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Structural Engineering and Mechanics
  Volume 71, Number 5, September10 2019 , pages 485-502

Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions
S. Alimirzaei, M. Mohammadimehr and Abdelouahed Tounsi

    In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton\'s principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.
Key Words
    nonlinear bending; buckling; vibration analysis; viscoelastic beam; various distributions of BNNTs; initial geometrical imperfection; MSGT; FEM
S. Alimirzaei, M. Mohammadimehr: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-51167, Kashan, Iran
Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia
Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria

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