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Free vibration analysis of viscoelastic plates with simultaneous calculation of natural frequency and viscous damping

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  • Jafari, Nasrin
  • Azhari, Mojtaba

Abstract

This paper presents a new solution for the free vibration analysis of moderately thick viscoelastic plates with different shapes, based on free vibration analysis of elastic plates. The advantage of this method is that all natural frequencies and viscous damping can be easily calculated with low computational cost and high precision. Also, critical damped natural frequencies of Mindlin viscoelastic plates are calculated. The constitutive equation is written utilizing the Boltzmann integral law with constant bulk modulus. The Laplace transformation is used to convert equations from the time domain to the Laplace domain. The displacement vector is approximated using the separation of variables method. Besides, the effects of material and geometrical properties on the natural frequency, viscous damping, and critical damped natural frequency of viscoelastic Mindlin plates are investigated.

Suggested Citation

  • Jafari, Nasrin & Azhari, Mojtaba, 2021. "Free vibration analysis of viscoelastic plates with simultaneous calculation of natural frequency and viscous damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 646-659.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:646-659
    DOI: 10.1016/j.matcom.2021.01.019
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    1. Jafari, Nasrin & Azhari, Mojtaba & Boroomand, Bijan, 2019. "Large deformation analysis of moderately thick viscoelastic plates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 146-167.
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