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Volumn 9, Issue 1, 2004, Pages 61-79

Asymptotically approximate model equations for weakly nonlinear long waves in compressible elastic rods and their comparisons with other simplified model equations

Author keywords

Elastic rods; Model equations; Nonlinear waves

Indexed keywords

ACOUSTIC DISPERSION; ACOUSTIC WAVE PROPAGATION; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; ELASTICITY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; THREE DIMENSIONAL;

EID: 1242286490     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/1081286503035199     Document Type: Article
Times cited : (57)

References (21)
  • 1
    • 0022045748 scopus 로고
    • Nonlinear waves in rods: Results for incompressible elastic materials
    • Wright, T.: Nonlinear waves in rods: results for incompressible elastic materials. Stud. Appl. Math., 72, 149-160 (1985).
    • (1985) Stud. Appl. Math. , vol.72 , pp. 149-160
    • Wright, T.1
  • 2
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • Dai, H.-H.: Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech., 127, 193-207 (1998).
    • (1998) Acta Mech. , vol.127 , pp. 193-207
    • Dai, H.-H.1
  • 3
    • 0000171588 scopus 로고    scopus 로고
    • Splitary shock waves and other travelling waves in a general compressible hyperelastic rod
    • Dai, H.-H., Huo, Y.: Splitary shock waves and other travelling waves in a general compressible hyperelastic rod. Proc. R. Soc. Lond. A, 456, 331-363 (2000).
    • (2000) Proc. R. Soc. Lond. A , vol.456 , pp. 331-363
    • Dai, H.-H.1    Huo, Y.2
  • 4
    • 0036132610 scopus 로고    scopus 로고
    • Solitary waves in an inhomogeneous rod composed of a general hyperelastic material
    • Dai, H.-H., Huo, Y.: Solitary waves in an inhomogeneous rod composed of a general hyperelastic material. Wave Motion, 35, 55-69 (2002).
    • (2002) Wave Motion , vol.35 , pp. 55-69
    • Dai, H.-H.1    Huo, Y.2
  • 5
    • 0003224511 scopus 로고
    • Nonlinear waves in rods
    • ed. D. E. Carlson & R. T. Shields, Martinus Nijhoff, The Hague
    • Wright, T.: Nonlinear waves in rods, in Proc. IUTAM Symp. on Finite Elasticity, ed. D. E. Carlson & R. T. Shields, Martinus Nijhoff, The Hague, 1982.
    • (1982) Proc. IUTAM Symp. on Finite Elasticity
    • Wright, T.1
  • 7
    • 0038551976 scopus 로고    scopus 로고
    • Nonlinear traveling waves in a rod composed of a modified Mooney-Rivlin material I: Bifurcation of equilibra and non-singular case
    • Dai, H.-H., Zhao, X.-H.: Nonlinear Traveling waves in a rod composed of a modified Mooney-Rivlin material I: bifurcation of equilibra and non-singular case. Proc. R. Soc. Lond. A, 455, 3845-3874 (1999).
    • (1999) Proc. R. Soc. Lond. A , vol.455 , pp. 3845-3874
    • Dai, H.-H.1    Zhao, X.-H.2
  • 8
    • 0038551977 scopus 로고    scopus 로고
    • Nonlinear dispersive waves in a circular rod composed of a Mooney-Rivlin material
    • ed. Y. Fu & R. W. Ogden; Cambridge University Press, Cambridge
    • Dai, H.-H.: Nonlinear dispersive waves in a circular rod composed of a Mooney-Rivlin material, in Nonlinear Elasticity: Theory and Applications, ed. Y. Fu & R. W. Ogden, pp. 392-432 Cambridge University Press, Cambridge.
    • Nonlinear Elasticity: Theory and Applications , pp. 392-432
    • Dai, H.-H.1
  • 9
    • 0021496906 scopus 로고
    • Solitary waves on nonlinear rods
    • Soerensen, M. P. et al.: Solitary waves on nonlinear rods. Int. J. Acoust. Soc. Am., 78, 871-879 (1984).
    • (1984) Int. J. Acoust. Soc. Am. , vol.78 , pp. 871-879
    • Soerensen, M.P.1
  • 10
    • 0022796834 scopus 로고
    • Solitary-wave interaction in elastic rods
    • Clarkson, P.A. et al.: Solitary-wave interaction in elastic rods. Stud. Appl. Math., 75, 95-122 (1986).
    • (1986) Stud. Appl. Math. , vol.75 , pp. 95-122
    • Clarkson, P.A.1
  • 11
    • 0006848887 scopus 로고
    • Nonlinear strain waves in elastic waveguides
    • ed. A. Jeffrey & J. Engelbreght, Springer, Vienna
    • Samsonov, A. M.: Nonlinear strain waves in elastic waveguides, in Nonlinear Waves in Solids, ed. A. Jeffrey & J. Engelbreght, Springer, Vienna, 1994.
    • (1994) Nonlinear Waves in Solids
    • Samsonov, A.M.1
  • 12
    • 0000885725 scopus 로고
    • Nonlinear axisymmetric waves in compressible hyperelastic rods: Long finite amplitude waves
    • Cohen, H., Dai, H.-H.: Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves. Acta Mech., 100, 223-239 (1993).
    • (1993) Acta Mech. , vol.100 , pp. 223-239
    • Cohen, H.1    Dai, H.-H.2
  • 13
    • 0642322496 scopus 로고
    • Refinement of the model for the propagation of longitudinal strain waves in a rod with nonlinear elasticity
    • Porubov, A. V., Samsonov, A. M.: Refinement of the model for the propagation of longitudinal strain waves in a rod with nonlinear elasticity. Tech. Phys. Lett., 19, 365-366 (1993).
    • (1993) Tech. Phys. Lett. , vol.19 , pp. 365-366
    • Porubov, A.V.1    Samsonov, A.M.2
  • 14
    • 0001167818 scopus 로고    scopus 로고
    • Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod
    • Samsonov, A. M. et al.: Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod. Phys. Rev. B, 57, 5778-5787 (1998).
    • (1998) Phys. Rev. B , vol.57 , pp. 5778-5787
    • Samsonov, A.M.1
  • 15
    • 0001618340 scopus 로고    scopus 로고
    • Strain solitary waves in an elastic rod embedded in another elastic externa medium with sliding
    • Porubov, A. V. et al.: Strain solitary waves in an elastic rod embedded in another elastic externa medium with sliding. Phys. Rev. E, 58, 3854-3864 (1998).
    • (1998) Phys. Rev. E , vol.58 , pp. 3854-3864
    • Porubov, A.V.1
  • 16
    • 0036376046 scopus 로고    scopus 로고
    • Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods
    • Dai, H.-H., Huo, Y.: Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods. Acta Mech., 157, 97-112 (2002).
    • (2002) Acta Mech. , vol.157 , pp. 97-112
    • Dai, H.-H.1    Huo, Y.2
  • 17
    • 0001487729 scopus 로고
    • Finite deformation of an elastic solid
    • Murnaghan, F. D.: Finite deformation of an elastic solid. Am. J. Math., 59, 235-260 (1937).
    • (1937) Am. J. Math. , vol.59 , pp. 235-260
    • Murnaghan, F.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.