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Abstract
A 4-noded finite element with seven degrees of freedom per node, based on higher-order shear deformation theory, is used for the analysis of smart composite plates. This model does not include voltage/electric potential as a degree of freedom and is valid for both surface-mounted and embedded piezoelectric elements either distributed or placed in patches. The effect of actuator voltage on the static and dynamic behaviour of such plates is studied. It is seen that the reduction in deflection is proportional to the actuator voltage and the actuator voltage does not have significant influence on the frequency of vibration. An active control of vibration is achieved by suitably amplifying the voltage sensed by the sensor.
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References
- Chee, C.Y. K., Tong, L. and Steven, G.P., "A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures", J. Intel. Mat. Syst. and Structures, Vol. 9, 1998, pp.3-19.
- Sunar, M. and Rao, S.S., "Recent Advances in Sensing and Control of Flexible Structures via Piezoelectric Materials Technology", Appl. Mech. Rev., Vol.52, No.1, 1999, pp. 1-16.
- Saravanos, D. A. and Heyliger, P.R., "Mechanics and Computational Models for Laminated Piezoelectric beams, Plates and Shells", Appl. Mech. Rev., Vol. 52, No. 10, 1999, pp. 305-319.
- Mackerle, J, "Smart Materials and Structures: FEM and BEM Simulations", A Bibliography (19971999), Finite Elements in Analysis and Design, Vol. 37, 2001, pp. 71-83.
- Tiersten, H. F., "Linear Piezoelectric Plate Vibrations", Plenum Press, Newyork, 1969.
- Heyliger, P., "Exact Solutions for Simply Supported Laminated Piezoelectric Plates", J. Applied Mechanics, Vol. 64,1997, pp. 299-306.
- Lee, C. K., "Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators, Part I: Governing Equations and Reciprocal Relationships", J. Acoustical Society of America, Vol. 87, No. 3, 1990, pp. 1144-1158.
- Crawley, E. F. and K. B. Lazarus, "Induced Strain Actuation of Isotropic and Anisotropic Plates", AlAA Journal, Vol. 29, No. 6, 1991, pp. 944-951.
- Detwiler, D. T., Shen, M.H.H. and Venkayya, V.B., "Finite Element Analysis of Laminated Composite Structures Containing Distributed Piezoelectric Actuators and Sensors", Finite Elements in Analysis and Design, Vol. 20, 1995, pp. 87-100.
- Bhattacharya, P., Suhail, H. and Sinha, P.K., "Finite Element Free Vibration Analysis of Smart Laminated Composite Beams and Plates", J. Intel. Mat. Syst. and Structures, Vol. 9, 1998, pp. 20-28.
- Lin, C. C., Hsu, C.Y. and Huang, H., "Finite Element Analysis on Deflection Control of Plates with Piezoelectric Actuators", Compos. Struct., Vol. 35, 1996, pp. 423- 433.
- Qu, Z. and Tong, S.J., "An Efficient Modeling Method for Laminated Composite Plates with Piezoelectric Sensors and Actuators", Smart Mat. and Struct., Vol.10, No. 4, 2001, pp. 807-818.
- Mitchell, J. A. and Reddy, J.N., "A Refined Hybrid Plate Theory for Composite Laminates with Piezoelectric Laminae", Int. J. of Solids and Structures," Vol. 32, No. 16, 1995, pp. 2345-2367.
- Ray, M. C., Bhattacharya, R. and Samanta, B., "Exact Solutions for Static Analysis of Intelligent Structures", AIAA Journal, Vol. 31, No. 9, 1993, pp.1684-1691.
- Ray, M. C., Bhattacharya, R. and Samanta, B., "Static Analysis of an Intelligent Structure by the Finite Element Method", Comput. and Struct., Vol. 52, No. 4, 1994, pp.617-631.
- Ha, S. K., Keilers, C. and Chang, F.K., "Finite Element Analysis of Composite Structures Containing Distributed Piezoceramic Sensors and Actuators", AIAA Journal, Vol. 30, No. 3, 1992, pp. 772-780.
- Cen, S., Soh, A., Long, Y. and Yao, Z., "A New 4-Node Quadrilateral Finite Element Model with Variable Electrical Degrees of Freedom for the Analysis of Piezoelectric Laminated Composite Plates", Compos. Struct., Vol. 58, No. 4, 2002, pp. 583-599.
- Lam, X. Y., Peng, X.Q., Liu, G.R. and Reddy, J.N., "A Finite Element Model for Piezoelectric Composite Laminates", Smart Mat. and Struct., Vol. 6, 1997, pp. 583- 591.
- Chandrashekhara, K. and Agarwal, A.N., "Active Vibration Control of Laminated Composite Plates using Piezoelectric Devices: A Finite Element Approach", J. Intel. Mat. Syst. and Structures, Vol. 4, 1993, pp. 496-508.
- Wang, S. Y., Quek, S.T. and Ang, K.K., "Vibration Control of Smart Piezoelectric Composite Plates", Smart Mat. and Struct., Vol. 10, No. 4, 2001,pp. 637-644.
- Latheswary S., VaIsarajan, K.V. and Sadasiva Rao, Y.V.K., "Behavior of Shear Deformable Plate Bending Finite Elements for Composites", J. Aerospace Sciences and Technologies, Vol. 55, No. 3, 2003, pp. 223-230.
- Latheswary, S., "Finite Element Analysis of Laminated Composite Plates with Piezoelectric Elements", Ph.D. Thesis, August 2003.
- Reddy, J. N., "A Simple Higher-order Theory for Laminated Composite Plates," J. Applied Mechanics, Vol. 51, 1984, pp. 745-752.
