Skip to main content
SpringerLink
Log in

Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The piezoelectric materials are used to investigate the active vibration control of ordered/disordered periodic two-span beams. The equation of motion of each sub-beam with piezoelectric patches is established based on Hamilton’s principle with an assumed mode method. The velocity feedback control algorithm is used to design the controller. The free and forced vibration behaviors of the two-span beams with the piezoelectric actuators and sensors are analyzed. The vibration properties of the disordered two-span beams caused by misplacing the middle support are also researched. In addition, the effects of the length disorder degree on the vibration performances of the disordered beams are investigated. From the numerical results, it can be concluded that the disorder in the length of the periodic two-span beams will cause vibration localizations of the free and forced vibrations of the structure, and the vibration localization phenomenon will be more and more obvious when the length difference between the two sub-beams increases. Moreover, when the velocity feedback control is used, both the forced and the free vibrations will be suppressed. Meanwhile, the vibration behaviors of the two-span beam are tuned.

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. Huang, B. W. and Kuang, J. H. Mode localization in a rotating mistuned turbo disk with Coriolis effect. International Journal of Mechanical Sciences, 43, 1643–1660 (2001)

    Article  MATH  Google Scholar 

  2. Sharma, D., Gupta, S. S., and Batra, R. C. Mode localization in composite laminates. Composite Structures, 94, 2620–2631 (2012)

    Article  Google Scholar 

  3. Yan, Z. Z., Zhang, C., and Wang, Y. S. Analysis of wave propagation and localization in periodic/disordered layered composite structures by a mass-spring model. Applied Physics Letters, 94, 161909 (2009)

    Article  Google Scholar 

  4. Yan, Z. Z., Zhang, C., and Wang, Y. S. Attenuation and localization of bending waves in a periodic/disordered fourfold composite beam. Journal of Sound and Vibration, 327, 109–120 (2009)

    Article  Google Scholar 

  5. Li, F. M., Wang, Y. S., Hu, C., and Huang, W. H. Localization of elastic waves in periodic ribstiffened rectangular plates under axial compressive load. Journal of Sound and Vibration, 281, 261–273 (2005)

    Article  Google Scholar 

  6. Liu, Y., Su, J. Y., and Gao, L. T. The influence of the micro-topology on the phononic band gaps in 2D porous phononic crystals. Physics Letters A, 372, 6784–6789 (2008)

    Article  MATH  Google Scholar 

  7. Matar, O. B., Robillard, J. F., Vasseur, J. O., Hladky-Hennion, A. C., Deymier, P. A., Pernod, P., and Preobrazhensky, V. Band gap tunability of magneto-elastic phononic crystal. Journal of Applied Physics, 111, 054901 (2012)

    Article  Google Scholar 

  8. Robillard, J. F., Matar, O. B., Vasseur, J. O., Deymier, P. A., Stippinger, M., Hladky-Hennion, A. C., Pennec, Y., and Djafari-Rouhani, B. Tunable magnetoelastic phononic crystals. Applied Physics Letters, 95, 124104 (2009)

    Article  Google Scholar 

  9. Feng, R. and Liu, K. Tuning the band-gap of phononic crystals with an initial stress. Physica B, 407, 2032–2036 (2012)

    Article  Google Scholar 

  10. Zhou, X. and Chen, C. Tuning the locally resonant phononic band structures of two-dimensional periodic electroactive composites. Physica B, 431, 23–31 (2013)

    Article  Google Scholar 

  11. Su, X. L., Gao, Y. W., and Zhou, Y. H. The influence of material properties on the elastic band structures of one-dimensional functionally graded phononic crystals. Journal of Applied Physics, 112, 123503 (2012)

    Article  Google Scholar 

  12. Wang, Y. Z., Li, F. M., Kishimoto, K., Wang, Y. S., and Huang, W. H. Wave localization in randomly disordered layered three-component phononic crystals with thermal effects. Archive of Applied Mechanics, 80, 629–640 (2010)

    Article  MATH  Google Scholar 

  13. Senesi, M. and Ruzzene, M. Piezoelectric superlattices as multi-field internally resonating metamaterials. AIP Advances, 1, 041504 (2011)

    Article  Google Scholar 

  14. Li, F. M. and Wang, Y. S. Study on wave localization in disordered periodic layered piezoelectric composite structures. International Journal of Solids and Structures, 42, 6457–6474 (2005)

