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A Wavelet-Based Approach for Dynamic Control of Intelli-Gent Piezoelectric Plate Structures with Linear and Non-Linear Deformation

  • You-He Zhou
  • Jizeng Wang
  • Xiao Jing Zheng
Conference paper
  • 183 Downloads
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 89)

Abstract

Piezoelectric devices present an important new group of sensors and actuators for active vibration control systems [1, 2, 3, 4]. Indeed, this technology allows to developing spatially distributed devices, which requires special control techniques to improve the dynamical behavior of this kind of smart structure. Especially to geometrically nonlinear plates with piezoelectric sensing and actuating, there is a little of numerical results in the literature to quantitatively analyze the behavior of the vibration control of the structures [5, 6, 7]. This paper is concerned with the mathematical model of this kind of vibration control for a geometrically nonlinear plate with piezoelectric sensors and actuators by means of the scaling function transform of the wavelet theory [8, 9]. Based on the generalized Gaussian integral to the scaling function transform, an explicit formula or algorithm of identification for the deflection of plates from the measured electric signals, i.e., electric charges and currents, on piezoelectric sensors is established. When a control law of negative feedback of the identified signals is employed, the applied voltages on piezoelectric actuators are determined by the wavelet Galerkin method. Finally, some typical examples, e.g., beam-plates with either small deflection or geometrically nonlinear deformation, of simulation are taken to show the feasibility of this control approach. It is found that this control model may auto-avoid those undesired phenomena of control instability generated from the interaction between measurement and controller with spilling over of high-order signals since the scaling function transform is low-pass.

Keywords

Control Voltage Scaling Function Piezoelectric Actuator Vibration Control Piezoelectric Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Tzou, H.S., and Anderson, G.L. (eds.), Intelligent Structural Systems, Kluwer Academic Publications, Boston, 1992.Google Scholar
  2. 2.
    Zhou, Y.H., Wang, J.Z., Zheng, X.J., and Jiang, Q., Vibration control of variable thickness plates with Piezoelectric sensors and actuators based on wavelet theory, J. of Sound and Vib., (2000), (in press)Google Scholar
  3. 3.
    Lee C. K. (1992), Piezoelectric laminates: theory and experiments for distributed sensors and actuators, Intelligent Structural Systems, in H.S. Tzou and G.L. Anderson (eds.), Intelligent Structural Systems, Kluwer Academic Publishers, Boston, pp. 75–167.Google Scholar
  4. 4.
    Yu, Y.Y., Some recent advances in linear and nonlinear dynamical modeling of elastic and piezoelectric Plates, Adaptive Structures and Material Systems, 35 (1992), 185–195.Google Scholar
  5. 5.
    Tzou, H.S., and Zhou, Y.H., Nonlinear piezothermoelasticity and multi-field actuation, Part 2: control and nonlinear deformation, buckling and dynamics, ASME J. of Vibrations and Acoustics, 119(1997), 382–389.CrossRefGoogle Scholar
  6. 6.
    Zhou, Y.H., and Tzou, H.S., Active control of nonlinear piezoelectric Spherical shallow shells, Int. J. of Solidsand Struct., 37(2000), 1663–1677.CrossRefzbMATHGoogle Scholar
  7. 7.
    Tzou, H.S., and Zhou, Y.H., Dynamics and control of piezoelectric circular plates with geometrical non-nonlinearity, J. Sound and Vib., 188(1995), 189–207.CrossRefGoogle Scholar
  8. 8.
    Zhou, Y.H., and Wang, J.Z., Generalized Gaussian integral method for calculations of scaling function Transform of wavelets and its applications, Acta Mathematical Scientia, 19 (1999),293–300, (in Chinese)zbMATHGoogle Scholar
  9. 9.
    Zhou, Y.H., and Wang, J.Z., A dynamic control model of piezoelectric cantilevered beam-plate based on wavelet theory, Acta Mechanica Sinica (Chinese edition), 30 (1998), 719–727.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • You-He Zhou
    • 1
  • Jizeng Wang
    • 1
  • Xiao Jing Zheng
    • 1
  1. 1.Department of MechanicsLanzhou UniversityLanzhou, GansuP.R. China

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