Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod

Acta Mechanica

Volumn 127, Issue 1-4, 1998, Pages 193-207

  Dai, H H ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION (WAVES); MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

BENJAMIN BONA MAHONY (BBM) EQUATIONS; COMPRESSIBLE MOONEY RIVLIN ROD; KORTEWEG DE VRIES (KDV) EQUATIONS; NONLINEAR DISPERSIVE WAVES;

MECHANICAL WAVES;

EID: 0031679566     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01170373     Document Type: Article

References (25)

1. Green, W. A.: Dispersion relations for elastic waves in bars. In: Progress in solid mechanics, Vol. I (Sneddon, I. N., Hill, R., eds.), pp. 128-153. Amsterdam: North-Holland 1960.
2. Achenbach, J. D.: Wave propagation in elastic solids. Amsterdam: North-Holland 1973.
3. Wright, T. W.: Nonlinear waves in rods. In: Proceedings of the IUTAM Symposium on Finite Elasticity (Carlson, D. E., Shields, R. T., eds.), pp. 423-443. The Hague: Martinus Nijhoff 1982.
4. Wright, T. W.: Nonlinear waves in rods: results for incompressible materials. Stud. Appl. Math. 72, 149-160 (1985).
5. Coleman, B. D., Newman, D. C.: On waves in slender elastic rods. Arch. Rat. Mech. Anal. 109, 39-61 (1990).
6. Nariboli, G. A.: Nonlinear longitudinal dispersive waves in elastic rods. J. Math. Phys. Sci. 4, 64-73 (1970).
7. Soerensen, M. P., Christiansen, P. L., Lomdahl, P. S.: Solitary waves on nonlinear rods I. J. Acoust. Soc. Am. 78, 871-879 (1984).
8. 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).
9. Clarkson, P. A., LeVeque, R. J., Saxton, R.: Solitary-wave interaction in elastic rods. Stud. Appl. Math. 75, 95-122 (1986).
10. Cohen, H., Dai, H.-H.: Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves. Acta Mech. 100, 223-239 (1993).
11. Cohen, H.: A non-linear theory of elastic directed curves. Int. J. Eng. Sci. 4, 511-524 (1966).
12. Green, A. E., Naghdi, P. M., Wenner, M. L.: On the theory of rods. Part I. Derivations from three-dimensional equations. Proc. R. Soc. London Ser. A 337, 451-483 (1974).
13. Green, A. E., Naghdi, P. M., Wenner, M. L.: On the theory of rods. Part II. Developments by direct approach. Proc. R. Soc. London Ser. A 337, 485-507 (1974).
14. Antman, S. S.: The theory of rods. In: Handbuch der Physik, Bd. VI a/2. Berlin Göttingen Heidelberg: Springer 1972.
15. Benjamin, T. B., Bona, J. L., Mahony, J. J.: Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. London Ser. A 227, 47-78 (1972).
16. Ciarlet, P. G.: Mathematical elasticity. Berlin Heidelberg New York: Springer 1987.
17. Truesdell, C., Noll, W.: Non-linear field theories of mechanics. In: Handbuch der Physik, Bd. III/3. Berlin Heidelberg New York: Springer 1965.
18. Ogden, R. W.: Non-linear elastic deformations. New York Chichester Toronto: Ellis Horwood 1984.
19. Jeffrey, A., Kawahara, T.: Asymptotic methods in nonlinear wave theory. London: Pitman 1982.
20. Drazin, P. G., Johnson, R. S.: Solitons: an introduction. Cambridge New York: Cambridge University Press 1989.
21. Olver, P. J.: Euler operators and conservation laws of the BBM equation. Math. Proc. Camb. Phil. Soc. 85, 143-160 (1979).
22. Peregrine, D. H.: Calculations of the development of an undular bore. J. Fluid Mech. 25, 321-330 (1966).
23. Eilbeck, J. C., McGuire, G. R.: Numerical study of the regularized long wave equation. Part I. Numerical methods. J. Comput. Phys. 19, 43-57 (1975).
24. Bona, J. L., Pritchard, W. G., Scott, L. R.: Numerical schemes for a model for nonlinear dispersive waves. J. Comput. Phys. 60, 167-186 (1985).
25. Guo, B.-Y., Manoranjah, V. S.: A spectral method for solving the RLW equation. IMA J. Numer. Anal. 5, 307-318 (1985).