Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Active shape control of a cantilever by resistively interconnected piezoelectric patches

  • Schoeftner, J. (Institute of Technical Mechanics, Johannes Kepler University Linz) ;
  • Buchberger, G. (Institute for Microelectronics and Microsensors, Johannes Kepler University Linz)
  • Received : 2012.12.10
  • Accepted : 2013.04.05
  • Published : 2013.11.25
⟨ Previous Next ⟩

Abstract

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

Keywords

References

  1. Agrawal, B.N. and Treanor, K.E. (1999), "Shape control of a beam using piezoelectric actuators", Smart Mater. Struct., 8, 729-740. https://doi.org/10.1088/0964-1726/8/6/303
  2. Benjeddou, A. (2009), "New insights in piezoelectric free-vibrations using simplified modeling and analyses", Smart Struct. Syst., 5(6), 591-612. https://doi.org/10.12989/sss.2009.5.6.591
  3. Buchberger, G., Schwoediauer, R. and Bauer, S. (2008a), "Flexible large area ferroelectret sensors for location sensitive touchpads", Appl. Phys. Lett., 92, 123511 (3 pp). https://doi.org/10.1063/1.2903711
  4. Buchberger, G., Schwoediauer, R., Arnold, N. and Bauer, S. (2008b), "Cellular ferroelectrets for flexible touchpads, keyboards and tactile sensors", Proceedings of the IEEE Sensors Conference 2008.
  5. Buchberger, G., Bartu, P., Schwoediauer, R., Jakoby, B., Hilber, W. and Bauer, S. (2012a), "A flexible polymer sensor for light point localization", Procedia Eng., 47, 795-800. https://doi.org/10.1016/j.proeng.2012.09.267
  6. Buchberger, G., Schoeftner, J., Schwoediauer, R., Jakoby, B., Hilber, W. and Bauer, S. (2012b), "Modeling of large-area sensors with resistive electrodes for passive stimulus-localization", accepted for publication Sensor Actuat. A-Phys.
  7. Buchberger, G. and Schoeftner, J. (2013), "Modeling of slender laminated piezoelastic beams with resistive electrodes - comparison of analytical results with three-dimensional finite element calculations", Smart Mater. Struct., 22(3), 032001 (13pp). https://doi.org/10.1088/0964-1726/22/3/032001
  8. dell'Isola, F., Maurini, C. and Porfiri, M. (2011), "Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation", Smart Mater. Struct., 13(2), 299-308.
  9. Forward, R. L. (1979), "Electronic damping of vibrations in optical structures", Appl. Optics., 18(5), 690-697. https://doi.org/10.1364/AO.18.000690
  10. Godoy, T.C. and Trindade, M.A. (2011), "Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks", J. Sound Vib., 330(2), 194-216. https://doi.org/10.1016/j.jsv.2010.08.010
  11. Hafka, R.T. and Adelman, H.M. (1985), "An analytical investigation of shape control of large space structures by applied temperatures", AIAA J., 23(3), 450-457. https://doi.org/10.2514/3.8934
  12. Hagood, N.W. and Flotow, A. (1991), "Damping of structural vibrations with piezoelectric materials and passive electrical networks", J. Sound Vib., 146(2), 243-268. https://doi.org/10.1016/0022-460X(91)90762-9
  13. Hubbard, J.E. and Burke, S.E. (1992), Distributed transducer design for intelligent structural components, in: Intelligent Structural System, (Eds. H.S. Tzou and G.L. Anderson), Kluwer Academic Publishers, Norwell.
  14. Irschik, H., Krommer, M., Belyaev, A.K. and Schlacher, K. (1998), "Shaping of piezoelectric sensors/actuators for vibrations of slender beams: coupled theory and inappropriate shape functions", J. Intel. Mat. Syst. Struct., 9(7), 546-554. https://doi.org/10.1177/1045389X9800900706
  15. Irschik, H. (2002), "A review on static and dynamic shape control of structures by piezoelectric actuation", Eng. Struct., 24(1), 5-11. https://doi.org/10.1016/S0141-0296(01)00081-5
  16. Irschik, H., Krommer, M. and Pichler, U. (2003), "Dynamic shape control of beam-type structures by piezoelectric actuation and sensing", Int. J. Appl. Electrom., 17(1-3), 251-258.
