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Modellierung, Simulation und Schwingungsreduktion dünner Schalen mit piezoelektrischen Wandlern

Modeling, simulation and vibration reduction of thin shells with piezoelectric transducers

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Zusammenfassung

In diesem Beitrag wird zuerst eine elektromechanisch gekoppelte Theorie für dünne Schalen mit piezoelektrischen Wandlern im Rahmen einer geometrisch nichtlinearen Formulierung vorgestellt. Hierbei wird eine Schale als materielle Fläche mit mechanischen und elektrischen Freiheitsgraden modelliert. Eine Finite Elemente Implementierung beschließt den ersten Teil der Arbeit. Im zweiten Teil des Beitrags wird die vorgestellte Theorie mit Hilfe von Vergleichsrechnungen mit dem kommerziell erhältlichen Finite Elemente Programm Abaqus sowie mit Ergebnissen aus der Literatur verifiziert, um dann im dritten Teil der Arbeit zur Schwingungsreduktion zur Anwendung gebracht zu werden. Der vorliegende Beitrag endet mit einer experimentellen Untersuchung der passiven Schwingungsreduktion einer dünnen Schale mit piezoelektrischen Wandlern unter Verwendung der Methode des passiven Shunt Dampings.

Abstract

In the present paper a geometrically nonlinear electromechanically coupled theory for thin shells with piezoelectric transducers is presented. Within this theory the shell is modelled as a material surface with mechanical and electrical degrees of freedom. A Finite Element implementation completes the first part of the paper. In the second part of the paper the shell theory is verified by a comparison to results computed with the commercially available Finite Element code Abaqus as well as to results from the literature. In the third part of the paper the theory is applied to the problem of vibration reduction in thin shells with piezoelectric transducers. Simulation results and experimental results are presented, in which the method of passive shunt damping is used.

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Literatur

  1. Crawley, E. F. (1994): Intelligent structures for aerospace: a technology overview and assessment. AIAA J., 32(8), 1689–1699.

    Article  Google Scholar 

  2. Tani, J., Takagi, T., Qiu, J. (1998): Intelligent material systems: application of functional materials. Appl. Mech. Rev., 51, 505–521.

    Article  Google Scholar 

  3. Liu, S.-C., Tomizuka, M., Ulsoy, G. (2005): Challenges and opportunities in the engineering of intelligent structures. Smart Struct. Syst., 1(1), 1–12.

    Article  Google Scholar 

  4. Nader, M. (2008): Compensation of vibrations in smart structures: shape control, experimental realization and feedback control. Linz: Trauner.

    Google Scholar 

  5. Alkhatib, R., Golnaraghi, M. F. (2003): Active structural vibration control: a review. Shock Vib. Dig., 35(5), 367–383.

    Article  Google Scholar 

  6. Nestorović, T., Lefèfre, J., Gabbert, U. (2007): Model-based active noise control of a piezoelectric structure. Meccanica, 26(2), 71–77.

    Google Scholar 

  7. Gabbert, U., Tzou, H. S. (2000): Preface. In U. Gabbert, H. S. Tzou (Hrsg.), Proceedings of the IUTAM-symposium on smart structures and structronic systems, September 2000, Magdeburg, Germany. Dordrecht: Kluwer.

    Google Scholar 

  8. Krommer, M. (2003): The significance of non-local constitutive relations for composite thin plates including piezoelastic layers with prescribed electric charge. Smart Mater. Struct., 12(3), 318–330.

    Article  Google Scholar 

  9. Batra, R. C., Vidoli, S. (2002): Higher order piezoelectric plate theory derived from a three dimensional variational principle. AIAA J., 40, 91–104.

    Article  Google Scholar 

  10. Carrera, E., Boscolo, M. (2007): Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates. Int. J. Numer. Methods Eng., 70(10), 1135–1181.

    Article  MathSciNet  MATH  Google Scholar 

  11. Zheng, S., Wang, X., Chen, W. (2004): The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators. Smart Mater. Struct., 13, 43–50.

    Article  Google Scholar 

  12. Tan, X., Vu-Quoc, L. (2005): Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control. Int. J. Numer. Methods Eng., 64, 1981–2013.

    Article  MATH  Google Scholar 

  13. Klinkel, S., Wagner, W. (2006): A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation. Int. J. Numer. Methods Eng., 65, 349–382.

    Article  MATH  Google Scholar 

  14. Klinkel, S., Wagner, W. (2008): A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications. Comput. Struct., 86, 38–46.

    Article  Google Scholar 

  15. Marinkovic, D., Köppe, H., Gabbert, U. (2007): Accurate modeling of the electric field within piezoelectric layers for active composite structures. J. Intell. Mater. Syst. Struct., 18, 503–513.

    Article  Google Scholar 

  16. Marinkovic, D., Köppe, H., Gabbert, U. (2008): Degenerated shell element for geometrically nonlinear analysis of thin-walled piezoelectric active structures. Smart Mater. Struct., 17(1), 10.

    Article  Google Scholar 

  17. Lentzen, S., Klosowski, P., Schmidt, R. (2007): Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells. Smart Mater. Struct., 16, 2265–2274.

    Article  Google Scholar 

  18. Vetyukov, Y., Kuzin, A., Krommer, M. (2011): Asymptotic splitting in the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates. Int. J. Solids Struct., 48, 12–23.

    Article  MATH  Google Scholar 

  19. Naghdi, P. M. (1972): The theory of shells and plates. In S. Flügge, C. Truesdell (Hrsg.) Handbuch der Physik (Vol. VIa/2). Berlin: Springer.

    Google Scholar 

  20. Eliseev, V., Vetyukov, Y. (2010): Finite deformation of thin shells in the context of analytical mechanics of material surfaces. Acta Mech., 209, 43–57.

    Article  MATH  Google Scholar 

  21. Vetyukov, Y. (2014): Nonlinear mechanics of thin-walled structures: asymptotics, direct approach and numerical analysis. Vienna: Springer.

    Book  Google Scholar 

  22. Vetyukov, Y. (2014): Finite element modeling of Kirchhoff-Love shells as smooth material surfaces. Z. Angew. Math. Mech., 94, 150–163.

    Article  MathSciNet  MATH  Google Scholar 

  23. Pastor, M., Binda, M., Harcarik, T. (2012): Modal assurance criterion. Proc. Eng., 48, 543–548.

    Article  Google Scholar 

  24. Varelis, D., Saravanos, D. A. (2002): Nonlinear coupled mechanics and initial buckling of composite plates with piezoelectric actuators and sensors. Smart Mater. Struct., 11, 330–336.

    Article  Google Scholar 

  25. Ahmadian, M., Jeric, K. M. (2001): On the application of shunted piezoceramics for increasing accoustic transmission loss in structures. J. Sound Vib., 243(2), 347–359.

    Article  Google Scholar 

  26. Hagood, N. W., von Flotow, A. (1991): Damping of structural vibrations with piezoelectric materials and passive electrical networks. J. Sound Vib., 146(2), 243–268.

    Article  Google Scholar 

  27. Trindade, M. A., Benjeddou, A. (2009): Effective electromechanical coupling coefficients of piezoelectric adaptive structures: critical evaluation and optimization. Mech. Adv. Mat. Struct., 16(3), 210–223.

    Article  Google Scholar 

  28. Zenz, G., Berger, W., Gerstmayr, J., Nader, M., Krommer, M. (2013): Design of piezoelectric transducer arrays for passive and active modal control of thin plates. Smart Struct. Syst., 12(5), 547–577.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Mechanik und Mechatronik, Technische Universität Wien, Getreidemarkt 9, 1060, Wien, Österreich

    Michael Krommer & Yury Vetyukov

  2. Institut für Mechatronik, Universität Innsbruck, Technikerstraße 13a, 6020, Innsbruck, Österreich

    Michael Pieber

Authors
  1. Michael Krommer
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  2. Michael Pieber
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  3. Yury Vetyukov
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Correspondence to Michael Krommer.

Additional information

Die Autoren bedanken sich für die Unterstützung durch die Linz Center of Mechatronics GmbH im Rahmen des COMET-K2 Zentrums ACCM und beim Fraunhofer Zentrum LBF sowie beim LOEWE Zentrum AdRIA in Darmstadt für die Unterstützung bei der Durchführung der experimetellen Untersuchungen.

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Krommer, M., Pieber, M. & Vetyukov, Y. Modellierung, Simulation und Schwingungsreduktion dünner Schalen mit piezoelektrischen Wandlern. Elektrotech. Inftech. 132, 437–447 (2015). https://doi.org/10.1007/s00502-015-0375-5

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  • DOI: https://doi.org/10.1007/s00502-015-0375-5

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