Use of Classical Plate Finite Elements for the Analysis of Electroactive Composite Plates: Theoretical Aspects

Abstract

Smart structures including piezoelectric materials have been under interest for many years. As a consequence many piezoelectric finite elements have been developed to simulate the behavior of such structures. The present article is focused on the development of an original plate theory based upon a priori assumptions for active vibration control applications. The main result of this theory lies in the removal of electrical variables from the problem unknowns, according to the electric boundary conditions. The electromechanical effects are then taken into account via elastic coefficient modifications and external electric loads.

Keywords

piezoelectricity plate theory a priori assumptions no electric degree of freedom.

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References

Aráujo, A.L. , Mota Soares, C.M. , Herskovits, J. and Pedersen, P. 2002. ‘‘Development of a Finite Element Model for the Identification of Mechanical and Piezoelectric Properties through Gradient Optimisation and Experimental Vibration Data,’’ Composite Structures, 58:307-318.

Auricchio, F. , Bisegna, P. and Lovadina, C. 2001. ‘‘Finite Element Approximation of Piezoelectric Plates,’’ International Journal for Numerical Methods in Engineering, 50:1469-1499.

Baz, A. and Ro, J. 1996. ‘‘Vibration Control of Plates with Active Constrained Layer Damping,’’ Smart Materials and Structures, 5:272-280.

Benjeddou, A. 2000. ‘‘Advances in Piezoelectric Finite Element Modeling of Adaptive Structural Elements: A Survey,’’ Computers and Structures, 76:347-363.

Bhattacharya, P. , Suhail, H. and Sinha, P. 2002. ‘‘Finite Element Analysis and Distributed Control of Laminated Composite Shells Using LQR/IMSC Approach, ’’ Aerospace Science and Technology, 6:273-281.

Bisegna, P. and Caruso, G. 2000. ‘‘Mindlin-type Finite Elements for Piezoelectric Sandwich Plates,’’ Journal of Intelligent Materials, Systems and Structures, 11:14-25.

Cady, W. 1946. Piezoelectricity, McGraw Hill, New York.

Cen, S. , Soh, A.-K. , Long, Y.-Q. and Yao, Z.-H. 2002. ‘‘A New 4-node Quadrilateral Fe Model with Variable Elelctrical Degrees of Freedom for the Analysis of Piezoelectric Laminated Composite Plates,’’ Composite Structures , 58:583-599.

Chandrashekhara, K. and Bhatia, K. 1993. ‘‘Active Buckling Control of Smart Composite Plates - Finite Element Analysis,’’ Smart Materials and Structures, 2:31-39.

10.

Chandrashekhara, K. and Agarwal, A.N. 1993. ‘‘Active Vibration Control of Laminated Composite Plates using Piezoelectric Devices: A Finite Element Approach, ’’ Journal of Intelligent Materials, Systems and Structures, 4:496-508.

11.

Chandrashekhara, K. and Tenneti, R. 1995. ‘‘Thermally Induced Vibration Suppression of Laminated Plates with Piezoelectric Sensors and Actuators, ’’ Smart Materials and Structures, 4:281-290.

12.

Comstock, R.H. 1976. ‘‘Reducing the Strain Uncertainty of Piezoelectric Transducers by the Use of Charge Feedback,’’ Technical Report C4753, Charles Starck Draper Laboratory, Cambridge, MA.

13.

Debus, J.C. , Dubus, B. and Coutte, J. 1998. ‘‘Finite Element Modeling of Lead Magnesium Niobate Electrostrictive Materials: Static Analysis,’’ Journal of the Acoustical Society of America, 103(6):3336-3343.

14.

Detwiler, D.T. , Shen, M.-H.H. and Venkayya, V.B. 1995. ‘‘Finite Element Analysis of Laminated Composite Structures Containing Distributed Piezoelectric Actuators and Sensors,’’ Finite Elements in Analysis and Design, 20:87-100.

15.

Di Sciuva, M. , Icardi, U. and Villani, M. 1996. ‘‘Finite Element Analysis of Composite Plates with Induced-Strain Actuators: An Evaluation of Smeared and Discrete-Layer Models,’’ In: Santini, P., Rogers, C.A. and Morotsu, Y. (eds), 7th International Conference on Adaptive Structures and Technologies, pp. 435-448, Rome, Italy.

16.

Dubus, B. , Debus, J.C. and Coutte, J. 1999. ‘‘Modélisation de Matériaux Piézoélectriques et Electrostrictifs par la Méthode des Eléments Finis,’’ Revue Européenne des Eléments Finis, 8(5-6):581-606.

17.

Fung, Y.C. 1965. Foundations of Solid Mechanics, Prentice-Hall, Inc., Englewood Cliffs, NJ.

18.

Gaudenzi, P. and Bathe, K.J. 1995. ‘‘An Iterative Finite Element Procedure for the Analysis of Piezoelectric Continua,’’ Journal of Intelligent Materials, Systems and Structures, 6(2):266-273.

19.

Han, J.-H. and Lee, I. 1997. ‘‘Active Damping Enhancement of Composite Plates with Electrode Designed Piezoelectric Materials,’’ Journal of Intelligent Materials, Systems and Structures, 8:249-259.

20.

Hom, C.L. and Shankar, N. 1996. ‘‘A Finite Element Method for Electrostrictive Ceramic Devices,’’ International Journal of Solids and Structures, 33(12):1757-1779.

