Skip to main content
SpringerLink
Log in

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Lee, B.H.K., Price, S.J., Wong, Y.S.: Nonlinear aeroelastic analysis of airfoil: bifurcation and chaos. Prog. Aerospace Sci. 35, 205–334 (1999)

    Article  Google Scholar 

  2. Arrison, M., Birocco, K., Gaylord, C., et al.: 2002–2003 AE/ME morphing wing design. Virginia Tech Aerospace Engineering Senior Design Project Spring Semester Final Report. (2003)

  3. Tabarrok, B., Leech, C.M., Kim, Y.I.: On the dynamics of an axially moving beam. J. Frankl. Inst. 297, 201–220 (1974)

    Article  MATH  Google Scholar 

  4. Taleb, I.A., Misra, A.K.: Dynamics of an axially moving beam submerged in a fluid. J. Hydronaut. 15, 62–66 (1981)

    Article  Google Scholar 

  5. Wang, P.K.C., Wei, J.D.: Vibration in a moving flexible robot arm. J. Sound Vib. 116, 149–160 (1987)

    Article  Google Scholar 

  6. Behdinan, K., Stylianou, M., Tabarrok, B.: Dynamics of flexible sliding beams non-linear analysis. Part I: formulation. J. Sound Vib. 208, 517–539 (1997)

    Article  Google Scholar 

  7. Deng, Z.C., Zheng, H.J., Zhao, Y.L., et al.: On computation of dynamic properties for deploying cantilever beam based on precision integration method. J. Astronaut. 22, 110–113 (2001). (in Chinese)

    Google Scholar 

  8. Zhu, W.D., Zheng, N.A.: Exact response of a translating string with arbitrarily varying length under general excitation. J. Appl. Mech. 75, 519–525 (2008)

    Google Scholar 

  9. Gosselin, F., Paidoussis, M.P., Misra, A.K.: Stability of a deploying/deploying beam in dense fluid. J. Sound Vib. 299, 124–142 (2007)

    Article  Google Scholar 

  10. Wang, L., Ni, Q.: Vibration and stability of an axially moving beam immersed in fluid. Int. J. Solids Struct. 45, 1445–1457 (2008)

    Article  MATH  Google Scholar 

  11. Zhang, W., Sun, L., Yang, X.D., et al.: Nonlinear dynamic behaviors of a deploying-and-retreating wing with varying velocity. J. Sound Vib. 332, 6785–6797 (2013)

    Article  Google Scholar 

  12. Huang, R., Qiu, Z.P.: Transient aeroelastic responses and flutter analysis of a variable-span wing during the morphing process. Chin. J. Aeronaut. 26, 1430–1438 (2013)

    Article  Google Scholar 

  13. Wang, L.H., Hu, Z.D., Zhong, Z.: Dynamic analysis of an axially translating plate with time-variant length. Acta Mech. 215, 9–23 (2010)

    Article  MATH  Google Scholar 

  14. Zhang, W., Lu, S.F., Yang, X.D.: Analysis on nonlinear dynamics of a deploying cantilever laminated composite plate. Nonlinear Dyn. 76, 69–93 (2014)

    Article  MATH  Google Scholar 

  15. Yang, X.D., Zhang, W., Chen, L.Q., et al.: Dynamical analysis of axially moving plate by finite difference method. Nonlinear Dyn. 67, 997–1006 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ding, H., Chen, L.Q.: Nonlinear dynamics of axially accelerating viscoelatic beams based on differential quadrature. Acta Mechanica Solida Sinica 22, 267–275 (2009)

  17. Matsuzaki, Y., Torii, H., Toyama, M.: Vibration of a cantilevered beam during deployment and retrieval: analysis and experiment. Smart Mater. Struct. 4, 334–339 (1995)

    Article  Google Scholar 

  18. Liu, K.F., Deng, L.Y.: Experimental verification of an algorithm for identification of linear time-varying systems. J. Sound Vib. 279, 1170–1180 (2005)

    Article  Google Scholar 

  19. Liu, K.F., Deng, L.Y.: Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm. Mech. Syst. Signal Process. 20, 94–113 (2006)

    Article  Google Scholar 

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

    Google Scholar 

  21. Reddy, J.N., Mitchell, J.A.: On refined nonlinear theories of laminated composite structures with piezoelectric laminae. Sadhana 20, 721–747 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  22. Rafiee, M., Mohammadi, M., Sobhani Aragh, B., et al.: Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part I: Theory and analytical solutions. Compos. Struct. 103, 179–187 (2013)

    Article  Google Scholar 

  23. Fu, Y.M., Wang, X.Q., Yang, J.H.: Nonlinear dynamic response of piezoelastic laminated plates considering damage effects. Compos. Struct. 81, 353–361 (2007)

    Article  Google Scholar 

  24. Huang, X.L., Shen, H.S.: Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators. Int. J. Mech. Sci. 47, 187–208 (2005)

    Article  MATH  Google Scholar 

  25. Dash, P., Singh, B.N.: Nonlinear free vibration of piezoelectric laminated composite plate. Finite Elem. Anal. Des. 45, 686–694 (2009)

    Article  Google Scholar 

  26. Wang, Y., Hao, Y.X., Wang, J.H.: Nonlinear vibration of a cantilever FGM Rectangular plate with piezoelectric layers based on third- order plate theory. Adv. Mater. Res. 415–417, 2151–2155 (2012)

    Article  Google Scholar 

  27. Zhang, W., Yao, Z.G., Yao, M.H.: Periodic and chaotic dynamics of laminated composite plated piezoelectric rectangular plate with one-to-two internal resonance. Sci. China Ser. E Technol. Sci. 52, 731–742 (2009)

    Article  MATH  Google Scholar 

  28. Zhang, H.Y., Shen, Y.P.: Vibration suppression of laminated plates with 1–3 piezoelectric fiber-reinforced composite layers equipped with interdigitated electrodes. Compos. Struct. 79, 220–228 (2007)

    Article  Google Scholar 

  29. Wang, S.Y., Quek, S.T., Ang, K.K.: Vibration control of smart piezoelectric composite plates. Smart Mater. Struct. 10, 637–644 (2001)

    Article  Google Scholar 

  30. Ray, M.C., Reddy, J.N.: Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites. Compos. Sci. Technol. 65, 1226–1236 (2005)

    Article  Google Scholar 

  31. Qiu, Z.C., Zhang, X.M., Wu, H.X., et al.: Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. J. Sound Vib. 301, 521–543 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Dong, X.J., Meng, G., Peng, J.C.: Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study. J. Sound Vib. 297, 680–693 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press LLC, Boca Raton (2004)

    MATH  Google Scholar 

  34. Ashley, H., Zartarian, G.: Piston theory-a new aerodynamic tool for the aeroelastician. J. Aeronaut. Sci. 23, 1109–1118 (1956)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The project was supported by the National Natural Science Foundation of China (Grants 11402126, 11502122, and 11290152) and the Scientific Research Foundation of the Inner Mongolia University of Technology (Grant ZD201410).

Author information

Authors and Affiliations

  1. College of Science, Inner Mongolia University of Technology, Hohhot, 010051, China

    S. F. Lu & X. J. Song

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

    W. Zhang

Authors
  1. S. F. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. J. Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, S.F., Zhang, W. & Song, X.J. Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force. Acta Mech. Sin. 34, 303–314 (2018). https://doi.org/10.1007/s10409-017-0705-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-017-0705-4

Keywords

Search

Navigation