Applications and improvements of the summed progressing wave formalism
Author:
D. Gamby
Journal:
Quart. Appl. Math. 38 (1980), 159-168
MSC:
Primary 73D25; Secondary 45K05
DOI:
https://doi.org/10.1090/qam/580876
MathSciNet review:
580876
Full-text PDF Free Access
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Additional Information
- Robert M. Lewis, Asymptotic theory of wave-propagation, Arch. Rational Mech. Anal. 20 (1965), 191–250. MR 184551, DOI https://doi.org/10.1007/BF00276444
W. W. Recker, A discontinuity expansion to plane problems in elastodynamics, J. Sound Vibr. 23, 41–53 (1972)
W. W. Recker, Series solution to problems in elastodynamics, Proc. Am. Soc. Civ. Eng. 97 EM 4, 1257–1275 (1971)
W. H. Wittrick, On elastic wave propagation in helical springs. Int. J. Mech. Sci. 8, 25–47 (1966)
A. Blanchard, Etude theorique des éecoulements non permanents en conduite viscoélastique: application au phénoméne du coup de bélier, Thése de Doctorat de Spécialité, Université Claude Bernard, Lyon (13 Octobre 1978)
G. Turchetti and F. Mainardi, Wave-front expansions and Padé approximants for transient wave in linear dispersive media, in Padé approximant method and its applications to mechanics, edited by H. Cabannes, Springer-Verlag, Berlin, 1976, pp. 189–208
- George M. C. Fisher and Morton E. Gurtin, Wave propagation in the linear theory of viscoelasticity, Quart. Appl. Math. 23 (1965), 257–263. MR 191196, DOI https://doi.org/10.1090/S0033-569X-1965-0191196-X
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Interscience, New York, 1962
K. Yosida, Functional analysis, 2d edition, Springer-Verlag, Berlin, 1968
- Andrew Majda and Stanley Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28 (1975), no. 5, 607–675. MR 410107, DOI https://doi.org/10.1002/cpa.3160280504
D. Gamby and R. Lamy, Propagation d’ondes dispersives dans une poutre longue de section rectangulaire dont une extrémité est soumise á un choc, J. Mécanique Appliquée, forthcoming
- D. Gamby and R. Lamy, Numerical implementation of the “summed progressing wave” formalism. Computation of short-time and long-time transients, Internat. J. Numer. Methods Engrg. 15 (1980), no. 6, 843–854. MR 580358, DOI https://doi.org/10.1002/nme.1620150605
- Michael Taylor, Pseudo differential operators, Lecture Notes in Mathematics, Vol. 416, Springer-Verlag, Berlin-New York, 1974. MR 0442523
R. M. Lewis, Asymptotic theory of wave propagation, Arch. Rat. Mech. Anal. 20, 191–250 (1965)
W. W. Recker, A discontinuity expansion to plane problems in elastodynamics, J. Sound Vibr. 23, 41–53 (1972)
W. W. Recker, Series solution to problems in elastodynamics, Proc. Am. Soc. Civ. Eng. 97 EM 4, 1257–1275 (1971)
W. H. Wittrick, On elastic wave propagation in helical springs. Int. J. Mech. Sci. 8, 25–47 (1966)
A. Blanchard, Etude theorique des éecoulements non permanents en conduite viscoélastique: application au phénoméne du coup de bélier, Thése de Doctorat de Spécialité, Université Claude Bernard, Lyon (13 Octobre 1978)
G. Turchetti and F. Mainardi, Wave-front expansions and Padé approximants for transient wave in linear dispersive media, in Padé approximant method and its applications to mechanics, edited by H. Cabannes, Springer-Verlag, Berlin, 1976, pp. 189–208
G. M. C. Fisher, and M. E. Gurtin, Wave propagation in the linear theory of viscoelasticity, Quart. Appl. Math. 23, 257–263 (1965)
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Interscience, New York, 1962
K. Yosida, Functional analysis, 2d edition, Springer-Verlag, Berlin, 1968
A. Majda and S. Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28, 607–675 (1975)
D. Gamby and R. Lamy, Propagation d’ondes dispersives dans une poutre longue de section rectangulaire dont une extrémité est soumise á un choc, J. Mécanique Appliquée, forthcoming
D. Gamby and R. Lamy, Numerical implementation of the summed progressing wave formalism: computation of short-time and long-time transients. Int. J. Numer. Methods in Eng., forthcoming
M. Taylor, Lectures on pseudo-differential operators, Springer-Verlag, New York, 1974
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Article copyright:
© Copyright 1980
American Mathematical Society
