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Dynamics of cantilever plates and its hybrid vibration control

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Abstract

Applying Lagrange-Germain’s theory of elastic thin plates and Hamiltonian formulation, the dynamics of cantilever plates and the problem of its vibration control are studied, and a general solution is finally given. Based on Hamiltonian and Lagrangian density function, we can obtain the flexural wave equation of the plate and the relationship between the transverse and the longitudinal eigenvalues. Based on eigenfunction expansion, dispersion equations of propagation mode of cantilever plates are deduced. By satisfying the boundary conditions of cantilever plates, the natural frequencies of the cantilever plate structure can be given. Then, analytic solution of the problem in plate structure is obtained. An hybrid wave/mode control approach, which is based on both independent modal space control and wave control methods, is described and adopted to analyze the active vibration control of cantilever plates. The low-order (controlled by modal control) and the high-order (controlled by wave control) frequency response of plates are both improved. The control spillover is avoided and the robustness of the system is also improved. Finally, simulation results are analyzed and discussed.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, 200092, Shanghai, China

    Bo Ni & Chao Hu

  2. Shanghai Institute of Spaceflight Fundamental Technology, 201109, Shanghai, China

    Bo Ni

  3. College of Civil Science and Engineering, Yangzhou University, 225127, Yangzhou, China

    Chao Hu

Authors
  1. Bo Ni
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  2. Chao Hu
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Corresponding author

Correspondence to Chao Hu.

Additional information

The project was supported by the National Natural Science Foundation of China (10572045).

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Ni, B., Hu, C. Dynamics of cantilever plates and its hybrid vibration control. Acta Mech Sin 29, 738–748 (2013). https://doi.org/10.1007/s10409-013-0064-8

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  • DOI: https://doi.org/10.1007/s10409-013-0064-8

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