Skip to main content
SpringerLink
Log in

On the nonlinear dynamics of bimodular laminated composite conical panels

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The nonlinear dynamics of bimodular laminated composite conical panels subjected to harmonic excitation is investigated using Bert’s constitutive model and first-order shear deformation theory based finite element. The governing equations of motion are solved to obtain the state vector representing the periodic response by employing shooting technique coupled with Newmark time marching and arc length/pseudo-arc length continuation algorithms. The influence of bimodularity, geometric nonlinearity and curvature on the steady state response characteristics of bimodular material laminated composite conical panels is analyzed for the first time. The through the thickness variations of normal strain/stress, steady state stress history, phase plane plots and frequency spectra are presented to explore the nonlinear periodic response characteristics of bimodular conical panels. The frequency response curves reveal increase in hardening nonlinearity with the increase in bimodularity ratio, load amplitude and semi-cone angle. The frequency response curves tend toward softening nonlinear behavior with the increase in curvature and/or decrease in semi-cone angle.

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

Similar content being viewed by others

References

  1. Jones, R.M., Morgan, H.S.: Bending and extension of cross-ply laminates with different moduli in tension and compression. Comput. Struct. 11, 181–190 (1980)

    Article  MATH  Google Scholar 

  2. An, Y.H., Draughn, R.A.: Mechanical Testing of Bone and the Bone–Implant Interface. CRC Press, Boca Raton (2000)

    Google Scholar 

  3. Bert, C.W., Reddy, J.N., Chao, W.C., Reddy, V.S.: Vibration of thick rectangular plates of bimodulus composite material. J. Appl. Mech. Trans. ASME 48, 371–376 (1981)

    Article  MATH  Google Scholar 

  4. Doong, J.L., Chen, L.W.: Vibration of a bimodulus thick plate. J. Vib. Acoust. Stress Trans. ASME 107, 92–97 (1985)

    Article  Google Scholar 

  5. Doong, J.L., Chen, L.W.: Axisymmetric vibration of an initially stressed bimodulus thick circular plates. J. Sound Vib. 94, 461–468 (1984)

  6. Chen, L.W., Chen, C.C.: Asymmetric vibration and dynamic stability of bimodulus thick annular plates. Comput. Struct. 31, 1013–1022 (1989)

  7. Patel, B.P., Gupta, S.S., Sarda, R.: Free flexural vibration behavior of bimodular material angle-ply laminated composite plates. J. Sound Vib. 286, 167–186 (2005)

    Article  Google Scholar 

  8. Bert, C.W., Kumar, M.: Vibration of cylindrical shells of bimodulus composite materials. J. Sound Vib. 81, 107–121 (1982)

    Article  MATH  Google Scholar 

  9. Khan, K., Patel, B.P., Nath, Y.: Vibration analysis of bimodulus laminated cylindrical panels. J. Sound Vib. 321, 166–183 (2009)

    Article  Google Scholar 

  10. Bert, C.W., Tran, A.D.: Transient response of a thick beam of bimodular material. Earthq. Eng. Struct. 10, 551–560 (1982)

    Article  Google Scholar 

  11. Reddy, J.N.: Transient response of laminated, bimodular-material, composite rectangular plates. J. Compos. Mater. 16, 139–152 (1982)

    Article  Google Scholar 

  12. Patel, B.P., Gupta, S.S., Joshi, M., Ganapathi, M.: Transient response analysis of bimodulus anisotropic laminated composite plates. J. Reinf. Plast. Compos. 24, 795–821 (2005)

    Article  Google Scholar 

  13. Zhang, H.W., Zhang, L., Gao, Q.: An efficient computational method for mechanical analysis of bimodular structures based on parametric variational principle. Comput. Struct. 89, 2352–2360 (2011)

    Article  Google Scholar 

  14. Zhang, H.W., Zhang, L., Gao, Q.: Numerical method for dynamic analysis of two-dimensional bimodular structures. AIAA J. 50, 1933–1942 (2012)

    Article  Google Scholar 

  15. Khan, K., Patel, B.P., Nath, Y.: Frequency response of bimodular cross-ply laminated cylindrical panels. J. Sound Vib. 327, 55–69 (2009)

    Article  Google Scholar 

  16. Bert, C.W.: Models for fibrous composites with different properties in tension and compression. J. Eng. Mater. Trans. ASME. 99, 344–349 (1977)

    Article  Google Scholar 

  17. Prathap, G., Naganarayana, B.P., Somasekhar, B.R.: Field consistency analysis of the isoparametric eight-noded plate bending element. Comput. Struct. 29, 857–863 (1988)

    Article  MATH  Google Scholar 

  18. Kraus, H.: Thin Elastic Shells. Wiley, New York (1976)

    Google Scholar 

  19. Jones, R.M.: Mechanics of Composite Materials. Mc-Graw Hill, New York (1975)

    Google Scholar 

  20. Rajasekaran, S., Murray, D.W.: Incremental finite element matrices. J. Struct. Div. Trans. ASCE 99, 2423–2438 (1973)

    Google Scholar 

  21. Khan, A.H., Patel, B.P.: Nonlinear forced vibration response of bimodular laminated composite plates. Compos. Struct. 108, 524–537 (2014)

    Article  Google Scholar 

  22. Ibrahim, S.M., Patel, B.P., Nath, Y.: Nonlinear periodic response of composite curved beam subjected to symmetric and antisymmetric mode excitation. J. Comput. Nonlinear Dyn. Trans. ASME 5, 021009-1-11 (2010)

    Google Scholar 

  23. Ibrahim, S.M., Patel, B.P., Nath, Y.: Modified shooting approach to the non-linear periodic forced response of isotropic/composite curved beams. Int. J. Nonlinear Mech. 44, 1073–1084 (2009)

    Article  Google Scholar 

  24. Nayfeh, A.H., Balachandaran, B.: Applied Nonlinear Dynamics. Wiley, New York (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    A. H. Khan & B. P. Patel

Authors
  1. A. H. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. P. Patel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. P. Patel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, A.H., Patel, B.P. On the nonlinear dynamics of bimodular laminated composite conical panels. Nonlinear Dyn 79, 1495–1509 (2015). https://doi.org/10.1007/s11071-014-1756-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1756-8

Keywords

Search

Navigation