Abstract
Current status of research on decay of dynamic end effects in elastic structures aiming at formulation of a dynamic analogue to Saint-Venant’s principle (DSVP) are critically reviewed. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. Nearly 200 references are examined in context of DSVP, starting with early ideas by Boley. Special attention is placed on available experimental findings on end effects and decay rate in dynamically excited structures. Current perception of possible versions of DSVP is classified into several categories, one of which, namely that of dynamic equivalence, is compatible with much of known experimental data and has been tacitly applied at various engineering situations. That observation, along with a perspective view on evolution of the traditional SVP, provides inspiring ground for renewed interest in both practical and theoretical aspects of DSVP formulation.
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Bibliography
Abramson H.N., Plass H.J., Ripperger E.A., 1958, Stress waves in rods and beams, Advances in Applied Mechanics 5 111–194
Achenbach J.D., 1973, Wave propagation in elastic solids, North-Holland, Amsterdam
Ames K.A., Payne L.E., Schaefer P.W., 1993, Spatial decay estimates in time-dependent stokes flow, SIAM J. Math. Anal. 24(6) 1395–1413
Aron M., Chirita S., 1997, Decay and continuous dependence estimates for harmonic vibrations of micropolar elastic cylinder, Arch. Mech. 49 665–675
Aslanyan A., Parnovski L, Vassiliev D., 2000, Complex resonances in acoustic waveguides, Q. J. Mech. Appl. Math. 53(3) 429–447
Awrejcewicz J., Pyryev Y., 2003, The Saint-Venant’s principle and an impact load acting on an elastic half-space, J. Sound Vib. 264 245–251
Babenkova E., 2004, A dynamic analog of the Saint–Venant principle and boundary conditions for vibrating plates, Ph.D. dissertation, University of Manchester
Babenkova E., Kaplunov J., 2003, The two-term interior asymptotic expansion in the case of low-frequency longitudinal vibrations of an elongated elastic rectangle, A.B. Movchan (ed.), IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Book Series - Solid Mechanics and its Applications, Vol. 113, Kluwer, 137–145
Babenkova E., Kaplunov J., 2004, Low-frequency decay conditions for a semi-infinite elastic strip, Proceedings of the Royal Society of London A 460 2153–2169
Babenkova E., Kaplunov J., 2005, Radiation conditions for a semiinfinite elastic strip, Proceedings of the Royal Society of London A 461 1163–1179
Babenkova E., Kaplunov J., Ustinov Y.A., 2005, Saint-Venant’s principle in the case of the low-frequency oscillations of a half-strip, PMM Journal of Applied Mathematics and Mechanics 69 405–416
Baker W.E., Dove R.C., 1962, Measurement of internal strains in a bar subjected to longitudinal impact, Experimental Mechanics 2 307–311
Barton C.S., Volterra E.G., 1959, On the elastic impact of short cylindrical rods on long cylindrical rods, Proc. 4th Midwestern Conference on Solid Mechanics, Austin, Texas, 318–330
Bell J.F., 1960, The initial development of an elastic strain pulse propagating in a semi-infinite bar, Johns Hopkins University, November 1960, 1–31
Bell J.F., 1973, The experimental foundations of solid mechanics, in Mechanics of solids, Vol. VIa/1, in HNBK der Phys., S. Flugge ed., Springer-Verlag, New-York
Benvenuto E., 1997, Engineering, Mathematics and Natural Philosophy in the Work of Barre de Saint Venant, Plenary lecture in 3rd EUROMECH Solid Mechanics Conference, KTH, Royal Institute of Technology, Stockholm, Sweden, August 18–22
Berdichevsky V., Foster D.J., 2003, On Saint-Venant’s principle in the dynamics of elastic beams, Int. J. Solids Struct., 40, 3293–3310
Bertholf L.D., 1967, Numerical solution for two-dimensional elastic wave propagation in finite bars, J. Appl. Mech. (Trans. ASME), 34, 725–734
Bertholf L.D., Karnes C.H., 1969, Axisymmetric elastic-plastic wave propagation in 6061-T6 Aluminum bars of finite length, J. Appl. Mech. (Trans. ASME), 36, 533–541
Bhattacharyya, S.K., Vendhan, C.P., 1991, Wave propagation in semiinfinite plane anisotropic thin circular shells, J. Sound Vib., 149, 71–82
Binkowski J.F., 1975, Analysis of a dynamic Saint-Venant region in a semi-infinite circular cylinder, Ph.D. Thesis, Michigan State Univ., East Lansing
Boley B.A., 1955, Application of Saint-Venant’s principle in dynamical problems, J. Appl. Mech. (Trans. ASME), 22, 204–206
Boley B.A., 1958, Some observations on Saint-Venant’s principle, in Proc. of the third U.S. national congress of Applied Mechanics, ASME, 259–64
Boley B.A., 1960a, On a dynamical Saint Venant principle, J. Appl. Mech. (Trans. ASME), 27, 74–78
Boley B.A., 1960b, Upper bounds and Saint Venant’s principle in transient heat conduction, Quart. Appl. Math., 18, 205–207
Boley B.A., 2006, Private communication
Borg S.F., 1961, On Saint-Venant’s principle under dynamic conditions; Discussion, Experimental Mechanics, 1(9), 119–120
Borrelli A., Patria M.C., 1995, Energy bounds for mixture of two linear elastic solids occupying a semi-infinite cylinder, Acta Mech., 109, 191–206
Borrelli A., Patria M.C., 1996, Energy bounds in dynamical problems for a semi-infinite magnetoelastic beam, ZAMP, 47, 880–893
Borrelli A., Patria M.C., 2000, Spatial decay estimates in dynamical problems for a semi-infinite piezoelectric beam, IMA J. Appl. Math., 64, 73–93
Budaev B.V., Morozov N.F., Narbut M.A., 1994, Torsion of a circular cone with static and dynamic loading, J. Appl. Maths Mechs, 58(6), 1097–1100
Budaev B.V., Morozov N.F., Narbut M.A., 1996, Saint Venant’s principle in statical and dynamical problems for an elastic wedge and a cone, Mathematische Nachrichten, 177, 31–39
Chamberlain P.G., 2004, The effect of evanescent wave modes on scattering and near-trapping, IMA Journal of Applied Mathematics 69, 205–218
Chen W.Q., Lv C.F., Bian Z.G., 2003, Elasticity solution for free vibration of laminated beams, Composite Structures 62, 75–82
Cherepanov G.P., 1979, Mechanics of Brittle Fracture, McGRAW-Hill International Book Company
Cherukuri H. P., Shawki T. G., 1996, A finite-difference scheme for elastic wave propagation in a circular disk, J. Acoust. Soc. Am. 100(4), 2139–2155
Chirita S., 1995, On the spatial decay estimates in certain timedependent problems of continuum mechanics, Arch. Mech., 47, 755–771
Chirita S., 1997, On Saint-Venant’s principle in dynamic linear viscoelasticity, Q. Appl. Math., LV, 139–149
Chirita S., Ciarletta M., 1999, Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua, Eur. J. Mech. A/Solids, 18, 915–933
Chirita S., Ciarletta M., 2003, Some further growth and decay results in linear thermoelastodynamics, Journal of Thermal Stresses, 26, 889–903
Chirita S., Ciarletta M., 2008, Spatial evolution of harmonic vibrations in linear elasticity, Journal of Mechanics of Materials and Structures, 3(9), 1675–1693
Chirita S., Nappa L., 1999, Effects of Saint-Venant type and uniqueness and continuous dependence results for incremental elastodynamics, Int. J. Non-Linear. Mech., 34, 159–167
Chirita S., Quintanilla R., 1996a, Spatial decay estimates of Saint-Venant type in generalized thermoelasticity, Int. J. Engng. Sci., 34, 299–311
Chirita S., Quintanilla R., 1996b, On Saint-Venant’s principle in linear elastodynamics, J. Elasticity, 42, 201–215
Ciarletta M., 2002, On the spatial behaviour of the transient and steady-state solutions in thin plates with transverse shear deformation, International Journal of Engineering Science 40, 485–498
Ciarletta M., Chirita S., 1999, Thermodynamic restrictions, free energies and Saint-Venant’s principle in the linear theory of viscoelastic materials with voids, Int. J. Solids Srtuct. 36, 1949–1964
Ciarletta M., Iovane G., Passarella F., 2002, On the spatial and temporal behavior in dynamics of porous elastic mixtures, Ukrainian Mathematical Journal 54(4) 647–670
Choi I., Horgan C.O., 1977, Saint-Venant principle and end effects in anisotropic elasticity, J. Appl. Mech. (Trans. ASME), 44, 424–430
Choi I., Horgan C.O., 1978, Saint-Venant end effects for deformation of sandwich strips, Int. J. Solids. Struct., 14, 187–95
Clausing D.P., 1959, Impact of cylinders of different areas. In Proc. 4th Midwestern Conference on Solid Mechanics, Austin, Texas, 349–357
Cunningham D.M., Goldsmith W., 1959, Short-time impulse produced by longitudinal impact, Proc. Soc. Exp. Stress Anal. XVI (2), 153–162
D’Apice C., 2005, Convexity considerations and spatial behavior for the harmonic vibrations in thermoelastic plates, J. Math. Anal. Appl., 312(1) 44–60
Dally J.E., Rilet W.F., Durelli A.J., 1959, A photoelastic approach to transient stress problems employing low-modulus materials, J. Appl. Mech. (Trans. ASME), 26, 613–620
Davies R.M., 1948, A critical study of the Hopkinson pressure bar. Philosophical Transactions of the Royal Society of London A, 240, 375–457
Davies R.M., 1956, Stress waves in solids, Brit. J. Appl. Phys., 7, 203–209
De Cicco S., Nappa L., 1999, On Saint-Venant’s principle for micropolar viscoelastic bodies, Int. Journal of Engineering Science 37, 883–893
DeVault G.P., Curtis C.W., 1962, Elastic cylinder with free lateral surface and mixed time-dependent end conditions. J. Acoust. Soc. Am., 34(4), 421–432
Diligent O., Lowe M.J.S., Le Clezio E., Castaings M., Hosten B., 2003, Prediction and measurement of nonpropagating Lamb modes at the free end of a plate when the fundamental antisymmetric mode A[0] is incident, J. Acoust. Soc. Am., 113, 3032–3042
Dong S.B., Goetschel D.B., 1982, Edge effects in laminated composite plates, J. Appl. Mech. (Trans. ASME), 49, 129–135
Dong S.B., Huang K.H., 1985, Edge vibrations in laminated composite plates, J. Appl. Mech. (Trans. ASME), 52, 433–438
Donnell L.H., 1962, About Saint-Venant’s principle, J. Appl. Mech. (Trans. ASME), 29, 753
Durban D., Stronge W.S., 1988a, Diffusion of self-equilibrating end loads in plane strain plasticity, J. Mech. Phys. Solids, 36, 459–476
Durban D., Stronge W.J., 1988b, Diffusion of self-equilibrating end loads in elastic solids, J. Appl. Mech. (Trans. ASME), 55, 492–495
Duva J.M. and Simmonds J.G., 1991, The usefulness of elementary theory of the linear vibrations of layered, orthotropic elastic beams and corrections due to two-dimensional end effects, J. Appl. Mech. (Trans. ASME), 58, 175–180
Duva J.M. and Simmonds J.G., 1992, The influence of two-dimensional end effects on the natural frequencies of cantilevered beams weak in shear, J. Appl. Mech. (Trans. ASME), 59, 230–232
Ericksen J.L., 1979, On St.-Venant’s problem for thin-walled tubes, Arch. Rational Mech. Anal. 70, 7–12
Evans D.V., 1992, Trapped acoustic modes, IMA Journal of Applied Mathematics, 49, 45–60
Evans D.V., Porter R., 2008, Flexural waves on a pinned semi-infinite thin elastic plate, Wave Motion 45, 745–757
Field J.E., Proud W.G., Walley S.M., Goldrein H.T., 2001, Review of experimental techniques for high rate deformation and shock studies, In: New Experimental Methods in Material Dynamics and Impact. Eds. W.K. Nowacki and J.R. Klepaczko, pp. 109-177, Institute of Fundamental Technological Research, Warsaw, Poland
Flavin J.N., Knops R.J., 1987, Some spatial decay estimates in continuum dynamics, J. Elasticity, 17, 249–64
Flavin J.N., Knops R.J., Payne L.E., 1990, Energy bounds in dynamical problems for a semi-infinite elastic beam, in Elasticity. Mathematical Methods and Applications. The Ian N. Sneddon 70th Birthday volume. Eason G and Ogden R.W. Eds., Ellis Horwood, 101–112
Flynn P.D., Feder J.C., Gilbert J.T., Roll A.A., 1962. Stress waves due to explosive and mechanical loading of low modulus photoelastic materials, Frankford Arsenal Report No. A 62–4
Flynn P.D., Frocht M.M., 1961. On Saint-Venant’s principle under dynamic conditions. Experimental Mechanics 1, 16–20
Folk R., Fox G., Shook C.A., Curtis C.W., 1958, Elastic strain produced by sudden application of pressure to one end of a Cylindrical bar. I. Theory, J. Acoust. Soc. Am., 30(6), 552–58
Follansbee P.S., 1985, The Hopkinson bar, Mechanical Testing, Vol. 8, ASM Handbook, American Society for Metals, 198–203
Foster D.J., 2003, On Saint-Venant’s principle in the dynamics of elastic beams, Ph.D dissertation, Wayne State University
Foster D.J., Berdichevsky V., 2000, Probabilistic characterization of dynamical Saint-Venant effects, 8th ASCE Specialty Conferebceon on Probabilistic Mechanics and Structural Reliability, PMC 2000-134
Foster D.J., Berdichevsky V., 2004, On Saint-Venant’s principle in the two-dimensional flexural vibrations of elastic beams, Int. J. Solids Struct., 41, 2551–2562
Fox G., Curtis C.W., 1958, Elastic strain produced by sudden application of pressure to one end of a cylindrical bar. II. Experimental observations. The Journal of the Acoustical Society of America 30(6), 559–563
Frocht M.M., 1948, Photoelasticity, Vol. II, John Wiley and Sons, Inc. London
Gales C., 2002, On the spatial behavior in the theory of swelling porous elastic soils, International Journal of Solids and Structures 39, 4151–4165
Gales C., 2003, Spatial decay estimates for solutions describing harmonic vibrations in the theory of swelling porous elastic soils, Acta Mechanica 161, 151–163
Gilat A., Schmidt T.E., Walker A.L., 2009. Full field strain measurement in compression and tensile split Hopkinson bar experiments. Experimental Mechanics 49, 291–306
Goetschel D.B., Hu T.H., 1985, Quantification of Saint-Venant’s principle for a general prismatic member, Comp. Struct., 21, 869–874
Gomilko A.M., Gorodetskaya N.S., Meleshko V.V., 1995, A dynamic Saint-Venant principle for an elastic semi-infinite strip, Journal of a Mathematical Sciences, 74(4), 1150–1153
Gorham R.A., Ripperger E.A., 1959, A comparison of surface strains to average strains in longitudinal elastic wave propagation. In: Proc. 4th Midwestern Conference on Solid Mechanics, Austin, Texas, pp. 382–395
Graff K.F., 1975, Wave motion in elastic solids, Clarendon Pr., Oxford
Grandin H.T. Jr., 1972, Investigation of a dynamic Saint-Venant region in a semi-infinite strip, Ph.D. Thesis, Michigan State University
Grandin H.T., Little R.W., 1974, Dynamic Saint-Venant’s region in a semi-infinite elastic strip, J. Elasticity, 4, 131–46
Gray III G.T., 2000, Classic Split-Hopkinson pressure bar testing, Mechanical Testing, Vol. 8, ASM Handbook, American Society for Metals, pp. 462–476
Gurtin M.E., 1972, The linear theory of elasticity, Mechanics of solids II, Vol. VIa/2, in HNBK der Phys., S. Flugge ed., Springer-Verlag, New-York
Habberstad J.L., Hoge K.G., Foster J.E., 1972, An experimental and numerical study of elastic strain waves on the center line of a 6061-T6 Aluminum bar. J. Appl. Mech. (Trans. ASME), 39, 367–371
Hertelendy P., 1968, An approximate theory governing symmetric motions of elastic rods of rectangular or square cross section, J. Appl. Mech. (Trans. ASME) 35, 333–341
Hettche L.R., Au T., 1967, Edge impact of an elastic-plastic semiinfinite plate, Experimental Mechanics, 7, 302–308
Hoff N.J., 1945, The applicability of Saint-Venant’s principle to airplane structures, Journal of the Aeronautical Sciences, 12, 455–460
Horgan C.O., 1989, Recent developments concerning Saint-Venant’s principle: An update, Appl. Mech. Rev., 42, 295–303
Horgan C.O., 1996, Recent developments concerning Saint-Venant’s principle: A second update, Appl. Mech. Rev., 48, 101–111
Horgan C.O., Knowles J.K., 1983, Recent developments concerning Saint-Venant’s principle, Adv. Appl. Mech., 23, 179–269
Horgan C.O., Simmonds J.G., 1994, Saint-Venant’s end effects in composite structures, Comp. Engng., 4, 279–286
Horgan C.O., Quintanilla R., 2001, Spatial decay of transient end effects in functionally graded heat conducting materials, Q. Appl. Math., LIX, 529–542
Horgan C.O., Wheeler L.T., 1975, A spatial decay estimate for pseudoparabolic equations. Letters in Applied and Engineering Sciences 3, 237–243
Hornikx M., Forssen J., 2009, Noise abatement schemes for shielded canyons, Applied Acoustics 70, 267–283
Horvay G., 1953, The end problem of rectangular strips, J. Appl. Mech. (Trans. ASME), 20, 87–94
Horvay G., 1957, Saint-Venant’s principle: a biharmonic eigenvalue problem, J. Appl. Mech. (Trans. ASME), 24, 381–386
Huang C.G., 1989, Several rigorous counterexamples about Saint-Venant’s principle, Computers Math. Appl. 18(8), 729–738
Huang K.H., Dong S. B., 1984, Propagating waves and edge vibrations in anisotropic composite cylinders, J. Sound and Vibration, 96, 363–379
Iesan D., Scalia A., 1997, On Saint-Venant’s principle for microstretch elastic bodies, Int. J. Engng Sci. 35(14), 1277–1290
Ignaczak J., 1974, A dynamic version of Saint-Venant’s principle in the linear theory of elasticity, Academie Polonaise des Sciences, Bulletin, Serie des Sciences Techniques 22(6) 483–489, (313–319)
Ignaczak J., 2002, Saint-Venant’s principle for a microperiodic composite thermoelastic semispace: the dynamical refined average theory. J. Therm. Stresses, 25, 1065–1079
Iovane G., Passarella F., 2004, Saint-Venant’s principle in dynamic porous thermoelastic media with memory for heat flux, Journal of Thermal Stresses, 27, 983–999
Jones O.E., Norwood F.R., 1967, Axially symmetric cross-sectional strain and stress distributions in suddenly loaded cylindrical elastic bars, J. Appl. Mech. (Trans. ASME), 34, 718–724
Kaplunov J., Fu Y.B., 2012, Analysis of localized edge vibrations of cylindrical shells using the Stroh formalism, Mathematics and Mechanics of Solids, 17(1), 59–66
Kaplunov J., Lawrie J.B., 2012, Edge waves and resonance on elastic structures: An overview, Mathematics and Mechanics of Solids, 17(1), 4–16
Kaplunov J.D., Sorokin S.V., 1995, A simple example of a trapped mode in an unbounded waveguide, The Journal of the Acoustical Society of America 97(6), 3898–3899
Karal F., Alterman Z., 1971, Far-field dependence on the end conditions in a semi-infinite elastic rod of circular cross-section, J. Sound and Vibration, 17, 5–11
Karp, B., 1996. On Saint-Venant’s principle in Elastostatics and Elastodynamics, D.Sc. Thesis, Technion, Haifa. (Full text in Hebrew, Abstract in English)
Karp B., 2004, End effects in prestrained plates under compression, Journal of Applied Mechanics 71, 816–824
Karp B., 2005, Dynamic version of Saint-Venant’s principle - Historical account and recent results. Nonlinear Analysis, 63, e931–e942
Karp B., 2008, Generation of symmetric Lamb waves by non-uniform excitations, Journal of Sound and Vibration, 312 (1-2), 195–209
Karp B., 2009, Dynamic equivalence, self-equilibrated excitation and Saint-Venant’s principle for an elastic strip. Int. J. Solids Struct. 46, 3068–3077
Karp B., 2011, Study of dynamic end effects in an elastic strip with sliding boundary conditions, Int. J. Solids Struct. 48, 126–136
Karp B. and Durban D., 1997, Towards a dynamic version of Saint-Venant’s principle, In Modern practice in stress and vibration analysis, Gilchrist M.D. Ed., A.A. Balkema, ISBN 90 5410 896 7. 3rd international conference, Dublin, Ireland, 3-5 September 1997
Karp, B., Durban, D., 2002. Influence of Boundary Conditions on Decay Rates in a Prestrained Plate. J. Appl. Mech. - Trans of ASME 69, 515–520
Karp B., Durban D., 2005, Evanescent and Propagating Waves in Prestretched Hyperelastic Plates, Int. J. Solids Struct., 42, 1613–1647
Karp B., Durban D., 2011, Saint-Venant’s Principle in dynamics of structures - A Review. Applied Mechanics Reviews. 64, 020801:1-20
Karp B., Rittel D., Durban D., 2008, Health monitoring of joints using dynamic end effects, Journal of Sound and Vibration, 312 (1-2), 257–272
Karp B., Dorogoy A., Wang Z., 2009, Non-uniform impact excitation of a cylindrical bar, Journal of Sound and Vibration 323, 757–771
Karunasena W., Liew K.M., Kitipornchai S., 1995, Reflection of plate waves at the fixed edge of a composite plate, J. Acoust. Soc. Am., 98, 644–651
Kathnelson A.N., 1997, An asymptotic edge effect in thin rectangular vibrating plates, Journal of Sound and Vibration 207(2), 271–275
Kaul R.K., McCoy J.J., 1964, Propagation of axisymmetric waves in a circular semiinfinite elastic rod. Acoust. Soc. of Am. 26(4), 653–660
Kawata K., Hashimoto S., 1967. On some differences between dynamic- and static-stress distributions. Experimental Mechanics 7, 91–96
Kawata K., Hashimoto S., Masuda Y., Hayasi R., 2007. High-speed photoelastic analysis of axially-impacted finite column. Experimental Mechanics 47, 465–471
Kennedy L.W., Jones O.E., 1969, Longitudinal wave propagation in a circular bar loaded suddenly by a radially distributed end stress, J. Appl. Mech. (Trans. ASME), 36, 470–8
Kim J.S., Soedel W., 1988. On the response of three-dimensional elastic bodies to disturbed dynamic pressures, Part I: Half-space, J. Sound and Vibrations, 126, 279–295
Kim Y.Y., Steele C.R., 1989. End effects and time-harmonic longitudinal wave propagation in semi-infinite solid cylinder. J. Appl. Mech. (Trans. ASME), 56, 334–346
Knops R.J., 1989, Spatial decay estimates in the vibrating anisotropic elastic beam, in Waves and stability in continuous media, ed. Rionero S., Series on Advances in Mathematics for Applied Sciences - Vol. 4, World Scientific, pp. 192–203
Knops R.J., Payne L.E., 2005, Alternative spatial growth and decay for constrained motion in an elastic cylinder. Mathematics and Mechanics of Solids 10, 281–310
Knops R.J., Rionero S., Payne L.E., 1990, Saint-Venant’s principle on unbounded regions. Proceedings of the Royal Society of Edinburgh 115A, 319–336
Knowles J.K., 1966, On Saint-Venant’s principle in linear theory of elasticity, Arch. Ratio. Mech. Anal., 21, 1–22
Kroll R.J., Tatro C.A., 1964, Stress-wave propagation in axially symmetric test specimen, Experimental Mechanics, 4(5), 129–134
Kundu T., Mathur R.P., Desai C.S., 1991, Three dimensional soilstructure interaction analysis: Deformable structures in multilayered soil mass. Engineering Computations 8, 153–180
Kuznetsov G.N., Stepanov A. N., 2007, The Field of an equivalent multipole composite radiator in a waveguide, Acoustical Physics, 53(3), 326–334
Levine H.A., Quintanilla R., 1989, Some remarks on Saint-Venant’s principle. Math. Methods in the Applied Sciences 11, 71–77
Love A.E.H., 1944, A Treatise on the mathematical theory of elasticity, Dover Pub. New York
Ma G.W., He L., Karp B., Li Q.M., Investigation of Dynamic Saint-Venant’s Principle in a Cylindrical Waveguide Part I: Experimental and numerical approaches. In preperation
Maremonti P. Russo R., 1989, A domain of influence theorem in finite elasticity, in Waves and stability in continuous media, ed. Rionero S., Series on Advances in Mathematics for Applied Sciences - Vol. 4, World Scientific. pp. 237–242
Markenscoff X., 1994, Some remarks on the wedge paradox and Saint-Venant’s principle, J. Appl. Mech. (Trans. ASME), 61, 519–523
McCoy J.J., 1964, Propagation of Torsional Waves in a Circular Elastic Rod, ZAMP, 15, 456–465
McIver M., Linton C.M., Zhang J., 2002, The branch structure of embedded trapped modes in two-dimensional waveguides, Q. J. Mech Appl. Math. 55(2), 313–326
Mei C., 2005, Effect of material coupling on wave vibration of composite Euler-Bernoulli beam structures, Journal of Sound and Vibration 288, 177–193
Meitzler A.H., 1955, Propagation of elastic pulses near the stressed end of a cylindrical bar, Dissertation, Lehigh University
Meng H., Li Q.M., 2001, Modification of SHPB set-up based on wave separation technique and dynamic Saint-Venant’s principle, Second International Conference on Experimental Mechanics, F. S. Chau, and C. Quan Eds., Proceedings of the SPIE - The international Society for Optical Engineering, 4317, 85–93
Meng H., Li Q.M., 2003, An SHPB set-up with reduced time-shift and pressure bar length, Int. J. Impact Eng., 28, 677–696
Meyer M.L., 1964. On spherical near fields and far fields in elastic and visco-elastic solids. Journal of Mechanics and Physics of Solids 12, 77–111
Miklowitz J., 1957, The propagation of compressional waves in a dispersive elastic rod; Part I - Results from the theory, J. Appl. Mech., 24, 231–239
Miklowitz J., 1978, The Theory of Elastic Waves and Waveguides, North-Holand Pub. Comp., Amsterdam
Miklowitz J., Nisewanger C.R., 1957, The propagation of compressional waves in a dispersive elastic rod; Part II - Experimental results and comparison with theory, J.Appl.Mech., 24 (1957), 240–244
Miles A.W., 1976, Shock-front loading method for studies in dynamic photoelasticity, Exp.Mech., 11, 349–355
Mindlin R.D., 1960. Waves and vibrations in isotropic, elastic plates. In: Structural Mechanics, Ed. Goodier J.N. and Hoff N.J., Pergamon, New York
Miyao S., Tsuchida E., Matsumoto H., Nakahara I., 1975, A semiinfinite body subjected to an impulsive torque on a hemispherical pit of a free surface. Bulletin of the JSME, 18 (123), 959–964
Morozov N.F., Narbut M.A., 1995, Antiplane deformation of an elastic wedge under action concentrated near the corner point, J Appl Maths Mechs, 59(2), 307–309
Munoz Rivera J.E., Lapa E.C., Barreto R., 1996, Decay rates for viscoelastic plates with memory, Journal of Elasticity, 44, 61–87
Murray J.D., 1970, Perturbation effects on the decay of discontinuous solutions of nonlinear first order wave equations, SIAM J. Appl. Math., 19(2), 273–298
Naghdi P.M., 1960, On Saint Venant’s principle: elastic shells and plates, J. Appl. Mech. (Trans. ASME), 27, 417–422
Nappa L., 1998, Spatial decay estimates for the evolution equations of linear thermoelasticity without energy dissipation, J. Therm. Stresses, 21, 581–592
Nerubailo B. V., Zotova N. V., Orlov R. Kh., Sukhorukova S. V., 2005, The applicability of Saint-Venant’s principle to monocoque structures, Journal of Engineering Physics and Thermophysics, 78(3), 586–589
Novozhilov V.V., Slepian L.I., 1965, On Saint-Venant’s principle in the dynamics of beams, PMM, 29, 261–81
Oleinik O.A., Iosif’yan G.A., 1976, An analogue of Saint-Venant’s principle and the uniquiness of solutions of boundary value problems for parabolic equations in unbounded domains. Russian Math. Surveys 31(6), 153–178
Oleinik O.A., Iosif’yan G.A., 1978, The Saint-Venant principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains. Siberian Mathematical Journal 19(5), 813–822
Orazov M.B., 1983, The Saint-Venant principle for equations of steady-state vibrations in an elastic semi-cylinder, Akademiia Nauk Turkmenskoi SSR, Izvestiia, Seriia Fiziko-Tekhnicheskikh, Khimicheskikh i Geologicheskikh Nauk , 5, 3-8. (In Russian)
Pagneux V., 2006, Revisiting the edge resonance for Lamb waves in a semi-infinite plate, J. Acoust. Soc. Am., 120(2), 649–656
Pagneux V., 2012, Complex resonance and localized vibrations at the edge of a semi-infinite elastic cylinder, Mathematics and Mechanics of Solids, 17(1), 17–26
Payne L.E., Song J.C., 1997, Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Continuum Mechanics and Thermodynamics, 9, 175–190
Pichugin A.V., Rogerson G.A., 2012, Extensional edge waves in prestressed incompressible plates, Mathematics and Mechanics of Solids, 17(1), 27–42
Pope P.H., Field J.E., 1984, Determination of strain in a dynamic compression test, J. Phys. E: Sci. Instrum., 17, 817–820
Quintanilla R., 1999, On the spatial behavior in thermoelasticity without energy dissipation, J. Thermal Stresses, 22, 213–224
Quintanilla R., 2002, On the spatial decay for the dynamical problem of thermo-mictostretch elastic solids, Int. J. Engng. Sci., 40, 109–121
Rauch J., 1976, Qualitative behavior of dissipative wave equations on bounded domains, Arch. Ratio. Mech. Anal. 62, 77–85
Ratassepp M., Klauson A., Chati F., Leon F., Maze G., 2008, Edge resonance in semi-infinite thick pipe: numerical predictions and measurements, J. Acoust. Soc. Am., 124, 875–885
Roseman J.J., 1976, Principle of Saint-Venant in linear and non-linear plane elasticity, Arch. Rational Mech. Anal. 26, 142–162
Rosenhouse G., 2002. Physical aspects in active noise and vibration control. In: Theoretical and Computational Acoustics. Eds. Shang E.-C., Qihu Li, Gao T.F., World Scientific
Ruan X, Danforth S.C., Safari A., Chou T-W., 2000, Saint-Venant end effects in piezoceramic materials, International Journal of Solids and Structures 37, 2625–2637
Sasso M., Newaz G., Amodio D. , 2008, Material characterization at high strain rate by Hopkinson bar tests and finite element optimization, Materials Science and Engineering A 487, 289–300
de Saint-Venant A.-J.-C.B., 1856, Memoire sur la Flexion des Prismes, J. de Mathematiques Pures et Appliquees (Liouville), Deuxieme Serie, Tome I., 89–189
Scalia A., 2001, Spatial and temporal behavior in elastic materials with voids, Acta Mechanica 151, 47–60
Sigillito V.G., 1970, On the spatial decay solutions of parabolic equations, ZAMP, 21, 1078–1081
Sinclair G.B., Miklowitz J., 1975, Two nonmixed symmetric endloadings of an elastic waveguide, Int. J. Solids Struct., 11, 275–294
Stephen N.G., 2008, On state-space elastostatics within a plane stress sectorial domain - the wedge and the curved beam, International Journal of Solids and Structures 45(20), 5437–5463
Sternberg E., 1954, On Saint-Venant’s principle, Quart. of Applied Math. XI(4), 393–402
Theocaris P.S., 1959. The stress distribution in a semi-infinite strip subjected to a concentrated load. ASME Journal of the Applied Mechanics 26, 401–406
Tibullo V., Vaccaro M., 2008, Spatial behaviour for constrained motion of a cylinder made of a strongly elliptic anisotropic material, Journal of Mechanics of Materials and Structures, 3(5), 983–993
Timoshenko S.P., Goodier J.N., 1972, Theory of Elasticity, 3rd Ed., McGraw Hill Int.
Torvik P.J., 1967, Reflection of wave trains in semi-infinite plates, J. Acoust. Soc. Am., 41, 346–53
Toupin R.A, 1965a, Saint-Venant’s principle, Arch. Rational Mech. Anal., 18, 83–96
Toupin R.A, 1965b, Saint-Venant and a matter of principle, Transactions of The New York Academy of Sciences 28(2), 221–232
Tyas A., Watson A.J., 2000, A study of the effect of spatial variation of load in the pressure bar, Meas. Sci. Technol., 11, 1539–1551
von-Mises R., 1945, On Saint-Venant’s principle, Bull. Amer. Math. Soc., 51, 555–562
Waldman S.D., Lee J., 2002, Boundary conditions during bi-axial testing of planar connective tissues. Part 1: Dynamic behavior. Journal of Material Sciences: Material in Medicine, 13, 933–938
Walley S.M., Mason T.A., 2000, Waves in rods, Presented at a website of DYMAT 2000
Wang, C., Kim, J., 1997. The dynamic analysis of a thin beam impacting against a stop of general three-dimensional geometry, J. Sound and Vibrations, 203, 237–249
Wijeyewickrema A.C., Ushida Y., Kayestha P., 2008, Wave propagation in a prestressed compressible elastic layer with constrained boundaries, Journal of Mechanics of Materials and Structures, 3(10), 1963–1976
Yeung Wey Kong Y.C.T., Parsons B., Cole B.N., 1974, The dispersive behaviour of a Hopkinson pressure bar in material property test. pp. 33–47. In: Mechanical Properties at High Rates of Strain, Proceedings of the Conference on Mechanical Properties of Metals at High Rates of Strain, Oxford, 2–4 April. The Institute of Physics, London and Bristol
Yilmaz Y., 2007, Spatial estimates for a system of coupled parabolichyperbolic equations under nonlinear boundary condition. Journal of the Franklin Institute 344, 489–494
Zakharov D.D., 2012, Surface and edge waves in solids with nematic coating, Mathematics and Mechanics of Solids, 17(1), 67–80
Zemanek J. Jr., 1971, Beam behavior within the nearfield of a vibrating, J. Acoust. Soc. Am., 49, 181–191
Zemanek J. Jr., 1972, An experimental and theoretical investigation of elastic wave propagation in a cylinder, J. Acoust. Soc. Am., 51, 265–283
Ziv M., 2002, Source signature and elastic waves in half-space under a sustainable line-concentrated impulsive normal force, Int. J. Numer. Anal. Meth. Geomech., 26, 373–406
Ziv M., 2003, Source signature and elastic waves in half-space under a momentary shear line impulse, Int. J. Numer. Anal. Meth. Geomech., 27, 233–258
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Karp, B., Durban, D. (2013). Elastodynamic End Effects in Structural Mechanics. In: Craster, R.V., Kaplunov, J. (eds) Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism. CISM International Centre for Mechanical Sciences, vol 547. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1619-7_4
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