Uniform asymptotic analysis for waves in an incompressible elastic rod I. Disturbances superimposed on an initially stress-free state

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 59, Issue 3, 1997, Pages 245-260

  Dai, H H ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ELASTICITY; NUMERICAL METHODS; STRAIN; WAVE TRANSMISSION;

ASYMPTOTIC EXPANSION METHOD; INCOMPRESSIBLE ELASTIC RODS;

ELASTIC WAVES;

EID: 0031377633     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/59.3.245     Document Type: Article

References (20)

1. ACHENBACH, J. D., 1973. Wave Propagation in Elastic Solids. New York: Elsevier.
2. COHEN, H., & DAI, H.-H., 1993. Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves. Acta Mech. 100, 223-239.
3. COHEN, H., DAI, H.-H., & MUNCASTER, R. G., 1996. Travelling waves in Mooney-Rivlin elastic rods. Arch. Rational Mech. Anal. submitted.
4. COLEMAN, B. D., & NEWMAN, D. C., 1990. On waves in slender elastic rods. Arch. Rational Mech. Anal. 109, 39-61.
5. DAI, H.-H., 1996. Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech. to appear.
6. DAI, H.-H., & NAYLOR, D., 1992 On an asymptotic expansion of Fourier integrals. Proc. R. Soc. A 436, 109-120.
7. DAI, H.-H., & WONG, R. 1994. A uniform asymptotic expansion for the shear-wave front in a layer. Wave Motion 19, 293-308.
8. FELSEN, L. B., & MARCUVITZ, N., 1972. Radiation and Scattering of Waves. Englewood Cliffs: Prentice-Hall.
9. FREZEN, C. L. & WONG, R., 1988. Uniform asymptotic expansions of Laguerre polynomials. SIAM J. Math. Anal. 19, 1232-1248.
10. GRAFF, K. F., 1991. Wave Motion in Elastic Solids. New York: Dover.
11. MARTIN, P. A., & WICKHAM, G. R., (ed.) 1992. Wave Asymptotics. Cambridge: University Press.
12. MIKLOWITZ, J. 1978. The Theory of Elastic Waves and Waveguides. New York: North-Holland.
13. MINDLIN, R. D., & HERRMANN, G., 1950. A one-dimensional theory of compressional waves in an elastic rod. Proc. 1st. U.S. Natn. Congr. Appl. Mech., pp. 187-191.
14. TEMME, N. M., 1975 Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function. Math. Comp. 29, 1109-1114.
15. THURSTON, R. N., 1978. Elastic waves in rods and clad rods. J. Acoust. Soc. Am. 64, 1-37.
16. THURSTON, R. N., 1992. Elastic waves in rods and optical fibers. J. Sound Vib. 159, 441-467.
17. URSELL, F., 1984. Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Camb. Phil. Soc. 95, 367-380.
18. WONG, R., 1989. Asymptotic Approximations of Integrals. New York: Academic Press.
19. WRIGHT, T., 1982. Nonlinear waves in rods. In: D. E. Carlson and R. T. Shield (ed.) Proceedings of the IUTAM Symposium on Finite Elasticity. The Hague: Martinus Nijhoff.
20. WRIGHT, T., 1984. Nonlinear waves in rods: results for incompressible elastic materials. Stud. Appl. Math. 72, 149-160.