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Vibration analysis and active control for frame structures with piezoelectric rods using spectral element method

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Abstract

The dynamic responses and vibration suppression of frame structures considering the shear deformation are investigated using the spectral element method (SEM). Vibration suppression of the frame structures is studied through the active control technique using the piezoelectric rods. The local dynamic stiffness matrices of the spectral elements for the Timoshenko beams and longitudinal vibration of the rods are obtained in the Fourier phase space and that for the axial-bending-shear coupled vibration of the piezoelectric rod is also gotten. From the transformation between the local and global coordinates, the global dynamic stiffness matrix for the whole frame structures containing the piezoelectric rods is obtained. From the numerical simulation, the dynamic responses of the frame structures can be effectively and exactly calculated by the SEM comparing with the finite element method. It can be found that the dynamic responses of the frame structures can be effectively suppressed by the active control technique based on the piezoelectric rods. The influences of the structural parameters on the dynamic responses and active control effect are also analyzed.

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Authors and Affiliations

  1. School of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Feng-Ming Li

  2. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China

    Chun-Chuan Liu

Authors
  1. Feng-Ming Li
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  2. Chun-Chuan Liu
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Correspondence to Feng-Ming Li or Chun-Chuan Liu.

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Li, FM., Liu, CC. Vibration analysis and active control for frame structures with piezoelectric rods using spectral element method. Arch Appl Mech 85, 675–690 (2015). https://doi.org/10.1007/s00419-014-0980-5

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  • DOI: https://doi.org/10.1007/s00419-014-0980-5

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