Skip to main content
Log in

Dynamic responses of cross-ply bi-stable composite laminates with piezoelectric layers

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this paper, static and dynamic behavior of bi-stable composite laminates with \([0-90]_{T}\) stacking sequence and piezoelectric layers is studied. The governing equations of system were obtained using Rayleigh–Ritz method and Hamilton’s principle. In order to improve the accuracy of results, a set of higher-order shape functions were employed. The dynamic response of the system under various electrical fields applied to the piezoelectric actuators was studied, and the effects of the presented shape functions on short-circuit natural frequency and the lowest electrical field required for snap-through were analyzed. The results obtained from the developed analysis have been compared with the conventional and FEM models. Good correlation was observed between the proposed model and the finite element method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Hyer, M.W.: Some observations on the cured shape of thin unsymmetric laminates. J. Compos. Mater. 15(2), 175–194 (1981a)

    Article  Google Scholar 

  2. Diaconu, C.G., Weaver, P.M., Mattioni, F.: Concepts for morphing airfoil sections using bi-stable laminated composite structures. Thin Walled Struct. 46(6), 689–701 (2008)

    Article  Google Scholar 

  3. Hyer, M.W.: Calculations of the room-temperature shapes of unsymmetric laminates. J. Compos. Mater. 15, 296–310 (1981b)

    Article  Google Scholar 

  4. Hyer, M.W.: The room-temperature shapes of four-layer unsymmetric cross-ply laminates. J. Compos. Mater. 16(4), 318–340 (1982a)

    Article  Google Scholar 

  5. Hamamoto, A., Hyer, M.W.: Non-linear temperature-curvature relationships for unsymmetric graphite-epoxy laminates. Int. J. Solids Struct. 23(7), 919–935 (1987)

    Article  Google Scholar 

  6. Jun, W.J., Hong, C.S.: Effect of residual shear strain on the cured shape of unsymmetric cross-ply thin laminates. Compos. Sci. Technol. 38(1), 55–67 (1990)

    Article  Google Scholar 

  7. Jun, W.J., Hong, C.S.: Cured shape of unsymmetric laminates with arbitrary lay-up angles. J. Reinf. Plast. Compos 11(12), 1352–1366 (1992)

    Article  Google Scholar 

  8. Schlecht, M., Schulte, K., Hyer, M.W.: Advanced calculation of the room-temperature shapes of thin unsymmetric composite laminates. Compos. Struct. 32(1), 627–633 (1995)

    Article  Google Scholar 

  9. Dano, M.L., Hyer, M.W.: Thermally-induced deformation behavior of unsymmetric laminates. Int. J. Solids Struct. 35(17), 2101–2120 (1998)

    Article  MATH  Google Scholar 

  10. Giddings, P.F., Bowen, C.R., Salo, A.I.T., Kim, H.A., Ive, A.: Bistable composite laminates: effects of laminate composition on cured shape and response to thermal load. Compos. Struct. 92(9), 2220–2225 (2010)

    Article  Google Scholar 

  11. Betts, D.N., Salo, A.I.T., Bowen, C.R., Kim, H.A.: Characterisation and modelling of the cured shapes of arbitrary layup bistable composite laminates. Compos. Struct. 92(7), 1694–1700 (2010)

    Article  Google Scholar 

  12. Pirrera, A., Avitabile, D., Weaver, P.M.: Bistable plates for morphing structures: a refined analytical approach with high-order polynomials. Int. J. Solids Struct. 47(25), 3412–3425 (2010)

    Article  MATH  Google Scholar 

  13. Moore, M., Ziaei-Rad, S., Salehi, H.: Thermal response and stability characteristics of bistable composite laminates by considering temperature dependent material properties and resin layers. Appl. Compos. Mater. 20(10), 87–106 (2013)

    Article  Google Scholar 

  14. Moore, M., Ziaei-Rad, S., Firouzian-Nejad, A.: Temperature-curvature relationships in asymmetric angle ply laminates by considering the effects of resin layers and temperature dependency of material properties. J. Compos. Mater. 48(9), 1071–1089 (2014)

