Active Vibration Suppression of Sandwich Beams using Piezoelectric Shear Actuators: Experiments and Numerical Simulations

Abstract

This article deals with the experimental and numerical assessment of the vibration suppression of smart structures using piezoelectric shear actuators. Experimental results are presented for an adaptive sandwich cantilever beam that consists of aluminum facings and a core composed of two piezoelectric shear actuators and foam. The electric field is applied perpendicular to the poling direction of the piezoelectric actuators to cause transverse shear deformation of the sandwich beam. Active vibration suppression is achieved using either positive position feedback or strain rate feedback. The control system is implemented in real-time using Matlab/Simulink and a dSPACE digital controller. First, the frequency response of the adaptive beam is investigated by using one shear actuator to excite the beam and the other to control its vibration. Parametric studies are conducted to assess the influence of controller parameters on the frequency response of the system. The experimental frequency response function compares well with numerical simulations using the finite element method. Next, the effectiveness of the active vibration suppression system in the time domain is analyzed using a proof-mass actuator that is attached to the tip of the cantilever beam to provide a repeatable vibration input. Experiments and numerical simulations show that the shear actuators can provide significant reduction in tip acceleration and settling time.

Keywords

smart/adaptive structure piezoelectric shear actuator positive position control strain-rate control active vibration suppression

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References

Aldraihem, O.J. and Khdeir, A.A. 2003. ‘‘Exact Deflection Solutions of Beams with Shear Piezoelectric Actuators,’’ International Journal of Solids and Structures, 40: 1-12 .

Bailey, T. and Hubbard, Jr., J.E. 1985. ‘‘Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam,’’ AIAA Journal of Guidance, Control and Dynamics, 8: 605-611 .

Baillargeon, B.P. and Vel, S.S. 2005. ‘‘Exact Solution for the Vibration and Active Damping of Composite Plates with Piezoelectric Shear Actuators,’’ Journal of Sound and Vibration, 282: 781-804 .

Benjeddou, A. and Deu, J.-F. 2001a. ‘‘Piezoelectric Transverse Shear Actuation and Sensing of Plates, Part 1: A Three-dimensional Mixed State Space Formulation,’’ Journal of Intelligent Material Systems and Structures, 12: 435-449 .

Benjeddou, A. and Deu, J.-F. 2001b. ‘‘Piezoelectric Transverse Shear Actuation and Sensing of Plates, Part 2: Application and Analysis,’’ Journal of Intelligent Material Systems and Structures, 12: 451-467 .

Benjeddou, A. and Deu, J.-F. 2002. ‘‘A Two-dimensional Closed-form Solution for the Free-vibration Analysis of Piezoelectric Sandwich Plates,’’ International Journal of Solids and Structures, 39: 1463-1486 .

Benjeddou, A. , Trindade, M.A. and Ohayon, R. 1999. ‘‘New Shear Actuated Smart Structure Beam Finite Element,’’ AIAA Journal, 37: 378-383 .

Berlincourt, D. and Krueger, H.H.A. (nd). Properties of Morgan Electroceramic Ceramics, Revised by C. Near, <http://www.morganelectroceramics.com/pdfs/tp226.pdf> (05 August 2002).

Dosch, J.J. , Inman, D.J. and Garcia, E. 1992. ‘‘Self-sensing Piezoelectric Actuator for Collocated Control,’’ Journal of Intelligent Material Systems and Structures, 3: 166-185 .

10.

Fanson, J.L. and Caughey, T.K. 1990. ‘‘Positive Position Feedback Control for Large Space Structures,’’ AIAA Journal, 28: 717-724 .

11.

Friswell, M.I. and Inman, D.J. 1999. ‘‘The Relationship between Positive Position Feedback and Output Feedback Controllers,’’ Smart Materials and Structures, 8: 285-291 .

12.

Fuller, C.R. , Elliott, S.J. and Nelson, P.A. 1996. Active Control of Vibration, Academic Press, San Diego .

13.

Garcia, E. , Dosch, J. and Inman, D.J. 1992. ‘‘The Application of Smart Structures to the Vibration Suppression Problem,’’ Journal of Intelligent Material Systems and Structures, 3: 659-667 .

14.

Glazounov, A.E. and Zhang, Q.M. 1998. ‘‘Piezoelectric Actuator Generating Torsional Displacement from Piezoelectric d15 Shear Response,’’ Applied Physics Letters, 72: 2526-2528 .

15.

Goh, C.J. and Caughey, T.K. 1985. ‘‘On the Stability Problem Caused by Finite Actuator Dynamics in the Collocated Control of Large Space Structures,’’ International Journal of Control, 41: 787-802 .

16.

Hibbitt, Karlsson & Sorensen, Inc. 2002. ABAQUS Users Manual, Version 6.3.

17.

Meyer, J.L. , Harrington, W.B. , Agrawal, B.N. and Song, G. 1998. ‘‘Vibration Suppression of a Spacecraft Flexible Appendage using Smart Materials,’’ Smart Materials and Structures, 7: 95-104 .

18.

Newman, S.M. 1992. ‘‘Active Damping Control of a Flexible Space Structure using Piezoelectric Sensors and Actuators,’’ Master’s Thesis, U.S. Naval Postgraduate School.

19.

Press, W.H. , Teukolsky, S.A. , Vetterling, W.T. and Flannery, B.P. 1992. Numerical Recipes in C, Cambridge University Press, Cambridge .

20.

Raja, S. , Prathap, G. and Sinha, P.K. 2002. ‘‘Active Vibration Control Composite Sandwich Beams with Piezoelectric Extension-bending and Shear Actuators,’’ Smart Materials and Structures, 11: 63-71 .

21.

Rao, S.S. 1995. Mechanical Vibrations, 3rd Edn, Addison-Wesley, Reading .

22.

Sun, C.T. and Zhang, X.D. 1995. ‘‘Use of Thickness-shear Mode in Adaptive Sandwich Structures , Smart Materials and Structures, 4: 202-206 .

23.

Trindade, M.A. , Benjeddou, A. and Ohayon, R. 2000. ‘‘Parametric Analysis of the Vibration Control of Sandwich Beams Through Shear-based Piezoelectric Actuation,’’ Journal of Intelligent Material Systems and Structures, 10: 377-385 .

24.

Vel, S.S. and Baillargeon, B.P. 2004. ‘‘Analysis of Static Deformation, Vibration and Active Damping of Cylindrical Composite Shells with Piezoelectric Shear Actuators,’’ Journal of Vibration and Acoustics (submitted).

25.

Vel, S.S. and Batra, R.C. 2001a. ‘‘Exact Solution for the Cylindrical Bending of Laminated Plates with Embedded Piezoelectric Shear Actuators,’’ Smart Materials and Structures, 10: 240-251 .

26.

Vel, S.S. and Batra, R.C. 2001b. ‘‘Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators,’’ AIAA Journal, 39: 1363-1373 .

27.

Zhang, X.D. and Sun, C.T. 1996. ‘‘Formulation of an Adaptive Sandwich Beam,’’ Smart Materials and Structures, 5: 814-823 .

28.

Zhang, X.D. and Sun, C.T. 1999. ‘‘Analysis of a Sandwich Plate Containing a Piezoelectric Core,’’ Smart Materials and Structures, 8: 31-40 .