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**A wavelet approach for active-passive vibration control of laminated plates.**
*(English)*
Zbl 1288.74033

Summary: 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.

### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

74M05 | Control, switches and devices (“smart materials”) in solid mechanics |

74E30 | Composite and mixture properties |

### Keywords:

wavelets; piezoelectric structures; hybrid active-passive control; rectangular plate; viscoelastic material; numerical simulation
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\textit{J. Wang} et al., Acta Mech. Sin. 28, No. 2, 520--531 (2012; Zbl 1288.74033)

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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) |

[2] | Zhou, Y.H., Tzou, H.S.: Active control of nonlinear piezoelectric spherical shallow shells. Int. J. Solids Struct. 37, 1663–1677 (2000) · Zbl 0999.74083 |

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

[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) |

[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) |

[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) |

[8] | Baz, A., Poh, S.: Independent modal space control with positive position feedback. J. Dyn. Sys., Meas., Control. 114, 96–103 (1992) · Zbl 0775.93069 |

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

[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) · Zbl 1242.74060 |

[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) |

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

[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) · Zbl 1035.65159 |

[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) · Zbl 1147.65080 |

[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) · Zbl 1107.65347 |

[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) · Zbl 1141.74374 |

[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) |

[18] | Christensen, R.V.: Theory of Viscoelasticity. Academic Press, New York (1971) · Zbl 0215.48303 |

[19] | Bock, I.: On large deflection of viscoelastic plates. Math. Comput. Simulat. 50, 135–143 (1999) · Zbl 1053.74560 |

[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) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.