    Article  Google Scholar 

  15. Cantera, M.A., Romera, J.M., Adarraga, I., Mujika, F.: Modelling of [0/90] laminates subject to thermal effects considering mechanical curvature and through-the-thickness strain. Compos. Struct. 110, 77–87 (2014)

    Article  Google Scholar 

  16. Hufenbach, W., Gude, M., Kroll, L.: Design of multistable composites for application in adaptive structures. Compos. Sci. Technol. 62(16), 2201–2207 (2002)

    Article  Google Scholar 

  17. Dano, M.L., Hyer, M.W.: SMA-induced snap-through of unsymmetric fiber-reinforced composite laminates. Int. J. Solids Struct. 40(22), 5949–5972 (2003)

    Article  MATH  Google Scholar 

  18. Schultz, M.R., Hyer, M.W.: Snap-through of unsymmetric cross-ply laminates using piezoceramic actuators. J. Intell. Mater. Syst. Struct. 14(12), 795–814 (2003)

    Article  Google Scholar 

  19. Schultz, M.R., Wilkie, W.K., Bryant, R.G.: Investigation of self-resetting active multi-stable laminates. J. Aircraft 44(4), 1069–1076 (2007)

    Article  Google Scholar 

  20. Ren, L.B.: A theoretical study on shape control of arbitrary lay-up laminates using piezoelectric actuators. Compos. Struct. 83(1), 110–118 (2008)

    Article  Google Scholar 

  21. Kim, H.A., Betts, D.N., Salo, A.I.T., Bowen, C.R.: Shape memory alloy-piezoelectric active structures for reversible actuation of bistable composites. AIAA J. 48(6), 1265–1268 (2010)

    Article  Google Scholar 

  22. Arrieta, A.F., Mattioni, F., Neild, S.A., Weaver, P.M., Wagg, D.J., Potter, K.: Nonlinear dynamics of a bi-stable composite laminate plate with applications to adaptive structures. In 2nd European Conference for Aero-Space Sciences (2007)

  23. Arrieta, A.F., Neild, S.A., Wagg, D.J.: Nonlinear dynamic response and modeling of a bi-stable composite plate for applications to adaptive structures. Nonlinear Dyn. 58(1–2), 259–272 (2009)

    Article  MATH  Google Scholar 

  24. Diaconu, C.G., Weaver, P.M., Arrieta, A.F.: Dynamic analysis of bi-stable composite plates. J. Sound Vib. 322(4), 987–1004 (2009)

    Article  Google Scholar 

  25. Arrieta, A.F., Bilgen, O., Friswell, M.I., Hagedorn, P.: Dynamic control for morphing of bi-stable composites. J. Intell. Mater. Syst. Struct. 24(3), 266–273 (2013a)

    Article  Google Scholar 

  26. Arrieta, A.F., Bilgen, O., Friswell, M.I., Ermanni, P.: Modelling and configuration control of wing-shaped bi-stable piezoelectric composites under aerodynamic loads. Aerosp. Sci. Technol. 29(1), 453–461 (2013b)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  28. Hagood, N.W., Chung, W.H., Von Flotow, A.: Modelling of piezoelectric actuator dynamics for active structural control. J. Intell. Mater. Syst. Struct. 1(3), 327–354 (1990)

    Article  Google Scholar 

  29. Kyriazoglou, C., Guild, F.J.: Finite element prediction of damping of composite GFRP and CFRP laminates—a hybrid formulation–vibration damping experiments and Rayleigh damping. Compos. Sci. Technol. 66(3), 487–498 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Tikani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Taki, M.S., Tikani, R., Ziaei-Rad, S. et al. Dynamic responses of cross-ply bi-stable composite laminates with piezoelectric layers. Arch Appl Mech 86, 1003–1018 (2016). https://doi.org/10.1007/s00419-015-1075-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1075-7

Keywords

Navigation