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Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection

  • Jia-Qin Xu (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yin-Ping Li (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Lei-Lei Gan (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2023.01.09
  • Accepted : 2023.03.20
  • Published : 2023.06.25
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Abstract

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

Keywords

Acknowledgement

The authors acknowledge this work is supported by the talent introduction project of Chongqing University (02090011044159), and Fundamental Research Funds for the Central Universities (2022CDJXY-005).

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