Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T02:16:33.250Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 October 2010

John G. Harris
John G. Harris
Affiliation:
University of Illinois, Urbana-Champaign
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Elastic Waves at High Frequencies
Techniques for Radiation and Diffraction of Elastic and Surface Waves
 , pp. 157 - 162
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahams, I. D. (2000). The application of Padé approximants to Wiener–Hopf factorization. IMA J. Appl. Math., 65: 257–281.CrossRefGoogle Scholar
Achenbach, J. D. (1973). Wave Propagation in Elastic Solids. North-Holland, Amsterdam.Google Scholar
Achenbach, J. D. (2003). Reciprocity in Elastodynamics. Cambridge University Press, New York.Google Scholar
Achenbach, J. D., Gautesen, A. K. and McMaken, H. (1982). Ray Methods for Waves in Elastic Solids. Pitman, Boston.Google Scholar
Aki, K. and Richards, P. G. (2002). Quantitative Seismology. University Science Books, Sausalito, CA, second edition.Google Scholar
Atkin, R. J. and Fox, N. (1980). An Introduction to the Theory of Elasticity, volume 1. Longman, London, second edition.Google Scholar
Auld, B. A. (1979). General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients. Wave Motion, 1: 3–10.CrossRefGoogle Scholar
Auld, B. A. (1990a). Acoustic Fields and Waves in Solids, volume 1. Krieger, Malabar, FL, second edition.Google Scholar
Auld, B. A. (1990b). Acoustic Fields and Waves in Solids, volume 2. Krieger, Malabar, FL, second edition.Google Scholar
Babic, V. M. and Buldyrev, V. S. (1991). Short-Wavelength Diffraction Theory. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Baker, B. B. and Copson, E. T. (1987). The Mathematical Theory of Huygens' Principle. Chelsea, New York, third edition.Google Scholar
Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, U.K.Google Scholar
Bell, J. C. (1979). Stresses from arbitrary loads on a circular crack. Int. J. Fracture, 15: 85–104.CrossRefGoogle Scholar
Besserer, H. and Malischewsky, P. G. (2004). Mode series expansions at vertical boundaries in elastic waveguides. Wave Motion, 39: 41–59.CrossRefGoogle Scholar
Biryukov, S. V., Gulyaev, Yu. V., Krylov, V. V. and Plesky, V. P. (1995). Surface Acoustic Waves in Inhomogeneous Media. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Bleistein, N. and Handelsman, R. A. (1975). Asymptotic Expansions of Integrals. Holt, Rinehart and Winston, New York.Google Scholar
Block, G., Harris, J. G. and Hayat, T. (2000). Measurement models for ultrasonic nondestructive evaluation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 47: 604–611.CrossRefGoogle ScholarPubMed
Born, M. and Wolf, E. (1999). Principles of Optics. Cambridge University Press, Cambridge, U.K., seventh (expanded) edition.CrossRefGoogle Scholar
Borovikov, V. A. (1994). Uniform Stationary Phase Method. The Institution of Electrical Engineers, London.Google Scholar
Borovikov, V. A. and Kinber, B. Ye. (1994). Geometrical Theory of Diffraction. The Institution of Electrical Engineers, London.CrossRefGoogle Scholar
Boström, A. (2003). Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation. Appl. Mech. Rev., 56: 383–405.CrossRefGoogle Scholar
Boström, A. and Olsson, P. (1987). Scattering of elastic waves by non-planar cracks. Wave Motion, 9: 61–76.CrossRefGoogle Scholar
Bouwkamp, C. J. (1946). A contribution to the theory of acoustic radiation. Philips Res. Rep., 1: 251–277.Google Scholar
Bouwkamp, C. J. (1954). Diffraction theory. Rep. Prog. Phys., 17: 35–100.CrossRefGoogle Scholar
Brekhovskikh, L. M. and Godin, O. A. (1999). Acoustics of Layered Media, volume 2. Springer-Verlag, Berlin, second edition.CrossRefGoogle Scholar
Brekhovskikh, L. M. and Goncharov, V. (1985). Mechanics of Continua and Wave Dynamics. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Briggs, A. (1992). Acoustic Microscopy. Oxford University Press, New York.Google Scholar
Chako, N. (1965). Asymptotic expansions of double and multiple integrals occurring in diffraction theory. J. Inst. Math. Appl., 1: 372–422.CrossRefGoogle Scholar
Clemmow, P. C. (1966). The Plane Wave Spectrum Representation of Electromagnetic Waves. Pergamon, Oxford.Google Scholar
Collin, R. E. (1991). Field Theory of Guided Waves. IEEE Press, New York, second edition.Google Scholar
Comninou, M. and Dundurs, J. (1977). Reflexion and refraction of elastic waves in the presence of separation. Proc. R. Soc. A, 356: 509–528.CrossRefGoogle Scholar
Copson, E. T. (1971). Asymptotic Expansions. Cambridge University Press, Cambridge, U.K.Google Scholar
Davis, A. M. J. and Nagem, R. J. (2002). Acoustic diffraction by a half-plane in a viscous fluid medium. J. Acoust. Soc. Am., 112: 1288–1296.CrossRefGoogle Scholar
Davis, A. M. J. and Nagem, R. J. (2006). Curle's equation and acoustic scattering by a sphere. J. Acoust. Soc. Am., 119: 2018–2026.CrossRefGoogle Scholar
de Bruijn, N. G. (1970). Asymptotic Methods in Analysis. North-Holland, Amsterdam.Google Scholar
