Smart Beams: A Semi-Analytical Method

  • Y. W. Yang
  • C. K. Ju
  • C. K. Soh
Part of the Advanced Topics in Science and Technology in China book series (ATSTC)


One of the key challenges in structural engineering is to find better ways to control structural vibrations so as to better protect the structures from vibration-induced damages. Structural control methods can be classified into two main groups: passive control and active control. The basic role of passive control is to absorb or consume a portion of the input energy, thereby reducing the energy dissipation demand on the primary structural members and minimizing possible structural damage. On the other hand, in active control, the motion of a structure is controlled or modified by means of the action of a control system, which usually consists of sensors, actuators and controller, through certain external energy supply.


Mode Shape Axial Force Piezoelectric Actuator Vibration Control Piezoelectric Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bailey, T. and Hubbard, J.E. (1985). “Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam”, Journal of Guidance, Control and Dynamics, 8(5): 605–611.CrossRefzbMATHGoogle Scholar
  2. Bokaian, A. (1988). “Natural Frequencies of Beams under Compressive Axial Loads”, Journal of Sound and Vibration, 126(1): 49–65.CrossRefGoogle Scholar
  3. Bokaian, A. (1990). “Natural Frequencies of Beams under Tensile Axial Loads”, Journal of Sound and Vibration, 142(3): 481–498.CrossRefGoogle Scholar
  4. Chandiramani, N.K., Librescu, L.I., Saxena, V. and Kumar, A. (2004). “Optimal Vibration Control of a Rotating Composite Beam with Distributed Piezoelectric sensing and Actuation”, Smart Materials and Structures, 13: 433–442.CrossRefGoogle Scholar
  5. Chen, L.W., Lin, C.Y. and Wang, C.C. (2002). “Dynamic Stability Analysis and Control of a Composite Beam with Piezoelectric Layers”, Composite Structures, 56: 97–109.CrossRefGoogle Scholar
  6. Fazelzadeh, S.A. and Jafari, S.M. (2008). “Active Control Law Design for Flutter Suppression and Gust Alleviation of a panel with Piezoelectric Actuators”, Smart Materials and Structures, 17: 035013.CrossRefGoogle Scholar
  7. Fung, E.H.K. and Yau, D.T.W. (2004). “Vibration Characteristics of a Rotating Flexible Arm with ACLD Treatment”, Journal of Sound and Vibration, 269: 165–182.CrossRefGoogle Scholar
  8. Gardonio, P. and Elliott, S. (2005). “Modal Response of a Beam with Senor-Actuator Pair for the Implementation of Velocity Feedback Control”, Journal of Sound and Vibration, 284: 1–22.CrossRefGoogle Scholar
  9. Gaudenzi, P., Carbonaro, R. and Barboni, R. (1997). “Vibration Control of an Active Laminated Beam”, Composite Structures, 38(1–4): 413–420.CrossRefGoogle Scholar
  10. Han, J.H., Tani, J. and Qiu, J. (2006). “Active Flutter Suppression of a Lifting Surface Using Piezoelectric Actuation and Modern Control Theory”, Journal of Sound and Vibration, 291: 706–722.CrossRefGoogle Scholar
  11. Hong, S., Park, C.H. and Park, H.C. (2006), “Vibration Control of Beams using multiobjective State-Feedback Control”, Smart Materials and Structures, 15: 157–163.CrossRefGoogle Scholar
  12. Humar, J.L. (1990). Dynamics of Structures. Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
  13. Ikeda, T. (1990). Fundamentals of Piezoelectricity. Oxford; New York: Oxford University Press.Google Scholar
  14. Kamada, T., Fujita, T., Hatayama, T., Arikabe, T., Murai, N., Aizawa, S. and Tohyama, K. (1998). “Active Vibration Control of Flexural-Shear Type Frame Structures with Smart Structures Using Piezoelectric Actuators”, Smart Materials and Structures, 7: 479–488.CrossRefGoogle Scholar
  15. Karami-Mohammadi, A. and Sadri, A. (2009). “An Active Vibration Control of Beam by Piezoelectric with Fuzzy Approach”, International Journal of Signal System Control and Engineering Application, 2: 1–7.Google Scholar
  16. Kayacik, O., Bruch, J.C., Sloss, J.M., Adali, S. and Sadek, I.S. (2008). “Integral Equation Approach for Piezo Patch Vibration Control of Beams with Varioue types of Damping”, Computers and Structures, 86: 357–366.CrossRefGoogle Scholar
  17. Librescu, L. and Na, S. (1998a). “Boundary Control of Free and Forced Oscillation of Shearable Thin-Walled Beam Cantilevers”, European Journal of Mechanics — A/Solids, 17(4): 687–700.MathSciNetCrossRefzbMATHGoogle Scholar
