Skip to main content
SpringerLink
Log in

Stability enhancement of beam-type structures by piezoelectric transducers: theoretical, numerical and experimental investigations

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Subject of the present work is the enhancement of the buckling load of beam-type structures under a compressive force by means of active feedback control. The focus of this paper lies on experimental aspects that show the feasibility of the proposed approach. For this purpose, a cantilever beam loaded by a compressive force is considered. The compressive force is applied with the help of a cable which is fixed at the tip of the free end and passes through the foundation of the cantilever. A laser displacement sensor is used to measure the structural displacements at the beam’s tip. For actuation, piezoelectric transducers are attached on each side of the cantilever beam. Two kinds of constant gain feedback control approaches are investigated on the experimental setup. The buckling load could be increased by a factor of 2.05. The experimental results agree very well with the performed numerical simulations. As a theoretical basis, a consistent theoretical formulation is presented using the Bernoulli–Euler beam theory. The formulation of the system includes also a general feedback controller with discrete displacement measurements and distributed piezoelectric patches. The influence of the controller on the buckling load, control amount by means of applied voltage and limits of the investigated active buckling control approaches are emphasized.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Timoshenko S.P., Gere J.M.: Theory of Elastic Stability. McGraw-Hill, New York (1936)

    Google Scholar 

  2. Preumont A.: Vibration Control of Active Structures. Kluwer Academic Publishers, Dordrecht (1997)

    Book  MATH  Google Scholar 

  3. Euler, L.: Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti. Additamentum 1, The Euler Archive. eulerarchive.maa.org/pages/E065.html. Accessed 1 April 2013 (1744)

  4. Humer A.: Exact solutions for the buckling and postbuckling of shear-deformable beams. Acta Mech. 224, 1493–1525 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. Thompson S.P., Loughlan J.: The active buckling control of some composite column strips using piezoceramic actuators. Compos. Struct. 32, 59–67 (1995)

    Article  Google Scholar 

  6. Berlin, A.A.: Active control of buckling using piezoceramic actuators. In: Proceedings of the SPIE Smart Structures and Materials, pp. 141–154 (1995)

  7. Chase, J.G., Yim, M.: Optimal stabilization of column buckling. ASCE J. Eng. Mech. 125, 987–993 (1999)

  8. Enss, G.C., Platz, R., Hanselka, H.: An approach to control the stability in an active load carrying beam-column by one single piezoelectric stack actuator. In: Proceedings of the ISMA 2010, International Conference on Noise and Vibration Engineering, pp. 535–546 (2010)

  9. Meressi T., Paden B.: Buckling control of a flexible beam using piezoelectric actuators. J. Guidance 16, 977–980 (1993)

    Article  MATH  Google Scholar 

  10. Mukherjee A., Chaudhuri A.S.: Active control of dynamic instability of piezolaminated imperfect columns. Smart Mater. Struct. 11, 874–879 (2002)

    Article  Google Scholar 

  11. Fridman Y., Abramovich H.: Enhanced structural behavior of flexible laminated composite beams. Compos. Struct. 82, 140–154 (2008)

    Article  Google Scholar 

  12. Zenz, G., Humer, A.: Enhancement of the stability of beams with piezoelectric transducers. J. Syst. Cont. Eng. 227, 744–751 (2013)

  13. Zehetner Ch., Irschik H.: On the static and dynamic stability of beams with an axial piezoelectric actuation. Smart Struct. Syst. 4, 67–84 (2006)

    Article  Google Scholar 

  14. Simitses G.J., Hodges D.H.: Fundamentals of Structural Stability. Butterworth-Heinemann, Oxford (2006)

    MATH  Google Scholar 

  15. Marzani A., Tornabene F., Viola E.: Nonconservative stability problems via generalized differential quadrature method. J. Sound Vib. 315, 176–196 (2008)

    Article  Google Scholar 

  16. Leipholz, H.: Stabilität elastischer Systeme. Braun, G., Karlsruhe (1980).

  17. Luongo, A., D’Annibale, F.: On the destabilizing effect of damping on discrete and continuous circulatory systems. J. Sound Vib. 333, 6723–6741 (2014)

  18. Holmes Ph., Marsden J.: Bifurcation to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis. Automatica 14, 367–384 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ahmadian H., Azizi H.: Stability analysis of a nonlinear jointed beam under distributed follower force. J. Vib. Control 17, 27–38 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Gerstmayr, J., Dorninger, A., Eder, R., Gruber, P., Reischl, D., Saxinger, M., Schörgenhumer, M., Humer, A., Nachbagauer, K., Pechstein, A., Vetyukov, Y.: HOTINT—a script language based framework for the simulation of multibody dynamics systems. In: Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2013), Portland, Oregon, USA (2013)

  21. Gerstmayr J., Irschik H.: On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach. J. Sound Vib. 318, 461–487 (2008)

    Article  Google Scholar 

  22. Irschik H., Gerstmayr J.: A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli–Euler beams. Acta Mech. 206, 1–21 (2008)

    Article  Google Scholar 

  23. Gerstmayr, J., Stangl, M.: High-order implicit Runge–Kutta methods for discontinuous mechatronical systems.In: Indeitsev, D.A. (ed.) Proceedings of the Summerschool on Actual Problems in Mechanics (APM 2004), pp. 162–169. St. Petersburg, Russia (2004)

  24. Singer J., Arbocz J., Weller T.: Buckling Experiments, Experimental Methods in Buckling of Thin-Walled Structures Basic Concepts Columns Beams and Plates, Vol. 1. Wiley, New York (1998)

    Google Scholar 

  25. Irschik H.: A review on static and dynamic shape control of structures by piezoelectric actuation. Eng. Struct. 24, 5–11 (2002)

    Article  Google Scholar 

  26. Huber D.W.: Modeling and Control of Thin Plate Structures by Piezoelectric Actuators and Sensors. Trauner Verlag, Linz (2011)

    Google Scholar 

  27. Tzou H.S., Hollkamp J.J.: Collocated independent modal control with self-sensing orthogonal piezoelectric actuators (theory and experiment). Smart Mater. Struct. 3, 277–284 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Linz Center of Mechatronics GmbH, Altenberger Straße 69, 4040, Linz, Austria

    Georg Zenz

  2. Institute of Technical Mechanics, Johannes Kepler University Linz, Altenberger Straße 69, 4040, Linz, Austria

    Alexander Humer

Authors
  1. Georg Zenz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Humer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Georg Zenz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zenz, G., Humer, A. Stability enhancement of beam-type structures by piezoelectric transducers: theoretical, numerical and experimental investigations. Acta Mech 226, 3961–3976 (2015). https://doi.org/10.1007/s00707-015-1445-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1445-9

Keywords

Search

Navigation