Skip to main content
Log in

Analysis of nonlinear vibration for symmetric angle-ply laminated viscoelastic plates with damage

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The behavior of nonlinear vibration for symmetric angle-ply laminated plates including the material viscoelasticity and damage evolution is investigated. By employing the von Karman's nonlinear theory, strain energy equivalence principle and Boltzmann superposition principle, a set of governing equations of nonlinear integro-differential type are derived. By applying the finite difference method, Newmark method and iterative procedure, the governing equations are solved. The effects of loading amplitudes, exciting frequencies and different ply orientations on the critical time to failure initiation and nonlinear vibration amplitudes of the structures are discussed. Numerical results are presented for the different parameters and compared with the available data.

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.

Similar content being viewed by others

References

  1. Minahen, T.M., Knauss, W.G.: Creep buckling of viscoelastic structures. Int. J. Solids Struct. 30, 1075–1092 (1993)

    Google Scholar 

  2. Huang, N.N.: Viscoelastic analysis of Von Karman laminated plates under in-plane compression with initial deflection. Int. J. Non-linear Mech. 32, 1065–1075 (1997)

    Google Scholar 

  3. Aboudi, J., Cederbaum, G.: Dynamic stability analysis of viscoelastic plates by Lyapunov exponents. J. Sound Vibration 139, 459–467 (1990)

    Google Scholar 

  4. Cederbaum, G., Aboudi, J., Elishakoff, I.: Dynamic instability of shear-deformable viscoelastic laminated plates by Lyapunov exponents. Int. J. Solids Struct. 28, 317–327 (1991)

    Google Scholar 

  5. Cheng, C.J., Zhang, N.H.: Chaotic and hyperchaotic behaviors of viscoelastic rectangular plates under transverse periodic load. Acta Mech. Sinica 30, 690–699 (1998) (in Chinese)

    Google Scholar 

  6. Sun, Y.X., Zheng, S.Y.: Chaotic dynamic analysis of viscoelastic plates. Int. J. Mech. Sci. 43, 1195–1208 (2001)

    Google Scholar 

  7. Ladeveze, P., Dantec, E.L.: Damage modeling of the elementary ply for laminated composites. Composites Sci. Tech. 43, 257–267 (1992)

    Google Scholar 

  8. Chow, C.L., Wang, J.: An anisotropic theory of elasticity for continuum damage mechanics. Int. J. Fract. 33, 3–16 (1987)

    Google Scholar 

  9. Valliappan, S., Murti, V., Zhang, W.H.: Finite element analysis of anisotropic damage mechanics problems. Eng. Fract. Mech. 35, 1061–1071 (1990)

    Google Scholar 

  10. Kumar, R.S., Talreja, R.: A continuum damage model for linear viscoelastic composite materials. Mech. Mat. 35, 463–480 (2003)

    Google Scholar 

  11. Tawab, K.A., Weitsman, Y.J.: A strain-based formulation for the coupled viscoelstic/damage behavior. J. Appl. Mech. 68, 304–311 (2001)

    Google Scholar 

  12. Akshantala, N.V., Brinson, L.C.: A damage evolution model for viscoelastic composite laminates. J. Composite Tech. Res. 23, 3–14 (2001)

    Google Scholar 

  13. Schapery, R.A.: Homogenized constitutive equations for linear viscoelastic unidirectional composites with growing transverse cracks. Mechanics of Time-dependent Materials 6, 101–131 (2002)

    Google Scholar 

  14. Chia, C.Y.: Nonlinear Analysis of Plates. New York: McGraw-Hill, 1980

  15. Kachanov L.M.: Introduction to Continuum Damage Mechanics. Martinus Nijhoff Dordrecht, The Netherlands, 1986

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yufang Zheng.

Additional information

The project supported by the National Natural Science Foundation of China (10272042) and the Special Science Fund of the Doctoral Discipline of the Ministry of Education, China (20020532018)

The English text was polished by Ron Marshall.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, Y., Fu, Y. Analysis of nonlinear vibration for symmetric angle-ply laminated viscoelastic plates with damage. ACTA MECH SINICA 21, 459–466 (2005). https://doi.org/10.1007/s10409-005-0058-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-005-0058-2

Keywords

Navigation