Three-dimensional eigenstrain techniques are used in this paper to model mechanical interactions in an active structure containing small embedded sensors and actuators. Eigenstrain techniques are used to predict the state of the strain inside the devices (sensors and actuators) under external and internal loads. The elastic energy of the structure is written in terms of the strain inside the devices, and an analytical dynamic model is developed based on a generalized form of Hamilton’s variational principle. As an example, the dynamic response of an active cantilever beam containing embedded mini-devices is investigated analytically and experimentally. Specifically, active stiffness tailoring capabilities are explored. An analytical solution to the variational problem is obtained by using the Raleigh-Ritz approach. A numerical example is given and the response of the active structure is verified experimentally, using a cantilever beam made of Alplex plastic as host material and piezoelectric (PZT-5H) devices as active mini-devices for sensing and actuation. The analytical results show reasonable agreement with the experimental observations.
Get full access to this article
View all access options for this article.
References
1.
Alghamdi, A. A. 1995. “Response of Active Structures with Multiple Embedded Devices Using Eigenstrain Techniques,” Ph. D. Thesis, University of Maryland, College Park.
2.
Alghamdi, A. A. and Dasgupta, A. 1993. “Micromechanical Dynamic Analysis of an Active Beam with Embedded Distributions of Piezoelectric Actuator/sensor Devices,”Active Structures and Material Systems, The 1993 ASME Winter Annual Meeting, AD-Vol. 35, New Orleans, Louisiana, pp. 121-128.
3.
Allik, H. and Hughes, T. J. R.1970. “Finite Element Method for Piezoelectric Vibration,”International Journal for Numerical Methods in Engineering, 2: 151-157.
4.
Bailey, T. and Hubbard, J. E. Jr.1985. “Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam,”AIAA Journal of Guidance, Control and Dynamics, 8(5): 605-611.
5.
Burke, S. E. and Hubbard, J. E. Jr.1987. “Active Vibration Control of a Simply Supported Beam Using a Spatially Distributed Actuator,”IEEE Control Systems Magazine, 7(6): 25-30.
6.
Chee, C. Y. K.et al.1998. “A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures,”Journal of Intelligent Material Systems and Structures, 9(9): 3-19.
7.
Christensen, R. M.1991. Mechanics of Composite Materials, Krieger Publishing Company, Malabar, Florida.
8.
Crawley, E. F. and de Luis, J.1987. “Use of Piezoelectric Actuators as Elements of Intelligent Structures,”AIAA Journal, 25(10): 1373-1385.
9.
Crawley, E. F. and Lazarus, K. B.1991. “Induced Strain Actuation of Isotropic and Anisotropic Plates,”AIAA Journal, 29(6): 944-951.
10.
Dasgupta, A. and Alghamdi, A. A. A. 1992. “Interaction Mechanics Between Embedded Micro-Actuators and the Surrounding Host in Smart Structures,”Proceedings of the American Society for Composites, Seventh Technical Conference, University Park, Pennsylvania, pp. 919-928.
11.
Eshelby, J. D.1957. “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems,”Proceedings of the Royal Society, Series A, 241: 376-396.
12.
Eshelby, J. D.1959. “The Elastic Field Outside an Ellipsoidal Inclusion,”Proceedings of the Royal Society, Series A, 252: 561-569.
13.
Gaudenzi, P.1997. “On the Electromechanical Response of Active Composite Materials with Piezoelectric Inclusions,”Computers & Structures, 65 (2): 157-168.
14.
Ha, S. K.et al.1992. “Finite Element Analysis of Composite Structures Containing Distributed Piezoceramics Sensors and Actuators,”AIAA Journal, 30(3): 772-780.
15.
Hagood, N. W.et al.1990. “Modeling of Piezoelectric Actuator Dynamics for Active Structural Control,”Journal of Intelligent Material Systems and Structures, 1(3): 327-354.
16.
Hagood, N. W.et al.1991. “Damping of Structural Vibrations with Piezoelectric Materials and Passive Electric Networks,”Journal of Sound & Vibration, 146(2): 243-268.
17.
Ikeda, T.1990. Fundamentals of Piezoelectricity, Oxford Science Publications, Oxford.
18.
Im, S. and Atluri, S. N.1989. “Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading,”AIAA Journal, 27(12): 1801-1807.
19.
Lin, M. W. and Rogers, C. A. 1992. “Analysis of a Beam Structure with Induced Strain Actuators Based on an Approximated Linear Shear Stress Field,”Proceedings of the Recent Advances in Active and Sensory Materials and Their Applications, Blacksburg, Virginia, pp. 363-376.
20.
Mahut, T.et al.1998. “Dynamic Analysis of Piezoelectric Fiber Composite in an Active Beam Using Homogenization and Finite Element Methods,”Journal of Intelligent Material Systems and Structures, 9(12): 1009-1017.
21.
Moschovidis, Z. A. 1975. “Two Ellipsoidal Inhomogeneities and Related Problems Treated by the Equivalent Inclusion Method,” Ph.D. Dissertation, Northern University, Evanston, Illinois.
22.
Mura, T. , 1991. Micromechanics of Defects in Solids, 2ed Revised Edition, Kluwer Academic Publishing, Boston.
23.
Pratt, J. R.et al.1999. “Terfenol-D Nonlinear Vibration Absorber,”Journal of Intelligent Material Systems and Structures, 10(1): 38-58.
24.
Reddy, N. J. and Barbosa, J. I.2000. “On Vibration Suppression of Magnetostrictive Beams,”Journal of Smart Materials and Structures, 9(1): 49-58.
25.
Tiersten, H. F. , 1967. “Hamilton’s Principle for Linear Piezoelectric Media,”Proceedings Letters, Proceedings of the IEEE, pp. 1523-1524.
26.
Tiersten, H. F.1969. Linear Piezoelectric Plate Vibrations, Plenum Press, New York.
27.
Tzou, H. S. , 1993. Piezoelectric Shells: Distributed Sensing and Control of Continua, Kluwer Academic Publishers, Boston.
28.
Wang, B-T and Rogers, C. A.1991. “Modeling of Finite-Length Spatially-Distributed Induced Strain Actuators for Laminated Beams and Plates,”Journal of Intelligent Material Systems and Structures, 2(1): 38-58.