    Article  MATH  Google Scholar 

  15. Baz, A. Active control of periodic structures. Journal of Vibration and Acoustics, 123, 472–479 (2001)

    Article  Google Scholar 

  16. Oh, J. H., Lee, I. K., Ma, P. S., and Kim, Y. Y. Active wave-guiding of piezoelectric phononic crystals. Applied Physics Letters, 99, 083505 (2011)

    Article  Google Scholar 

  17. Wang, Y. Z., Li, F. M., Huang, W. H., Jiang, X. A., Wang, Y. S., and Kishimoto, K. Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals. International Journal of Solids and Structures, 45, 4203–4210 (2008)

    Article  MATH  Google Scholar 

  18. Wang, Y. Z., Li, F. M., Kishimoto, K., Wang, Y. S., and Huang, W. H. Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress. European Journal of Mechanics A/Solids, 29, 182–189 (2010)

    Article  Google Scholar 

  19. Mikata, Y. Orthogonality condition for a multi-span beam and its application to transient vibration of a two-span beam. Journal of Sound and Vibration, 314, 851–866 (2008)

    Article  Google Scholar 

  20. Gao, J. X. and Liao, W. H. Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments. Journal of Sound and Vibration, 280, 329–357 (2005)

    Article  Google Scholar 

  21. Chen, L. W., Lin, C. Y., and Wang, C. C. Dynamic stability analysis and control of a composite beam with piezoelectric layers. Composite Structures, 56, 97–109 (2002)

    Article  Google Scholar 

  22. Kim, H. W. and Kim, J. H. Effect of piezoelectric damping layers on the dynamic stability of plate under a thrust. Journal of Sound and Vibration, 284, 597–612 (2005)

    Article  Google Scholar 

  23. Ramesh-Kumar, K. and Narayanan, S. Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs. Smart Materials and Structures, 17, 055008 (2008)

    Article  Google Scholar 

  24. Li, F. M., Chen, Z. B., and Cao, D. Q. Improving the aeroelastic flutter characteristics of supersonic beams using piezoelectric material. Journal of Intelligent Material Systems and Structures, 22, 615–629 (2011)

    Article  Google Scholar 

  25. Li, F. M., Song, Z. G., and Chen, Z. B. Active vibration control of conical shells using piezoelectric materials. Journal of Vibration and Control, 18, 2234–2256 (2012)

    Article  MathSciNet  Google Scholar 

  26. Song, Z. G. and Li, F. M. Active aeroelastic flutter analysis and vibration control of supersonic beams using the piezoelectric actuator/sensor pairs. Smart Materials and Structures, 20, 055013 (2011)

    Article  Google Scholar 

  27. Li, F. M., Kishimoto, K., Wang, Y. S., Chen, Z. B., and Huang, W. H. Vibration control of beams with active constrained layer damping. Smart Materials and Structures, 17, 065036 (2008)

    Article  Google Scholar 

  28. Reddy, J. N. On laminated composite plates with integrated sensors and actuators. Engineering Structures, 21, 568–593 (1999)

    Article  Google Scholar 

  29. Choi, S. C., Park, J. S., and Kim, J. H. Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors. Composite Structures, 76, 362–374 (2006)

    Article  Google Scholar 

  30. Raja, S., Pashilkar, A. A., Sreedeep, R., and Kamesh, J. V. Flutter control of a composite plate with piezoelectric multilayered actuators. Aerospace Science and Technology, 10, 435–441 (2006)

    Article  MATH  Google Scholar 

  31. Mukherjee, A., Joshi, S. P., and Ganguli, A. Active vibration control of piezolaminated stiffened plates. Composite Structures, 55, 435–443 (2002)

    Article  Google Scholar 

  32. Park, C. H. and Baz, A. Vibration control of bending modes of plates using active constrained layer damping. Journal of Sound and Vibration, 227, 711–734 (1999)

    Article  Google Scholar 

  33. Lin, H. Y. and Tsai, Y. C. Free vibration analysis of a uniform multi-span beam carrying multiple spring-mass systems. Journal of Sound and Vibration, 302, 442–456 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Fengming Li

  2. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Fengming Li & Zhiguang Song

Authors
  1. Fengming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiguang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fengming Li.

Additional information

Project supported by the National Basic Research Program of China (973 Program) (No. 2011CB711100) and the National Natural Science Foundation of China (Nos. 10672017 and 11172084)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, F., Song, Z. Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs. Appl. Math. Mech.-Engl. Ed. 36, 279–292 (2015). https://doi.org/10.1007/s10483-015-1912-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-015-1912-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation