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Structural Engineering and Mechanics
  Volume 59, Number 3, August10 2016 , pages 431-454
DOI: https://doi.org/10.12989/sem.2016.59.3.431
 


Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM
M. Mohammadimehr and S. Alimirzaei

 
Abstract
    In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton\'s principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.
 
Key Words
    nonlinear static and free vibration analysis; Euler-Bernoulli composite beam model; various distribution patterns of SWCNTs; geometrical imperfection; FEM
 
Address
M. Mohammadimehr and S. Alimirzaei: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-51167, Kashan, Iran
 

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