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Combination resonances of porous FG shallow shells reinforced with oblique stiffeners subjected to a two-term excitation

  • Kamran Foroutan (Sino-Canada Research Centre of Computation and Mathematics, Qinghai Normal University) ;
  • Liming Dai (Sino-Canada Research Centre of Computation and Mathematics, Qinghai Normal University) ;
  • Haixing Zhao (Sino-Canada Research Centre of Computation and Mathematics, Qinghai Normal University)
  • Received : 2023.07.13
  • Accepted : 2024.04.30
  • Published : 2024.05.25
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Abstract

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

Keywords

Acknowledgement

The authors greatly appreciate the supports of the Natural Sciences and Engineering Research Council of Canada (NSERC), Qinghai Normal University and the University of Regina to the present research.

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