21.

Hwang, W.-S. and Park, H.C. 1993. ‘‘Finite Element Modeling of Piezoelectric Sensors and Actuators,’’ American Institute of Aeronautics and Astronautics Journal, 5(31):930-937.

22.

Hwang, W.-S. , Park, H.C. and Hwang, W. 1993. ‘‘Vibration Control of a Laminated Plate with Piezoelectric Sensor/ Actuator: Finite Element Formulation and Modal Analysis ,’’ Journal of Intelligent Materials, Systems and Structures, 4:317-329.

23.

Jonnalagadda, K.D. , Blandford, G.E. and Taucher, T.R. 1994. ‘‘Piezothermoelastic Composite Plate Analysis using First-order Shear Deformation Theory,’’ CS, 51(1):79-89.

24.

Kang, Y.K. , Park, H.C. , Hwang, W. and Han, K.S. 1996. ‘‘Prediction and Measurement of Modal Damping of Laminated Composite Beams with Piezoceramic Sensor/Actuator, ’’ Journal of Intelligent Materials, Systems and Structures, 7:25-32.

25.

Kim, J. , Varadan, V.V. and Varadan, V.K. 1997. ‘‘Finite Element Modeling of Structures Including Piezoelectric Active Devices,’’ International Journal for Numerical Methods in Engineering, 40:817-832.

26.

Lam, K.Y. , Peng, X.Q. , Liu, G.R. and Reddy, J.N. 1997. ‘‘A Finite-element Model for Piezoelectric Composite Laminates,’’ Smart Materials and Structures , 6:583-591.

27.

Landau, L. , Lifchitz, E. and Pitaevskii, L. 1984. Course in Theoretical Physics: Electrodynamics of Continuous Media, Butterworth-Heinemann.

28.

Lee, H.-J. and Savaranos, D.A. 1998. ‘‘The Effect of Temperature Dependent Material Properties on the Response of Piezoelectric Composite Materials, ’’ Journal of Intelligent Materials, Systems and Structures, 9:503-508.

29.

Lerch, R. 1990. ‘‘Simulation of Piezoelectric Devices by Two- and Three-dimensional Finite Elements,’’ IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 37(2):233-247.

30.

Lin, D.X. , Ni, R.G. and Adams, R.D. 1984. ‘‘Prediction and Measurement of the Vibrational Damping Parameters of Carbon and Glass Fibre-reinforced Plastic Plates, ’’ Journal of Composite Materials, 18:132-152.

31.

Liu, G.R. , Yili, Z. , Lam, K.Y. , Peng, X.Q. and Tani, J. 1997. ‘‘Finite Element Modeling of Piezoelectric Sensors and Actuators Bonded in Thick Composite Laminates,’’ In: Murotsu, Y., Rogers, C.A., Santini, P. and Okubo, H. (eds), 8th International Conference on Adaptive Structures and Technologies, pp. 113-122, Wakayama , Japan.

32.

Mesecke-Rischmann, S. and Lammering, R. 2002. ‘‘Hybrid Finite Element Formulation for Layered Structures with Piezoelectric Material,’’ In: Fifth World Congress on Computational Mechanics, Vienna , Austria.

33.

Narayanan, S. and Balamurugan, V. 2003. ‘‘Finite Element Modelling of Piezolaminated Smart Strucutres for Active Vibration Control with Distributed Sensors and Actuators,’’ JSV, 262:529-562.

34.

Pablo, F. , Osmont, D. and Ohayon, R. 2001. ‘‘A Plate Electrostrictive Element. Part One: Modeling and Variational Formulations,’’ Journal of Intelligent Materials, Systems and Structures, 12(11):745-760.

35.

Reddy, J.N. 1999. ‘‘On Laminated Composite Plates with Integrated Sensors and Actuators,’’ Engineering Structures , 21:568-593.

36.

Roccella, S. and Gaudenzi, P. 2005. ‘‘On the Formulation of a Piezoelectric Plate Model,’’ Journal of Intelligent Materials, Systems and Structures, 16:285-290.

37.

Seshu, P. and Naganathan, N.G. 1997. ‘‘Finite-element Analysis of Strain Transfer in an Induced Strain Actuator,’’ Smart Materials and Structures, 6:76-88.

38.

Shah, D.K. , Joshi, S.P. and Chan, W.S. 1993a. ‘‘Static Structural Response of Plates with Piezoceramic Layers,’’ Smart Materials and Structures , 2:172-180.

39.

Shah, D.K. , Chan, W.S. and Joshi, S.P. 1993b. ‘‘Finite Element Analysis of Plates with Piezoelectric Layers,’’ In: AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 34th and AIAA/ASME Adaptive Structures Forum, La Jolla, California, pp. 3189-3197.

40.

Sheikh, A.H. , Topdar, P. and Halder, S. 2001. ‘‘An Appropriate Fe Model for Through-thickness Variation of Displacement and Potential in Thin/Moderately Thick Smart Laminates ,’’ Composite Structures, 51:401-409.

41.

Shen, J.Y. and Sharpe, L.J. 1997. ‘‘A Finite Element Model of the Aeroelasticity Analysis of Hypersonic Panels. Part III: Flutter Suppression,’’ In: SPIE’s 4th Annual Symposium on Smart Structures and Materials: Smart Structures and Materials , San Diego, California, Vol. 3039, pp. 315-323.