Skip to main content
SpringerLink
Log in

Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

This paper investigates nonlinear axisymmetric waves in compressible hyperelastic circular cylindrical rods. We consider first a compressible Mooney-Rivlin material to obtain exact governing equations. To further study the problem, we introduce the notion of long finite amplitude waves and derive the corresponding simplified model equations, which gives the framework for studying problems like wave-interactions arising through collision or reflection. The asymptotically valid far-field equation is consequently deduced from the simplified model equations. Then, using a strained-coordinate method, we obtain the second-order solitary wave solution. The result is not only of interest itself, but also provides a suitable initial condition for wave interaction problems. Finally, the results for a general hyperelastic rod are presented.

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. Wright, T.: Nonlinear waves in rods. In: Proceedings of the IUTAM Symposium on Finite Elasticity (Carlson, D. E., Shields, R. T., eds.). The Hague: Martinus Nijhoff 1982.

    Google Scholar 

  2. Wright, T.: Nonlinear waves in rods: results for incompressible elastic materials. Stud. Appl. Math.72, 149–160 (1985).

    Google Scholar 

  3. Coleman, B. D., Newman, D. C.: On waves in slender elastic rods. Arch. Rat. Mech. Anal.109, 39–61 (1990).

    Google Scholar 

  4. Nariboli, G. A.: Nonlinear longitudinal dispersive waves in elastic rods. J. Math. Phys. Sci.4, 64–73 (1970).

    Google Scholar 

  5. Ostrovskii, L. A., Sutin, A. M.: Nonlinear elastic waves in rods. PMM J. Appl. Math. Mech.41, 543–549 (1977).

    Google Scholar 

  6. Soerensen, M. P., Christiansen, P. L., Lomdahl, P. S.: Solitary waves on nonlinear rods I. J. Acoust. Soc. Am.78, 871–879 (1984).

    Google Scholar 

  7. Soerensen, M. P., Christiansen, P. L., Lomdahl, P. S., Skovgaard, O.: Solitary waves on nonlinear rods II. J. Acoust. Soc. Am.81, 1718–1722 (1987).

    Google Scholar 

  8. Clarkson, P. A., LeVeque, R. J., Saxton, R.: Solitary-wave interaction in elastic rods. Stud. Appl. Math.75, 95–122 (1986).

    Google Scholar 

  9. Jeffrey, A., Kawahara, T.: Asymptotic methods in nonlinear wave theory. London: Pitman 1982.

    Google Scholar 

  10. Ciarlet, P. G.: Mathematical elasticity. New York: North-Holland 1987.

    Google Scholar 

Download references

Author information

Author notes

  1. H. Cohen & H. -H. Dai

    Present address: Department of Applied Mathematics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

Authors and Affiliations

    Authors
    1. H. Cohen
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. H. -H. Dai
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Cohen, H., Dai, H.H. Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves. Acta Mechanica 100, 223–239 (1993). https://doi.org/10.1007/BF01174791

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01174791

    Keywords

    Search

    Navigation