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DOI QR Code

Dynamic displacement tracking of a one-storey frame structure using patch actuator networks: Analytical plate solution and FE validation

  • Huber, Daniel (Linz Center of Mechatronics GmbH) ;
  • Krommer, Michael (Institute for Technical Mechanics, Johannes Kepler University Linz) ;
  • Irschik, Hans (Institute for Technical Mechanics, Johannes Kepler University Linz)
  • 투고 : 2008.11.17
  • 심사 : 2009.05.13
  • 발행 : 2009.11.25

초록

The present paper is concerned with the design of a proper patch actuator network in order to track a desired displacement of the sidewalls of a one-storey frame structure; both, for the static and the dynamic case. Weights for each patch of the actuator network found in our previous work were based on beam theory; in the present paper a refinement of these weights by modeling the sidewalls of the frame structure as thin plates is presented. For the sake of calculating the refined weights approximate solutions of the plate equations are calculated by an extended Galerkin method. The solutions based on the analytical plate model are compared with three-dimensional Finite Element results computed in the commercially available code ANSYS. The patch actuator network is put into practice by means of four piezoelectric patches attached to each of the two sidewalls of the frame structures, to which electric voltages proportional to the analytically refined patch weights are applied. Analytical and numerical results coincide very well over a broad frequency range.