  18. Librescu, L. and Na, S. (1998b). “Bending Vibration Control of Cantilevers via Boundary Moment and Combined Feedback Control Laws”, Journal of Vibration and Control, 17(4): 733–746.MathSciNetCrossRefGoogle Scholar
  19. Lin, J. and Liu, W.Z. (2006). “Experimental Evaluation of a Piezoelectric Vibration Absorber Using a Simplified Fuzzy Controller in a Cantilever Beam”, Journal of Sound and Vibration, 296: 567–582.CrossRefGoogle Scholar
  20. Lin, Y.J., Lee, T., Choi, B. and Saravanos, D. (1999). “An Application of Smart-Structure Technology to Rotor Blade Tip Vibration Control”, Journal of Vibration and Control, 5: 639–658.CrossRefGoogle Scholar
  21. Liu, L., Zhang, Z. and Hua, H. (2007). “Dynamic Characteristics of Rotating Cantilever Plates with Active Constrained Layer Damping Treatments”, Smart Materials and Structures, 16: 1849–1856.CrossRefGoogle Scholar
  22. Manning, W.J., Plummer, A.R. and Levesley, M.C. (2000). “Vibration Control of a Flexible Beam with Integrated Actuators and Sensors”, Smart Materials and Structures, 9: 932–939.CrossRefGoogle Scholar
  23. Maurizi, M.J. and Belles, P.M. (1991). “General Equation of Frequencies for Vibrating Uniform One-Span Beams under Compressive Axial Loads”, Journal of Sound and Vibration, 145(2): 345–347.CrossRefGoogle Scholar
  24. Moon, S.H. and Kim, S.J. (2003). “Suppression of Nonlinear Composite Panel Flutter with Active/Passive Hybrid Piezoelectric Networks Using Finite Element Method”, Composite Structures, 59: 525–533.CrossRefGoogle Scholar
  25. Mukherjee, A. and Chaudhuri, A.S. (2005). “Active Control of Piezolaminated Columns — Exact Solutions and Experimental Validation”, Smart Materials and Structures, 14: 475–482.CrossRefGoogle Scholar
  26. Nbendjo, B.R.N. (2009). “Amplitude Control on Hinged-Hinged Beam Using Piezoelectric Absorber: Analytical and Numerical Explanation”, International Journal of Non-Linear Mechanics, 44: 704–708.CrossRefGoogle Scholar
  27. Preumont, A. (1997). Vibration Control of Active Structures. Dordrecht, Kluwer Academic.CrossRefzbMATHGoogle Scholar
  28. Rao, G.V. and Singh, G. (2001). “A Smart Structures Concept for the Buckling Load Enhancement of Columns”, Smart Materials and Structures, 10: 843–845.CrossRefGoogle Scholar
  29. Sadri, A.M., Wright, J.R. and Wynne, R.J. (2002). “LQG Control Design for Panel Flutter Suppression Using Piezoelectric Actuators”, Smart Materials and Structures, 11: 834–839.CrossRefGoogle Scholar
  30. Sebastijanovic, N., Ma, T. and Yang, H.T.Y. (2007). “Panel Flutter Detection and Control Using the Eigenvector Orientation Method and Piezoelectric Layers”, AIAA Journal, 45, 118–127.CrossRefGoogle Scholar
  31. Shih, H.R. (2000). “Distributed Vibration Sensing and Control of a Piezoelectric Laminated Curved Beam”, Smart Materials and Structures, 9: 761–766.CrossRefGoogle Scholar
  32. Sloss, J.M., Bruch, J.C., Sadek, I.S. and Adali, S. (2003). “Piezo Patch Sensor/Actuator Control of the Vibrations of a Cantilever under Axial Load”, Composite Structures, 62: 423–428.CrossRefGoogle Scholar
  33. Sun, B. and Huang, D. (2001). “Vibration Suppression of Laminated Composite Beams with a Piezo-Electric Damping Layer”, Composite Structures, 53: 437–447.CrossRefGoogle Scholar
  34. Vasques, C.M.A. and Rodrigues, J.D. (2005). “Coupled Three-Layered Analysis of Smart Piezoelectric Beams with Different Electric Boundary Conditions”, International Journal for Numerical Methods in Engineering, 62: 1488–1518.CrossRefzbMATHGoogle Scholar
  35. Wang, Q. and Quek, S.T. (2000). “Flexural Vibration Analysis of Sandwich Beam Coupled with Piezoelectric Actuator”, Smart Materials and Structures, 9: 103–109.CrossRefGoogle Scholar
  36. Yang, Y.W., Ju, C.K. and Soh, C.K. (2003). “Analytical and semi-analytical solutions for vibration control of a cantilevered column using a piezoelectric actuator”, Smart Materials and Structures, 12: 193–203.CrossRefGoogle Scholar

Copyright information

© Zhejiang University Press, Hangzhou and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Y. W. Yang
    • 1
  • C. K. Ju
  • C. K. Soh
  1. 1.School of Civil and Environmental EngineeringNanyang Technological UniversitySingapore

Personalised recommendations