Robust control of plate vibration via active constrained layer damping

Abstract In this paper, the theoretical modeling of a plate partially treated with active constrained layer damping (ACLD) treatments and its vibration control in an H ∞ approach is discussed. Vibration of the flat plate is controlled with patches of ACLD treatments, each consisting of a viscoelastic damping layer which is sandwiched between the piezo-electric constrained layer and the host plate. The piezo-electric constrained layer acts as an actuator to actively control the shear deformation of the viscoelastic damping layer according to the vibration response of the plate excited by external disturbances. In the first part of this paper, the Mindlin–Reissner plate theory is adopted to express the shear deformation characteristics of the viscoelastic damping layer, meanwhile GHM (Golla–Hughes–McTavish) model of viscoelastic damping material and FEM (finite element model) are incorporated to describe the dynamics of the plate partially treated with ACLD treatment. In the second part, particular emphasis is placed on the vibration control of the first four modes of the treated plate using H ∞ robust control method. For this purpose, an H ∞ robust controller is designed to accommodate uncertainties of the ACLD parameters, particularly those of the viscoelastic damping core which arise from the variation of the operation temperature and frequency. Disturbances and measurement noise are rejected in the closed loop by H ∞ robust controller. In the experimental validation, external disturbances of different types are employed to excite the treated plate. The results of the experimental clearly demonstrate that the proposed modeling method is correct and the ACLD treatments are very effective in fast damping out the structural vibration as compared to the conventional passive constrained layer damping (PCLD).

[1]  I. Y. Shen,et al.  Hybrid Damping Through Intelligent Constrained Layer Treatments , 1994 .

[2]  A. Baz,et al.  Optimum Design and Control of Active Constrained Layer Damping , 1995 .

[3]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[4]  Amr M. Baz.  Robust control of active constrained layer damping , 1998 .

[5]  Usik Lee,et al.  A finite element for beams having segmented active constrained layers with frequency-dependent viscoelastics , 1996 .

[6]  M. Safonov,et al.  A Schur Method for Balanced Model Reduction , 1988, 1988 American Control Conference.

[7]  Hongxing Hua,et al.  A reduced‐order modeling technique for tall buildings with active tuned mass damper , 2001 .

[8]  M. Safonov,et al.  A Schur method for balanced-truncation model reduction , 1989 .

[9]  Roger Stanway,et al.  ACTIVE CONSTRAINED LAYER DAMPING OF CLAMPED-CLAMPED PLATE VIBRATIONS , 2001 .

[10]  D. Golla.  Dynamics of viscoelastic structures: a time-domain finite element formulation , 1985 .

[11]  Kenneth B. Lazarus,et al.  Induced strain actuation of isotropic and anisotropic plates , 1991 .

[12]  I. Y. Shen.  Bending vibration control of composite plate structures through intelligent constrained-layer treatments , 1994, Smart Structures.

[13]  P. Hughes,et al.  Modeling of linear viscoelastic space structures , 1993 .

[14]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[15]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .