Abstract
When a localized disturbance is applied suddenly into a medium, it will propagate to other parts of this medium. The local excitation is not detected at other positions of the medium instantaneously, as some time would be necessary for the disturbance to propagate from its source to other parts of the medium. This simple fact constitutes a general basis for the interesting subject of “wave propagation.” Well-cited examples of wave propagation in different media include, for instance, the transmission of sound in air, the propagation of a seismic disturbance in the earth, the transmission of radio waves, among others. In the particular case, when the suddenly applied disturbance is mechanical, e.g., an impact force, the resulting waves in the medium are due to mechanical stress effects and, thus, these waves are referred to as “mechanical stress waves” or simply “stress waves.” Our attention in this text is restricted to the study of the propagation of stress waves in engineering materials.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Achenbach, J. D. (1973) Wave Propagation in Elastic Solids, Elsevier, New York.
Chou, P. C. (1968) Introduction to wave propagation in composite materials, in Composite Materials Workshop, edited by S. W. Tsai, J. C. Halpin and N. J. Pagano, Technomic, Stamford, Ct, pp. 193216.
Dally, J. W., Durelli, A. J. and Riley, W. F. (1960) Photoelastic study of stress wave propagation in large plates, Proc. Soc. Exp. Stress Analysis 17, 33–50.
Dally, J. W. and Riley, W.F. (1965) Experimental Stress Analysis, McGraw-Hill, NewYork.
Dally, J. W. and Riley, W. F. (1967) Initial studies in three-dimensional dynamic photoelasticity, J. Appl. Mech. 34, 405–10.
Dally, J. W. (1968) A dynamic photoelastic study of a doubly loaded half-plane, Develop. Mech. 4, 649–64.
Davis, J. L. (1988) Wave Propagation in Solids and Fluids, Springer-Verlag, New York.
Donnell, L. H. (1930) Trans. ASME 52 (1), 153–67.
Dove, RC. and Adams, P. H. (1964) Experimental Stress Analysis and Motion Measurement, Charles Merril Books, Columbus, Ohio.
Eringen, A. C. and Suhubi, E. S. (1975) Elastodynamics, Academic Press, New York.
Ewing, M., Jardestsky, W. S., and Press, F. (1957) Elastic Waves in Layered Media, McGraw-Hill, New York
Graff, K.F. (1975) Wave Motion in Elastic Solids, Dover Publications, New York.
Hetenyi, M., Ed. (1950) Handbook of Experimental Stress Analysis, John Wiley and Sons, New York. Hillier, K. W. (1960) A review of the progress in the measurement of dynamic elastic properties, int. Symp.on Stress Wave Propagation in Materials, Ed. N. Davids, nter-science Publishers, London, pp. 183–98.
Keast, D. N. (1967) Measurements in Mechanical Dynamics, McGraw-Hill, New York.
Kinslow, R. (1970) High-Velocity Impact Phenomena, Academic Press, New York.
Kolsky, H. (1963) Stress Waves in Solids, Dover Publications, New York.
Lamb, H. (1904) On the propagation of tremors over the surface of an elastic solid, Phil. Trans. R. Soc. A203, 1–42.
Lamb, H. (1917) On waves in an elastic plate, Proc. Roy. Soc. A93, 114–28.
Magrab, E. B. and Blomquist, D.S. (1971) The Measurement of Time-Varying Phenomena, WileyInterscience, New York.
McCarthy, M. F. and Hayes, M.A. (1989) Elastic Wave Propagation, Elsevier, London.
Miklowitz, J. (1978) Elastic Waves and Waveguides, North Holland, New York.
Miklowitz, J. and Achenbach, J. D. (1977) Modern Problems in Elastic Wave Propagation, Elsevier, New York.
Morse, P. and Feshbach, H. (1953) Methods of Theoretical Physics, Vols. I and II, McGraw-Hill, New York. Pindera, J. T. (1986) New research perspectives opened by isodyne and strain gradient photoelasticity, in
Proceedings of the International Symposium on Photoelasticity, Tokyo,pp. 193–202.
Rayleigh, J. W. S. (1887) On waves propagated along the plane surface of an elastic solid, Proc. Lond. Math. Soc. 17, 4–11.
Skalak, R. (1957) Longitudinal impact of a semi-infinite circular elastic bar, J. Appl. Mech. 34, 59–64. Tolosty, I. (1973) Wave propagation, McGraw-Hill, New York.
Viktorov, I.A. (1967) Rayleigh and Lamb Waves: Physical Theory and Applications, Plenum Press, New York.
Worely, W. J. (Ed.) (1962) Experimental Techniques in Shock and Vibration, ASME, New York.
Zukas, J. A., Nicolas, T., Swift, M. F., Greszczuk, L. B. and Curran, D. R. (1982) Impact Dynamics, Elsevier, New York.
Further Reading
Abbott, B. W. and Cornish, R. H. (1965) A Stress wave technique for determining the tensile strength of brittle materials, Exp. Mech. 22, 148–53.
Bailey, P. and Chen, P. J. (1971) On the local and global behaviour of acceleration waves, Arch. Ration. Mech. Analysis 41, 121. Addendum: Asymptotic Behaviour, ibid 44, 212 (1972).
Baker, W. E. and Dove, R.C. (1962) Measurements of internal strains in a bar subjected to longitudinal impact, Exp. Mech. 19, 307–11.
Barker, L. M. and Hollenbach, R E. (1964) System for measuring the dynamic properties of materials, Rev. Sci. Inst. 35(6), 742–46.
Barker, L. M. and Hollenbach, R E. (1965) Interfermometer technique for measuring the dynamic mechanical properties of materials, Rev. Sci. Inst. 36, 1617–20.
Barker, L.M. (1968) The fine structure of compressive and release wave shapes in aluminium measured by the velocity interferometer technique, in Behaviour ofDense Media Under High Dynamic Pressures, Gordon and Breach, pp. 483–505.
Barton, C.S., Volterra, E.G. and Citron, S.J. (1958) On elastic impacts of spheres on long rods, Proc. 3r d U.S. Natn. Cong. Appl. Mech., pp. 89–94.
Becker, E.C.H. and Carl, H. (1962) Transient-loading technique for mechanical impedence measurement, in Experimental Techniques in Shock and Vibration, Ed. W.J. Worley, ASME, New York, pp. 1–10.
Chree, C. (1889) The equations of an isotropic elastic solid in polar and cylindrical coordinates, Their solutions and applications, Trans. Camb. Phil. Soc. Math. Phys. Sci. 6, 115–17.
Chu, B. T. (1965) Response of various material media to high velocity loadings. I. Linear elastic and viscoelastic materials, J. Mech. Phys. Solids 13, 165–87.
Daily, J. W. and Lewis, D. (1968) A Photoelastic analysis of propagation of Rayleigh waves past a step change in elevation, Bull. Seism. Soc. Am. 58, 539–63.
Dally, J. W. and Thau, S. A. (1967) Observations of stress wave propagation in a half-plane with boundary loading, Int. J. Solids Struct. 3, 293–307.
Davies, R. M. (1948) A Critical study of the Hopkinson Pressure Bar, Phil. Trans. R. Soc. A240 375–457. Dohrenwend, C. O., Drucker, D. C. and Moore, P. (1944) Transverse impact transients, Exp. Stress Analysis 1,1–10.
Doyle, J. F. (1989) Wave Propagation in Structures, Springer-Verlag, New York.
Dunwoody, J. (1966) Longitudinal wave propagation in a rate dependent material, Int. J. of Engineering Sci. 4, 277–87.
Evans, J. F., Hadley, C. F., Eisler, J. D. and Silverman, D. (1954) A three-dimensional seismic wave model with both electrical and visual observation of waves, Geophysics 19, 120–36.
Karnes, C.H. (1968) The plate impact configuration for determining mechanical properties of materialsat high strain rates, in Mechanical Behavior of Materials under Dynamic Loads, U.S. Lindholm, (Ed.), Springer-Verlag, New York, pp. 270–93.
Kolsky, H. and Prager, W. (1964) Stress Waves in Anelastic Solids, Springer-Verlag, New York. Leipholz, H. (1974) Theory of Elasticity, Noordhoff, The Netherlands.
Lindholm, U. S. (Ed.) (1968) Mechanical Behavior of Materials under Dynamic Loading, Springer-Verlag, New York.
Malvern, L. E. (1969) Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, New Jersey. Medick, M. A. (1961) On classical plate theory and wave propagation, J. Appl. Mech. 28, 223–8.
Fisher, H. C. (1954) Stress pulse in bar with neck or swell, Appl. Scient. Res. A4, 317–28. Frederick, J. R. (1965) Ultrasonic Engineering, John Wiley and Sons, New York.
Goldsmith, W., Polivka, M. and Yang, T. (1966) Dynamic behaviour of concrete, Exp. Mech. 23, 65–79. Goodier, J. N., Jahsman, W. E. and Ripperger, E. A. (1959) An experimental surface-wave method for recording force-time curves in elastic impacts, J. Appl. Mech. 26, 3–7.
Gopasamy, K. and Aggarwala, B. D. (1972) Propagation of disturbances from randomly moving sources, ZAMM52, 31–35.
Gorsky, W. S. (1936) On the transitions in the Cu Au Alloy III. On the influence of strain on the equilibrium in the ordered lattice of Cu Al, Phys. Zeit Sowjet 6, 77–81.
Green, W. A. (1960) Dispersion relations for elastic waves in bars, in Progress in Solid Mechanics, Vol. I
edited by I. N. Sneddon and R. Hill, Chapter 5, North Holland Publishing Co., Amsterdam. Green, W. A. (1964) The growth of plane discontinuities propagating into a homogeneously deformed elastic material, Arch. Ration. Mech. Anal. 16, 79–89.
Harris, C. M. and Crede, E. (1961) Shock and Vibration Handbook, Vols. I, II and III, McGraw-Hill, New York.
Hill, R. (1962) Acceleration waves in solids, J. Mech. Phys. Solids 10, 1–16.
Hsieh, D.Y. and Kolsky, H. (1958) An experimental study of pulse propagation in elastic cylinders, Proc. Phys. Soc. 71, 608–12.
Hudson, G. E. (1943) Dispersion of elastic waves in solid circular cylinders, Phys. Rev. 63, 46–51.
Janke, E. and Emde, F. (1945) Tables of Functions, Dover Publications, New York.
Jeffrey, A. (1978) Nonlinear wave propagation, ZAMM 58, T38 - T56.
Jeffrey, A. and Taniuti, T. (1964) Nonlinear Wave Propagation, Academic Press, New York.
Kolsky, H. (1949) An investigation of the mechanical properties of materials at very high rates of loading, Proc. Phys. Soc. B62, 676–700.
Kolsky, H. (1954) The Propagation of longitudinal elastic waves along cylindrical bars, Phil. Mag. 45, 71226.
Kolsky, H. (1960) Experimental wave-propagation in solids, in Structural Mechanics, edited by J.N. Goodier and N. Hoff, Pergamon Press, Oxford, pp. 233–62.
Kolsky, H. (1965) Experimental studies in stress wave propagation, Proc. Vth U.S. Natn. Congr. Appl. Mech., pp. 21–36.
Kolsky, H. and Prager, W., Eds. (1964) Stress waves in anelastic solids, Jt7TAM Symposium, Brown University, Providence, R.I., April 3–5, 1963, Springer-Verlag, Berlin.
Langhaar, H.L. (1962) Energy Methods in Applied Mechanics, John Wiley and Sons, New York.
Lifshitz, J. M. and Kolsky, H. (1965) The propagation of spherical divergent stress pulses in linear viscoelastic solids, J. Mech. Phys. Solids 13, 361–76.
Lindholm, U. S. (1964) Some experiments with the Split Hopkinson Pressure Bar, J. Mech. Phys. Solids 12, 317–35.
Lindsay, R. B. (1960) Mechanical Radiation,McGraw-Hill, New York.
Love, A. E. H. (1944) A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York. Malvern, L. E. (1951) Plastic wave propagation in a bar of material exhibiting a strain rate effect, Quart. Appl. Math. 8, 405–11.
Mason, W. P. and McSkimin, H. J. (1947) Attenuation and scattering of high frequency sound waves in metals and glasses, J. Acoust. Soc. Amer. 19, 464–73.
Medick, M. A. (1961) On classical plate theory and wave propagation, J. Appl. Mech. 28, 223–28.
Meyer, M. L. (1964) On spherical near fields and far fields in elastic and viscoelastic solids, J. Mech. Phys. Solids 12, 77–111.
Orowan, E. (1934) Ztir Kristall Plastizität.III. Über den mechanismus des gleitvorganges, Zeits f. Phys. 89, 634–59.
Polanyl, M. (1934) Ober eine Art gitterstönmg, die einen kristall plastisch machen Könnte, Zeds! Phys. 89, 660–64.
Prescott, J. (1942) Elastic waves and vibrations of thin rods, Phil. Mag. 33, 703–54.
Press, F. and Oliver, J. (1955) Model study of air-coupled surface waves, J. Acoust. Soc. Am. 27, 45–46. Rayleigh, J. W. S. (1894) Theory of Sound, Dover Publications Inc., New York.
Reinhardt, H. W. and Dally, J. W. (1970) Some characteristics of Rayleigh wave interaction with surface flaws, Mater. Eval. 28, 213–20.
Riley, W. F. and Dally, J. W. (1966) A photoelastic analysis of stress wave propagation in a layered model, Geophysics 31, 881–9.
Ripperger, E. A. (1953) The propagation of pulses in cylindrical bars. An experimental study, Proc. 1“ Midwest Conf. Solid Mech., pp. 29–39.
Rubin, J. R (1954) Propagation of longitudinal deformation waves in a prestressed rod of material exhibiting a strain-rate effect, J. Appl. Phys. 25, 528–36.
Snoek, J. E. (1941) Effect of small quantities of carbon and nitrogen on the elastic and plastic properties of iron, Physica 8, 711–33.
Sokolnikoff, I. S. (1956) Mathematical Theory of Elasticity, 2“ d edition, McGraw-Hill, New York. Stoneley, R. (1924) Elastic waves at the surface of separation of two Solids, Proc. R. Soc. A106, 416–28. Tatel, H. E. (1954) Note on the nature of a seismogram II., J. Geophys. Res. 59, 289–94.
Thau, S. A. and Dally, J. W. (1969) Subsurface characteristics of the Rayleigh wave, Int. J. Eng. Sci. 7, 3752.
Thomas, T. Y. (1957) The growth and decay of sonic discontinuities in ideal gases, J. Math. Mech. 6, 455–69.
Thomas, T. Y. (1961) Plastic Flow and Fracture in Solids, Academic Press, New York.
Timoshenko, S. P. (1921) On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Phil. Mag. Ser. 6 (41), 744–46.
Timoshenko, S. P. (1928) Vibration Problems in Engineering, Van Nostrand, New Jersey.
Truesdell, C. and Toupin, R. A. (1960) The classical field theories, Handbuch der Physik 11111, Ed. S.Flügge, Springer, Berlin.
Varley, E. and Cumberbatch, E. (1965) Nonlinear theory of wavefront propagation, J. Ins. Math. andAppl. 1, June 1965, 101–12.
Volterra, E. (1955) A one-dimensional theory of wave propagation in elastic rods based on the ‘method of internal constraints’, Ing. Arch. 23, 410.
Whitham, G. B. (1974) Linear and Nonlinear Waves, J. Wiley Sons, New York.
Wood, D., (1963) in Response of Metals to High Velocity Deformation, P.G. Shewmon and O.F. Zackay, (Eds.), Elsevier, New York.
Zemanek, J. (Jr.) and Rudnick, I. (1961) Attenuation and dispersion of elastic waves in a cylindrical bar, J. Acoust. Soc. Am. 33, 1283–8.
Zener, C. (1948) Elasticity and Anelasticity of Metals, Univ. Press, Chicago.
Zukas, J.A. (1982) Stress waves in solids, in Impact Dynamics, Eds. J.A. Zukas et al., John Wiley Sons, New York, Chapter 1, pp. 1–27.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Haddad, Y.M. (2000). Elastic Wave Propagation. In: Mechanical Behaviour of Engineering Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2231-5_4
Download citation
DOI: https://doi.org/10.1007/978-94-017-2231-5_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5473-9
Online ISBN: 978-94-017-2231-5
eBook Packages: Springer Book Archive