Active Control of the Piezoelastic Laminated Cylindrical Shell’s Vibration Under Hydrostatic Pressure

LI Hong-yun; LIN Qi-yong; LIU Zheng-xing; WANG Chao

Volume 24 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(2): 163-174

LI Hong-yun, LIN Qi-yong, LIU Zheng-xing, WANG Chao. Active Control of the Piezoelastic Laminated Cylindrical Shell’s Vibration Under Hydrostatic Pressure[J]. Applied Mathematics and Mechanics, 2003, 24(2): 163-174.

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Active Control of the Piezoelastic Laminated Cylindrical Shell’s Vibration Under Hydrostatic Pressure

Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P. R. China

Received Date: 2000-05-23
Rev Recd Date: 2002-09-20
Publish Date: 2003-02-15

Abstract

Abstract

The control of the piezoelastic laminated cylindrical shell. s vibration under hydrostatic pressure was discussed. From Hamilton. s principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which, the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using veloctity feedback control, a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system, the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.
- piezoelastic,
- cylindrical shell,
- vibration control,
- velocity feedback,
- hydrostatic pressure,
- sensor layer,
- actuator layer

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References

[1]	Clinton Y K,Li Y T,Grant P S.A review on the modeling of piezoelectric sensors and actuators incorporated in intelligent structures[J].Journal of Intelligent Material Systems and Structures,1998,9(1):3-19.
[2]	Tzou H S.Piezoelectric Shells(Distributed Sensing and Control of Continua)[M].Dordrecht:Kluwer Academic Publishers,1993.
[3]	Baumhanuer J C,Tiersten H F.Nonlinear electroelastic equations for small fields superposed on a bias[J].J Acoust Soc Amer,1973,54(4):1017-1033.
[4]	Pai P F,Nafeh A H,Mook D T.A refined nonlinear model of piezoelectric plate with integrated piezoelectric actuators and sensors[J].Internat J Solids Structures,1993,30(11):1603-1630.
[5]	Yu Y Y.On the ordinary,generalized,and pseudo-variational equations of motion in nonlinear elasticity,piezoelectricity and classical plate theories[J].J Appl Mech,1995,62(2):471-478.
[6]	Tzou H S,Bao Y.Nonlinear piezothermoelasticity and multi-field actuations,Part 1:nonlinear anisotropic piezothermoelastic shell laminates[J].Journal of Vibration and Acoustics,1997,119(3):374-381.
[7]	Tzou H S,Zhou Y H.Dynamics and control of nonlinear circular plates with piezoelectric actuators[J].J Sound Vibration,1995,188(2),189-207.
[8]	Donatus C D,Sergio F,Jorn S H.Stress stiffening effects in laminated beams with piezoelectric actuators[J].Journal of Intelligent Material Systems and Structures,1998,9(2):137-145.
[9]	Bao Y,Tzou H S,Venkayya V B.Analysis of nonlinear piezothermoelastic laminated beams with electric and temperature effects[J].J Sound Vibration,1998,209(3):505-518.
[10]	Cheng C Q,Shen Y P.Stability analysis of piezoelectric circular cylindircal shells[J].J Appl Mech,1997,64(4):847-852.
[11]	Tiersten H F.Linear Piezoelectric Plate Vibrations[M].New York:Plenum Publishers,1969.
[12]	Mitchell J A,Reddy J N.A refined hybrid plate theory for composite laminates with piezoelectric laminae[J].Internat J Solids Structures,1995,32(16):2345-2367.
[13]	Palazatto A N,Dennis S T.Nonlinear Analysis of Shell Structures[M].Washington D C:AIAA Pub,1992.
[14]	Li H Y,Lin Q R,Liu Z X,et al.Free vibration of piezoelastic laminated cylindrical shell under hydrostatic pressure[J].Internat J Solids Structures,2001,38(42/43):7571-7585.
[15]	Shen S P,Kuang Z B.An active control model of laminated piezothermoelastic plate[J].Internat J Solids Structures,1999,36(13):1925-1947.

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