Abstract
This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- t b ,t s ,t c :
-
thickness of plate, viscoelastic and piezoelectric layers, respectively
- x 1,x 2,y 1,y 2 :
-
end coordinates of viscoelastic and piezoelectric layers
- u b , υb :
-
mid-plane displacement of basis layer inx, y direction, respectively
- u c , υc :
-
mid-plane displacement of piezoelec tric layer inx, y direction, respectively
- w :
-
displacement of basis, viscoclastic and piezoelectric layers inz direction
- ϱb, ϱ3, ϱc :
-
mass density of plate, viscoelastic and piezoelectric layers, respectively
- ɛb :
-
strain vector of plate
- σb :
-
stress vector of plate
- D :
-
elasticity matrix of plate
- E :
-
Young's module of plate material
- ν:
-
Poisson's ratio of plate material
- ψ, ϕ:
-
shear deformation of viscoelastic layer inx, y direction, respectively
- τx, τy :
-
shear stress of viscoelastic layer inx, y direction, respectively
- g(t) :
-
relaxation function of viscoelastic material
- ɛc :
-
strain vector of piezoelectric layer
- σc :
-
stress vector of piezoelectric layer
- c :
-
elasticity matrix of piezoelectric layer
- E z :
-
electric field strength
- V(t) :
-
control voltage
- M b,T b,Q b :
-
inner forces of plate
- Q s :
-
inner force of viscoelastic layer
- M c,T c,Q c :
-
inner forces of piezoelectric layer
- f b x , f b y ,q b :
-
disturbance forces on plate
- q s :
-
disturbance force on viscoelastic layer
- f c x ,f c y ,q c :
-
disturbance forces on piezoelectric layer
- Q :
-
weighting matrix on output
- R :
-
weighting matrix on input or domain function
References
W. H. Liao and K. W. Wang, On the active-passive hybrid vibration control actions of structures with active constrained layer treatments,Design Engineering Technical Conferences, ASME,3 Part C (1995), 125–140.
I. Y. Shen, Hybrid damping through intelligent constrained layer treatments.Journal of Vibration and Acoustics,116, 3 (1994), 341–349.
I. Y. Shen, Bending vibration control of composite plate structures through intelligent layer treatments,Proceedings SPIE,2193 (1994), 115–125.
D. J. Inman,Vibration with Control, Measurement, and Stability, Prentice Hall (1989).
D. J. McTavish and P. C. Hughes, Modeling of linear viscoelastic space structures,Journal of Vibration and Acoustics,115, 1 (1993), 103–110.
Author information
Authors and Affiliations
Additional information
Project supported by the National Science Foundation of China (19632001) and the Research Foundation of Xian Jiaotong University
Rights and permissions
About this article
Cite this article
Xinong, Z., Jinghui, Z. The hybrid control of vibration of thin plate with active constrained damping layer. Appl Math Mech 19, 1119–1134 (1998). https://doi.org/10.1007/BF02456633
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02456633