Advances in Computational Design

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The damped vibration of the annular and rectangular graded beams in the presence of the attached lumped mass

  • Heydari, Abbas (Department of Civil Engineering, Technical and Vocational University (TVU))
  • Received : 2021.07.08
  • Accepted : 2021.09.19
  • Published : 2021.10.25
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Abstract

In earthquake engineering, vibration control is a set of engineering tools aimed at mitigating seismic effects on structural members. Once the seismic waves have penetrated a building, there are a number of ways to control them to mitigate their damaging effects and improve the seismic performance of the building. Dissipate the wave energy inside the structure with properly designed dampers, distributing the wave energy over a wider frequency range and absorbing the resonant portions of the entire wave frequency band using what are known as mass dampers. The effect of mass attenuator on the reduction of fundamental frequency of beams made of functionally graded material (FGM) with annular and rectangular cross sections is studied. Mori-Tanaka homogenization scheme, conventional mixing rule and power law functions are used to model the material gradation. Various classical boundary conditions as well as shear hinge natural condition are considered. The lumped mass attenuator is connected to the beam at an arbitrary position without sliding. The total potential energy is minimized by using the spectral Ritz method to calculate the fundamental frequency and the corresponding mode shape. A reduction in the frequencies is observed in the presence of the attached lumped mass attenuator. The dimensionless frequency reduction is affected by the amount and position of the lumped mass. The position of the lumped mass attenuator plays an important role in vibration control of the beam.

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