키워드

참고문헌

  1. Alkhatib, R. and Golnaraghi, M.F. (2003), "Active structural vibration control: a review", Shock Vib., 35(5), 367-383. https://doi.org/10.1177/05831024030355002
  2. Crawley, E.F. (1994), "Intelligent structures for aerospace: a technology overview and assessment", AIAA J., 32(8), 1689-1699. https://doi.org/10.2514/3.12161
  3. Da Mota Silva, S., Ribeiro, R., Dias Rodrigues, J., Vaz, M.A.P. and Monteiro, J.M. (2004), "The application of genetic algorithms for shape control with piezoelectric patches-an experimental comparison", Smart Mater. Struct., 13(1), 220-226. https://doi.org/10.1088/0964-1726/13/1/026
  4. Gabbert, U. and Tzou, H.S. (2001), Preface: Proc. of IUTAM-Symposium on Smart Structures and Structronic Systems, Magdeburg, Germany, September 2000.
  5. Gabbert, U., Nestorovic-Trajkov, T. and Koppe, H. (2006), "Finite element-based overall design of controlled smart structures", Struct. Control Health Monit., 13(6), 1052-1067. https://doi.org/10.1002/stc.93
  6. Gopinathan, S.V., Varadan, V.V. and Varadan, V.K. (2001), "Active noise control studies using the rayleigh-ritz method", Proc. of IUTAM Symposium on Smart Structures and Structronic Systems, September 26-29th, 2000, Magdeburg, Germany, U. Gabbert and H.S. Tzou (eds.), Solid Mechanics and its Applications, Kluwer, Dordrecht, 169-178.
  7. Huber, D., Krommer, M. and Irschik, H. (2008), "Dynamic displacement tracking for frame structures with a piezoelectric patch network based on plate theory", Adv. Sci. Technol., 56, Emboding Intelligence in Structures and Integrated Systems (Proc. of the 3rd Int. Conf. "Smart Materials, Structures and Systems", June 8-13th, 2008, Acireale, Sicily, Italy), 64-69.
  8. Huber, D., Krommer, M. and Irschik, H. (2008), "On the influence of lateral eigenstrains on the transverse displacement of wide beams", Proc. of the 79th Annual Meeting of the Int. Association of Applied Mathematics and Mechanics, March 31st - April 4th, 2008, Bremen, Germany, to be published in ZAMM.
  9. Ip, K.H. and Tse, P.C. (2001), "Optimal configuration of a piezoelectric patch for vibration control of isotropic rectangular plates", Smart Mater. Struct., 10(2), 395-403. https://doi.org/10.1088/0964-1726/10/2/401
  10. Irschik, H. and Krommer, M. (2005), "Dynamic displacement tracking of force-loaded linear elastic or viscoelastic bodies by eigenstrain-induced actuation stresses", CD-Rom Proc. of IDETC/CIE 2005, ASME 2005 Int. Design Engineering Technical Conf. & Computers and Information in Engineering Conf., September 24-28th, 2005, Long Beach, CA, U.S.A.
  11. Irschik, H. and Krommer, M. (2006), "Tracking of transient displacements in elastic solids and structures", CD-Rom Proc. of 4th World Conf. on Structural Control and Monitoring (4WCSCM), July 11-13th, 2006, San Diego, CA, U.S.A.
  12. Irschik, H. and Pichler, U. (2001), "Dynamic shape control of solids and structures by thermal expansion strains", J. Therm. Stresses, 24, 565-578. https://doi.org/10.1080/014957301300158102
  13. Irschik, H. and Ziegler, F. (1988), "Dynamics of linear elastic structures with selfstress: a unified treatment for linear and nonlinear problems", ZAMM, 68, 199-205. https://doi.org/10.1002/zamm.19880680602
  14. Irschik, H., Krommer, M., Nader, M. and Pichler, U. (2003), "Dynamic piezoelectric shape control applied of shells of revolution with translatory support excitation", Proc. of the US - Europe Workshop on Sensors and Smart Structures Technology, April 12-13th, 2002, Como and Somma Lombardo, Italy, L. Faravelli and B.F. Spencer, Jr., (eds.), Chichester, John Wiley & Sons, 139-148.
  15. Jha, A.K. and Inman, D.J. (2003), "Optimal sizes and placements of piezoelectric actuators and sensors for an inflated torus", J. Intel. Mat. Syst. Str., 14(9), 563-576. https://doi.org/10.1177/104538903038019
  16. Junkins, J.L. and Kim, Y. (1993), Introduction to Dynamics and Control of Flexible Structures, AIAA, Washington, DC.
  17. Krommer, M. and Irschik, H. (2007), "Sensor and actuator design for displacement control of continuous systems", Smart Struct. Syst., 3(2), 147-172. https://doi.org/10.12989/sss.2007.3.2.147
  18. Krommer, M. and Varadan, V.V. (2005), "Control of bending vibrations within sub - domains of thin plates - Part I: theory and exact solution", J. Appl. Mech., 72(3), 432-444. https://doi.org/10.1115/1.1839185
  19. Krommer, M. and Varadan, V.V. (2006), "Control of bending vibrations within sub - domains of thin plates - Part II: piezoelectric actuation and approximate solution", J. Appl. Mech., 73(2), 259-267. https://doi.org/10.1115/1.2083790
  20. Krommer, M., Irschik, H. and Zellhofer, M. (2008), "Design of actuator networks for dynamic displacement tracking of beams", Mech. Adv. Mater. Struc., 15(3&4), Special Issue - Design, Modelling and Experiments of Adaptive Structures and Smart Systems, 235-249. https://doi.org/10.1080/15376490801907764
  21. Kugi, A. (2001), Non - linear Control Based on Physical Models, Springer, London.
  22. Kugi, A., Thull, D. and Kuhnen, K. (2006), "An infinite-dimensional control concept for piezoelectric structures with complex hysteresis", J. Struct. Control Health Monit., 13(6), Special Issue - Third European Conf. on Structural Control: Selected Sectional Key Note Lectures, 1099-1119. https://doi.org/10.1002/stc.96
  23. Liu, S.C., Tomizuka, M. and Ulsoy, G. (2005), "Challenges and opportunities in the engineering of intelligent structures", Smart Struct. Syst., 1(1), 1-12. https://doi.org/10.12989/sss.2005.1.1.001
  24. Mura, T. (1991), Micromechanics of Defects in Solids (2nd ed.), Kluwer, Dordrecht.
  25. Nader, M., Pichler, U., von GarBen, H.G. and Irschik, H. (2003), "Dynamic shape control of shells of revolution by distributed piezoelectric actuation", Proc. of of XXX Summer School APM'2002 - Advanced Problems in Mechanics, June 27th - July 6th, 2002, St. Petersburg (Repino), Russia, A. Indeitsev, (ed.), Russian Academy of Sciences St. Petersburg, 10-17.
  26. Nemenyi, P. (1931), "Eigenspannungen und eigenspannungsquellen", ZAMM, 11, 1-8. https://doi.org/10.1002/zamm.19310110101
  27. Parkus, H. (1976), Thermoelasticity (2nd ed.), Springer, Wien, New York.
  28. Preumont, A. (2004), Vibration Control of Active Strucutres (2nd ed.), Kluwer, Dordrecht.
  29. Quek, S.T., Wang, S.Y. and Ang, K.K. (2003), "Vibration control of composite plates via optimal placement of piezoelectric patches", J. Intel. Mat. Syst. Str., 14, 229-245. https://doi.org/10.1177/1045389X03034686
  30. Reissner, H. (1931), "Selbstspannungen elastischer Gebilde", ZAMM, 11, 59-70. https://doi.org/10.1002/zamm.19310110108
  31. Sepulveda, A.E. and Schmidt, L.A. (1991), "Optimal placement of actuators and sensors in control-augmented structural optimization", Int. J. Numer. Meth. Eng., 32, 1165-1187. https://doi.org/10.1002/nme.1620320602
  32. Tani, J., Takagi, T. and Qiu, J. (1998), "Intelligent material systems: application of functional materials", Appl. Mech. Rev., 51, 505-521. https://doi.org/10.1115/1.3099019
  33. Tzou, H.S. (1998), "Multifield transducers, devices, mechatronic systems and structronic systems with smart materials", Shock Vib., 30, 282-294. https://doi.org/10.1177/058310249803000402
  34. Yang, Y., Jin, Z. and Soh, C.K. (2005), "Integrated optimal design of vibration control system for smart beams using genetic algorithms", J. Sound Vib., 282(3-5), 1293-1307. https://doi.org/10.1016/j.jsv.2004.03.048
  35. Zhang, W., Qiu, J. and Tani, J. (2004), "Robust vibration control of a plate using self-sensing actuators of piezoelectric patches", J. Intel. Mat. Syst. Str., 15, 923-931. https://doi.org/10.1177/1045389X04045153
  36. Ziegler, F. (1998), Mechanics of Solids and Fluids (2nd corr. ed.), Springer, New York.
  37. Ziegler, F. and Irschik, H. (1987), "Thermal stress analysis based on maysel's formula", Therm. Stresses II, R.B. Hetnarski, eds., North - Holland, Amsterdam, 120-188.

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