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Computers and Concrete
  Volume 30, Number 6, December 2022 , pages 433-443
DOI: https://doi.org/10.12989/cac.2022.30.6.433
 


On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations
Hao-Xuan Ding, Yi-Wen Zhang and Gui-Lin She

 
Abstract
    In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FGGPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.
 
Key Words
    boundary conditions; elastic foundations; graphene platelet reinforced beams; Modified Lindstedt-Poincare method; non-linear vibration
 
Address
Hao-Xuan Ding, Yi-Wen Zhang and Gui-Lin She: College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China
 

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