This paper presents the free vibrational analysis of the auxetic metamaterial beams applying the theory of first order shear deformation. Auxetic metamaterials are known for their negative Poisson’s ratio, which works on the reverse deformation mechanism thus they experience transverse expansion and contraction under axial loads. They are extensively utilized in the engineering field due to their less weight and higher energy absorption capability. The in-effect material characteristics of auxetic beams can be achieved by making the angle negative in the generalized formulation of the regular honeycomb structure. The governing mathematical equations have been constructed relying on the Timoshenko beam theory (FSDT) by employing variational principle. FEM is applied for obtaining the numerical result in terms of natural frequency, which is then compared with outcomes of previous investigations. The research on convergence and validation have been carried out to verify the effectiveness and performance of the proposed model.

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On the Free Vibration Behavior of Auxetic Metamaterial Beams Using First-Order Shear Deformation Theory

  • Arshnoor Singh,
  • Md. Aadil,
  • Mohammad Talha

摘要

This paper presents the free vibrational analysis of the auxetic metamaterial beams applying the theory of first order shear deformation. Auxetic metamaterials are known for their negative Poisson’s ratio, which works on the reverse deformation mechanism thus they experience transverse expansion and contraction under axial loads. They are extensively utilized in the engineering field due to their less weight and higher energy absorption capability. The in-effect material characteristics of auxetic beams can be achieved by making the angle negative in the generalized formulation of the regular honeycomb structure. The governing mathematical equations have been constructed relying on the Timoshenko beam theory (FSDT) by employing variational principle. FEM is applied for obtaining the numerical result in terms of natural frequency, which is then compared with outcomes of previous investigations. The research on convergence and validation have been carried out to verify the effectiveness and performance of the proposed model.