  17. Krommer, M. (2001), "On the correction of the Bernoulli-Euler beam theory for smart piezoelectric beams", Smart Mater. Struct., 10(4), 668-680. https://doi.org/10.1088/0964-1726/10/4/310
  18. Krommer, M. and Irschik, H. (2002), "An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics", Acta Mech., 154(1-4), 141-158. https://doi.org/10.1007/BF01170704
  19. Larbi, W., Deu, J.F. and Ohayon, R. (2012), "Finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid", Compos. Struct., 94(2), 501-509. https://doi.org/10.1016/j.compstruct.2011.08.010
  20. Lediaev, L. (2010), Finite element modeling of piezoelectric bimorphs with conductive polymer electrodes (Doctoral thesis Montana State University), Bozeman, Montana.
  21. Nader, M. (2007), Compensation of vibrations in smart structures: shape control, experimental realization and feedback control (doctoral thesis Johannes Kepler Universitaet Austria), Trauner Verlag, Linz.
  22. Porfiri, M. and dell'Isola, F. (2004), "Multimodal beam vibration damping exploiting PZT transducers and passive distributed circuits", J. Phys. IV, 115, 323-330.
  23. Rosi, G., Pouget, J. and dell'Isola, F. (2010), "Control of sound radiation and transmission by a piezoelectric plate with an optimized resistive electrode", Eur. J. Mech. A - Solid, 29(5), 859-70. https://doi.org/10.1016/j.euromechsol.2010.02.014
  24. Schoeftner, J. and Irschik, H. (2009), "Passive damping and exact annihilation of vibrations of beams using shaped piezoelectric layers and tuned inductive networks", Smart Mater. Struct., 18(12), 125008 (9pp). https://doi.org/10.1088/0964-1726/18/12/125008
  25. Schoeftner, J. and Irschik, H. (2011a), "A comparative study of smart passive piezoelectric structures interacting with electric networks: Timoshenko beam theory versus finite element plane stress calculations", Smart Mater. Struct., 20(2), 025007 (13 pp). https://doi.org/10.1088/0964-1726/20/2/025007
  26. Schoeftner, J. and Irschik, H. (2011b), "Passive shape control of force-induced harmonic lateral vibrations for laminated piezoelastic Bernoulli-Euler beams-theory and practical relevance", Smart Struct. Syst., 7(5), 417-432. https://doi.org/10.12989/sss.2011.7.5.417
  27. Schoeftner, J. and Buchberger, G. (2012), "An electromechanically-coupled Bernoulli-Euler beam theory taking into account the finite conductivity of the electrodes for sensing and actuation", Proceedings of the 2012 World Congress on Advances in Civil, Environmental, and Material Research (ACEM´12): CD-ROM, ( Ed. Chang-Koon Choi), 1051-65, 8-2012, Seoul, South Korea.
  28. Thomas, O., Deu, J.F. and Ducarne, J. (2009), "Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients", Int. J. Numer. Meth. Eng., 80(2), 235-268. https://doi.org/10.1002/nme.2632
  29. Vidoli, S and dell'Isola, F. (2000), "Modal coupling in one-dimensional electro-mechanical structured continua", Acta Mech., 141(1-2), 37-50. https://doi.org/10.1007/BF01176806
  30. Zhou, Y.G., Chen, Y.M. and Ding, H.J. (2005), "Analytical solutions to piezoelectric bimorphs based on improved FSDT beam model", Smart Struct. Syst., 1(3), 309-324. https://doi.org/10.12989/sss.2005.1.3.309

Cited by

  1. Theoretical prediction and experimental verification of shape control of beams with piezoelectric patches and resistive circuits vol.133, 2015, https://doi.org/10.1016/j.compstruct.2015.07.026
  2. Static and dynamic shape control of slender beams by piezoelectric actuation and resistive electrodes vol.111, 2014, https://doi.org/10.1016/j.compstruct.2013.12.015
  3. Optimal placement of piezoelectric actuators and sensors on a smart beam and a smart plate using multi-objective genetic algorithm vol.15, pp.4, 2015, https://doi.org/10.12989/sss.2015.15.4.1041
  4. Stochastic micro-vibration response characteristics of a sandwich plate with MR visco-elastomer core and mass vol.16, pp.1, 2015, https://doi.org/10.12989/sss.2015.16.1.141
  5. Displacement tracking of pre-deformed smart structures vol.18, pp.1, 2016, https://doi.org/10.12989/sss.2016.18.1.139