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A wavelet approach for active-passive vibration control of laminated plates

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Abstract

As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers. Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory, this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop, hence reducing the risk of residual coupling effects which are usually the source of spillover instability. Moreover, the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process. A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process. Numerical results demonstrate the efficiency of the proposed approach.

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References

  1. Dimitriadis, E.K., Fuller, C.R., Rogers, C.A.: Piezoelectric actuators for distributed vibration excitation of thin plates. Trans. ASME J. Vib. Acous. 113, 100–107 (1991)

    Article  Google Scholar 

  2. Zhou, Y.H., Tzou, H.S.: Active control of nonlinear piezoelectric spherical shallow shells. Int. J. Solids Struct. 37, 1663–1677 (2000)

    Article  MATH  Google Scholar 

  3. Reddy, J.N.: On laminated composite plates with integrated sensors and actuators. Eng. Struct. 21, 568–593 (1999)

    Article  Google Scholar 

  4. Lam, K.Y., Ng, T.Y.: Active control of composite plates with integrated piezoelectric sensors and actuators under various dynamic loading conditions. Smart Mater. Struct. 8, 223–237 (1999)

    Article  Google Scholar 

  5. Balamurgan, V., Narayanan, S.: Finite element formulation and active vibration control study on beams using smart constrained layer damping (SCLD) treatment. J. Sound Vib. 249, 227–250 (2002)

    Article  Google Scholar 

  6. Lee, C.K.: Piezoelectric laminates: theory and experiments for distributed sensors and actuators. Intell. Struct. Syst. 75–167 (1992)

  7. Sun, D.C., Wang, D.J.: Distributed piezoelectric element method for Vibration Control of the distribution of smart plates. Acta Mech. Sinica. 28, 692–699 (1996)

    Google Scholar 

  8. Baz, A., Poh, S.: Independent modal space control with positive position feedback. J. Dyn. Sys., Meas., Control. 114, 96–103 (1992)

    Article  MATH  Google Scholar 

  9. Ray, M.C.: Optimal control of laminated plate with piezoelectric sensor and actuator layers. AIAA J. 36, 2204–2208 (1998)

    Article  Google Scholar 

  10. Qiu, Z.C., Zhang, X.M., Wu, H.X., et al.: Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. J. Sound Vib. 301, 521–543 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Varadan, V.V., Lim, Y.H., Varadan, V.K.: Closed loop finite-element modeling of active passive damping in structural vibration control. Smart Mater. Struct. 5, 685–694 (1996)

    Article  Google Scholar 

  12. Trindade, M.A.: Optimization of active-passive damping treatments using piezoelectric and viscoelastic materials. Smart Mater. Struct. 16, 2159–2168 (2007)

    Article  Google Scholar 

  13. Wang, J.Z., Zhou, Y.H., Gao, H.J.: Computation of the Laplace inverse transform by application of the wavelet theory. Commun. Numer. Meth. En. 19, 959–975 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mehra, M., Kevlahan, N.K.R.: An adaptive wavelet collocation method for the solution of partial differential equations on the sphere. J. Comput. Phys. 227, 5610–5632 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bujurke, N.M., Salimath, C.S., Kudenatti, R.B., et al.: A fast wavelet-multigrid method to solve elliptic partial differential equations. Appl. Math. Comput. 185, 667–680 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, Y.H., Wang, J.Z.: Vibration control of piezoelectric beam-type plates with geometrically nonlinear deformation. Int. J. Nonlin. Mech. 39, 909–920 (2004)

    Article  MATH  Google Scholar 

  17. Zhou, Y.H., Wang, J.Z., Zheng, X.J., et al.: Vibration control of variable thickness plates with piezoelectric sensors and actuators based on wavelet theory. J. Sound Vib. 237, 395–410 (2000)

    Article  Google Scholar 

  18. Christensen, R.V.: Theory of Viscoelasticity. Academic Press, New York (1971)

    Google Scholar 

  19. Bock, I.: On large deflection of viscoelastic plates. Math. Comput. Simulat. 50, 135–143 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, J.Z.: Generalized theory and arithmetic of orthogonal wavelets and applications to researches of mechanics including piezoelectric smart structures. [Ph.D. Thesis], Lanzhou University, Lanzhou (2001) (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education of China, and Department of Mechanics and Engineering Sciences, School of Civil Engineering and Mechanics, Lanzhou University, 730000, Lanzhou, China

    Ji-Zeng Wang, Xiao-Min Wang & You-He Zhou

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  1. Ji-Zeng Wang
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  2. Xiao-Min Wang
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  3. You-He Zhou
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Correspondence to You-He Zhou.

Additional information

The project was supported by the National Natural Science Foundation of China (11032006, 11072094, 11121202), a grant from the Ph.D. Program Foundation of Ministry of Education of China (20100211110022) and the Program for New Century Excellent Talents in University (NCET-10-0445).

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Wang, JZ., Wang, XM. & Zhou, YH. A wavelet approach for active-passive vibration control of laminated plates. Acta Mech Sin 28, 520–531 (2012). https://doi.org/10.1007/s10409-012-0045-3

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  • DOI: https://doi.org/10.1007/s10409-012-0045-3

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