- Cook, R.D., Malcus, D. S. and Plesha, M. E., "Concepts and Applications of Finite Element Analysis", Third Edition, John Wiley & Sons, 1989.
- Bathe, K. J., "Finite Element Procedures," Prentice Hall of India, New Delhi, 1996.
References
Chee, C.Y. K., Tong, L. and Steven, G.P., "A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures", J. Intel. Mat. Syst. and Structures, Vol. 9, 1998, pp.3-19.
Sunar, M. and Rao, S.S., "Recent Advances in Sensing and Control of Flexible Structures via Piezoelectric Materials Technology", Appl. Mech. Rev., Vol.52, No.1, 1999, pp. 1-16.
Saravanos, D. A. and Heyliger, P.R., "Mechanics and Computational Models for Laminated Piezoelectric beams, Plates and Shells", Appl. Mech. Rev., Vol. 52, No. 10, 1999, pp. 305-319.
Mackerle, J, "Smart Materials and Structures: FEM and BEM Simulations", A Bibliography (19971999), Finite Elements in Analysis and Design, Vol. 37, 2001, pp. 71-83.
Tiersten, H. F., "Linear Piezoelectric Plate Vibrations", Plenum Press, Newyork, 1969.
Heyliger, P., "Exact Solutions for Simply Supported Laminated Piezoelectric Plates", J. Applied Mechanics, Vol. 64,1997, pp. 299-306.
Lee, C. K., "Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators, Part I: Governing Equations and Reciprocal Relationships", J. Acoustical Society of America, Vol. 87, No. 3, 1990, pp. 1144-1158.
Crawley, E. F. and K. B. Lazarus, "Induced Strain Actuation of Isotropic and Anisotropic Plates", AlAA Journal, Vol. 29, No. 6, 1991, pp. 944-951.
Detwiler, D. T., Shen, M.H.H. and Venkayya, V.B., "Finite Element Analysis of Laminated Composite Structures Containing Distributed Piezoelectric Actuators and Sensors", Finite Elements in Analysis and Design, Vol. 20, 1995, pp. 87-100.
Bhattacharya, P., Suhail, H. and Sinha, P.K., "Finite Element Free Vibration Analysis of Smart Laminated Composite Beams and Plates", J. Intel. Mat. Syst. and Structures, Vol. 9, 1998, pp. 20-28.
Lin, C. C., Hsu, C.Y. and Huang, H., "Finite Element Analysis on Deflection Control of Plates with Piezoelectric Actuators", Compos. Struct., Vol. 35, 1996, pp. 423- 433.
Qu, Z. and Tong, S.J., "An Efficient Modeling Method for Laminated Composite Plates with Piezoelectric Sensors and Actuators", Smart Mat. and Struct., Vol.10, No. 4, 2001, pp. 807-818.
Mitchell, J. A. and Reddy, J.N., "A Refined Hybrid Plate Theory for Composite Laminates with Piezoelectric Laminae", Int. J. of Solids and Structures," Vol. 32, No. 16, 1995, pp. 2345-2367.
Ray, M. C., Bhattacharya, R. and Samanta, B., "Exact Solutions for Static Analysis of Intelligent Structures", AIAA Journal, Vol. 31, No. 9, 1993, pp.1684-1691.
Ray, M. C., Bhattacharya, R. and Samanta, B., "Static Analysis of an Intelligent Structure by the Finite Element Method", Comput. and Struct., Vol. 52, No. 4, 1994, pp.617-631.
Ha, S. K., Keilers, C. and Chang, F.K., "Finite Element Analysis of Composite Structures Containing Distributed Piezoceramic Sensors and Actuators", AIAA Journal, Vol. 30, No. 3, 1992, pp. 772-780.
Cen, S., Soh, A., Long, Y. and Yao, Z., "A New 4-Node Quadrilateral Finite Element Model with Variable Electrical Degrees of Freedom for the Analysis of Piezoelectric Laminated Composite Plates", Compos. Struct., Vol. 58, No. 4, 2002, pp. 583-599.
Lam, X. Y., Peng, X.Q., Liu, G.R. and Reddy, J.N., "A Finite Element Model for Piezoelectric Composite Laminates", Smart Mat. and Struct., Vol. 6, 1997, pp. 583- 591.
Chandrashekhara, K. and Agarwal, A.N., "Active Vibration Control of Laminated Composite Plates using Piezoelectric Devices: A Finite Element Approach", J. Intel. Mat. Syst. and Structures, Vol. 4, 1993, pp. 496-508.
Wang, S. Y., Quek, S.T. and Ang, K.K., "Vibration Control of Smart Piezoelectric Composite Plates", Smart Mat. and Struct., Vol. 10, No. 4, 2001,pp. 637-644.
Latheswary S., VaIsarajan, K.V. and Sadasiva Rao, Y.V.K., "Behavior of Shear Deformable Plate Bending Finite Elements for Composites", J. Aerospace Sciences and Technologies, Vol. 55, No. 3, 2003, pp. 223-230.
Latheswary, S., "Finite Element Analysis of Laminated Composite Plates with Piezoelectric Elements", Ph.D. Thesis, August 2003.
Reddy, J. N., "A Simple Higher-order Theory for Laminated Composite Plates," J. Applied Mechanics, Vol. 51, 1984, pp. 745-752.
Cook, R.D., Malcus, D. S. and Plesha, M. E., "Concepts and Applications of Finite Element Analysis", Third Edition, John Wiley & Sons, 1989.
Bathe, K. J., "Finite Element Procedures," Prentice Hall of India, New Delhi, 1996.