Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32468
Implementation of State-Space and Super-Element Techniques for the Modeling and Control of Smart Structures with Damping Characteristics

Authors: Nader Ghareeb, R¨udiger Schmidt


Minimizing the weight in flexible structures means reducing material and costs as well. However, these structures could become prone to vibrations. Attenuating these vibrations has become a pivotal engineering problem that shifted the focus of many research endeavors. One technique to do that is to design and implement an active control system. This system is mainly composed of a vibrating structure, a sensor to perceive the vibrations, an actuator to counteract the influence of disturbances, and finally a controller to generate the appropriate control signals. In this work, two different techniques are explored to create two different mathematical models of an active control system. The first model is a finite element model with a reduced number of nodes and it is called a super-element. The second model is in the form of state-space representation, i.e. a set of partial differential equations. The damping coefficients are calculated and incorporated into both models. The effectiveness of these models is demonstrated when the system is excited by its first natural frequency and an active control strategy is developed and implemented to attenuate the resulting vibrations. Results from both modeling techniques are presented and compared.

Keywords: Finite element analysis, super-element, state-space model.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 731


[1] N. Ghareeb and Y. Radovcic, ”Fatigue Analysis of a Wind Turbine Power Train”, DEWI magazin, Germany, August 2009, pp 12-16.
[2] R. Vepa, ”Dynamics of Smart Structures”, John Wiley & Sons, 2010.
[3] S. Narayanan and V. Balamurugan, ” Finite Element Modeling of Piezolaminated Smart Structures for Active Vibration Control with Distributed Sensors and Actuators”, Journal of Sound and Vibration, 2003, vol. 262, pp 529-562.
[4] A. Mallock, ”A Method of Preventing Vibration in Certain Classes of Steamships”, Trans. Inst. Naval Architects, 1905, 47, pp 227-230.
[5] H. Hort, ”Beschreibung und Versuchsergebnisse ausgef¨uhrter Schiffsstabilisierungsanlagen”, Jahrb. Schiffbautechnik Ges., 1934, 35, pp 292-312.
[6] A. Vang, ”Vibration Dampening”, U.S. Patent US 2,361,071, Oct. 24, 1944.
[7] M. Balas, ”Active Control of Flexible Systems”, Journal of Optimization theory and Applications, 1978, vol. 25, no. 3, pp 415-436.
[8] V. Piefort, ”Finite Element Modelling of Piezoelectric Active Structures”, Universit Libre de Bruxelles, PhD Thesis, Belgium, 2001.
[9] T. Bailey, ”Distributed-Parameter Vibration Control of a Cantilever Beam Using a Distributed-Parameter Actuator”, Massachusetts Institute of Technology, Msc. Thesis, 1984.
[10] T. Bailey and J. Hubbard Jr., ”Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam”, AIAA Journal of Guidance and Control, 1985, vol. 6, no. 5, pp. 605-611.
[11] E. F. Crawley and J. de Luis, ”Use of Piezoelectric Actuators as Elements of Intelligent Structures”,AIAA Journal, 1987, vol. 25, no. 10, pp 1373-1385.
[12] E. Crawley and E. Anderson, ”Detailed Models of Piezoceramic Actuation of Beams”, Journal of Intelligent Material Systems and Structures, 1990, vol. 1, no. 1, pp. 4-24.
[13] J. Fanson and J. Chen, ”Structural Control by the Use of Piezoelectric Active Members”, Proceedings of NASA/DOD Control-Structures Interaction Conference, 1986, NASA CP-2447, part2, pp. 809-830.
[14] A. Preumont, ”Vibration Control of Active Structures, An Introduction”, Kluwer Academic Publishers, 2002.
[15] S. Moheimani and A. Fleming, ”Piezoelectric Transducers for Vibration Control and Damping”, Springer, 2006.
[16] W. Gawronski, ”Advanced Structural Dynamics and Active Control of Structures”, Springer, 2004.
[17] J. He and Z. Fu, ”Modal Analysis”, Butterworth-Heinemann, 2001.
[18] SAMTECH Products,
[19] S. Kapuria, G. Dube and P. Dumir, ”First-Order Shear Deformation Theory Solution for a Circular Piezoelectric Composite Plate under Axisymmetric Load”, Smart Materials and Structures, 2003, vol. 12, pp. 417-423.
[20] J. F. Semblat, ”Rheological Interpretation of Rayleigh Damping”, Journal of Sound and Vibration, 1997, vol. 5, pp. 741-744.
[21] I. Kreja and R. Schmidt, ”Large Rotations in First-Order Shear Deformation FE analysis of Laminated Shells”, International Journal of Non-Linear Mechanics, 2006, vol. 41, pp. 101-123.
[22] W. Ko and T. Olona, ”Effect of Element Size on the Solution Accuracies of Finite-Element Heat Transfer and Thermal Stress Analysis of Space Shuttle Orbiter”, NASA Technical Memorandum 88292, 1987.
[23] J. Butterworth, J. Lee and B. Davidson, ”Experimental Determination of Modal Damping From Full Scale Testing”, 13th World Conference on Earthquake Engineering, Vancouver, Canada, August 1-6, 2004, Paper no. 310.
[24] A. Puthanpurayil, R. Dhakal and A. Carr, ”Modelling of In-Structure Damping: A review of the State-of-the-art”, Proceedings of the Ninth Pacific Conference on Earthquake Engineering, Auckland, New Zealand, 14-16 April, 2011
[25] A. Alipour and F. Zareian, ”Study Rayleigh Damping in Structures; Uncertainties and Treatments”, The 14th World Conference on Earthquake Engineering, Beijing, China, October 12-17, 2008.
[26] L. Rayleigh, ”Theory of Sound (two volumes)”, Dover Publications, New York, 1877.
[27] R. Spears and S. Jensen, ”Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis”, Proceedings of PVP2009, ASME Vessels and Piping Division Conference, Prague, Czech Republic, July 26-30, 2009.
[28] S. Adhikari, ”Damping Models for Structural Vibration”, PhD Thesis, 2000.
[29] I. Chowdhury and S. Dasgupta, ”Computation of Rayleigh Damping Coefficients for Large Systems”, The Electronic Journal of Geotechnical Engineering, 2003, vol. 8, Bundle 8C.
[30] I. Giosan, ”Dynamic Analysis with Damping for Free-Standing Structures Using Mechanical Event Simulation”, Autodesk Report, 2010.
[31] D. Ewins, ”Modal Testing: Theory and Practice”, John Wiley & Sons Inc., 1984.
[32] M. Petyt, ”Introduction to Finite Element Vibration Analysis”, Cambridge University Press, 2003.
[33] R. Craig and M. Bampton, ”Coupling of Substructures for Dynamic Analyses”, AIAA Journal, 1968, vol. 6, no. 7, pp 1313-1319
[34] C. Rickelt-Rolf, ”Modellreduktion und Substrukturtechnik zur effizienten Simulation dynamischer, teilgesch¨adigter Systeme”, Technische Universit¨at Carolo-Wilhelmina zu Braunschweig, PhD Thesis, Germany, 2009.
[35] H. Khalil, ”Nonlinear Systems”, Prentice Hall, Madison, 1996.