fraction


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