Doetsch, G. (1974). Introduction to the Theory and Application of the Laplace Transformation. Springer-Verlag, New York. Translated from the German by W. Nader.CrossRefGoogle Scholar
Eringen, A. C. and Şuhubi, E. S. (1975). Elastodynamics, volume 2. Academic Press, New York.Google Scholar
L. B., Felsen, and G. A., Deschamps editors. (1974). Special Issue on Rays and Beams, volume 62 of Proc. IEEE.Google Scholar
Felsen, L. B. and Marcuvitz, N. (1994). Radiation and Scattering of Waves. IEEE and Oxford University Press, New York.CrossRefGoogle Scholar
Folguera, A. and Harris, J. G. (1998). Propagation in a slowly varying waveguide. In J. A., DeSanto, editor, Mathematical and Numerical Aspects of Wave Propagation, pages 434–436. SIAM, Philadelphia.Google Scholar
Friedman, B. (1956). Principles and Techniques of Applied Mathematics. Wiley, New York.Google Scholar
Glushkov, Y. V. and Glushkova, N. V. (1996). Diffraction of elastic waves by three-dimensional cracks of arbitrary shape in a plane. J. Appl. Math. Mech. (PMM), 60: 277–283.CrossRefGoogle Scholar
Gniadek, K. and Petykiewicz, J. (1971). Applications of optical methods in diffraction theory of elastic waves. In E., Wolf, editor, Progress in Optics, volume 9, pages 281–310. North Holland, Amsterdam.Google Scholar
Graff, K. F. (1991). Wave Motion in Elastic Solids. Dover, New York (reprint; first published in 1975).Google Scholar
Greenspan, M. (1979). Piston radiator: some extensions of the theory. J. Acoust. Soc. Am., 65: 608–621.CrossRefGoogle Scholar
Gridin, D., Craster, R. V. and Adamou, A. T. I. (2005). Trapped modes in curved elastic plates. Proc. R. Soc. A, 461: 1181–1197.CrossRefGoogle Scholar
Hansen, R. C., editor. (1981). Geometrical Theory of Diffraction, IEEE Press Selected Reprint Series. IEEE Press, New York.Google Scholar
Harris, J. G. (1987). Edge diffraction of a compressional beam. J. Acoust. Soc. Am., 82: 635–646.CrossRefGoogle Scholar
Harris, J. G. (1997). Modeling scanning acoustic imaging of defects at solid interfaces. In G., Chavent, G., Papanicolaou, P., Sacks, and W. W., Symes, editors, Inverse Problems in Wave Propagation, pages 237–257. Springer-Verlag, New York.CrossRefGoogle Scholar
Harris, J. G. (2001). Linear Elastic Waves. Cambridge University Press, New York. A list of errors is maintained at http://www.diffractedwave.com.CrossRefGoogle Scholar
Harris, J. G. and Block, G. (2005). The coupling of elastic, surface-wave modes by a slow, interfacial inclusion. Proc. R. Soc. A, 461: 3765–3783.CrossRefGoogle Scholar
Herrera, I. and Spence, D. A. (1981). Framework of biorthogonal series. Proc. Nat. Acad. Sci. Am., 78: 7240–7244.CrossRefGoogle ScholarPubMed
Hudson, J. A. (1980). The Excitation and Propagation of Elastic Waves. Cambridge University Press, Cambridge, U.K.Google Scholar
James, G. L. (1980). Geometrical Theory of Diffraction for Electromagnetic Waves. Peter Peregrinus, London, second edition.Google Scholar
Jull, E. V. (1981). Aperture Antennas and Diffraction Theory. IEE and Peter Peregrinus, London.CrossRefGoogle Scholar
Kaplunov, J. D., Rogerson, G. A. and Tovstik, P. E. (2005). Localized vibration in elastic structures with slowly varying thickness. Quart. J. Mech. Appl. Math., 58: 645–664.CrossRefGoogle Scholar
Keller, J. B. (1957). Diffraction by an aperture. J. Appl. Phys., 28: 426–444.CrossRefGoogle Scholar
Keller, J. B. (1958). A geometrical theory of diffraction. In L. M., Graves, editor, Calculus of Variations and its Applications, pages 27–52. AMS, Providence, RI.CrossRefGoogle Scholar
King, L. V. (1934). On the acoustic radiation field of the piezoelectric oscillator and the effect of viscosity on the transmission. Can. J. Res., 11: 135–155.CrossRefGoogle Scholar
Kirrmann, P. (1995). On the completeness of Lamb modes. J. Elast., 37: 39–69.CrossRefGoogle Scholar
Krenk, S. (1979). A circular crack under asymmetric loads and some related integral equations. J. Appl. Mech., 46: 821–826.CrossRefGoogle Scholar
Kreyszig, E. (1975). Introduction to Differential Geometry and Riemannian Geometry. University of Toronto Press, Toronto.Google Scholar
Lamb, H. (1906). On Sommerfeld's diffraction problem; and on reflection by a parabolic mirror. Proc. Lond. Math. Soc., 2: 190–203.Google Scholar
Levine, H. (1978). Unidirectional Wave Motions. North-Holland, Amsterdam.Google Scholar
Liang, K. K., Kino, G. S. and Khuri-Yakub, B. T. (1985). Material characterization by the inversion of v(z). IEEE Trans. Sonics Ultrason., SU 32: 213–224.CrossRefGoogle Scholar
Lighthill, M. J. (1965). Group velocity. J. Inst. Math. Appl., 1: 1–28.CrossRefGoogle Scholar
Lighthill, M. J. (1978a). Fourier Analysis and Generalized Functions. Cambridge University Press, Cambridge, U.K.Google Scholar
Lighthill, M. J. (1978b). Waves in Fluids. Cambridge University Press, Cambridge, U.K.Google Scholar
Magnus, W., Oberhettinger, F. and Soni, R. P. (1966). Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, New York, third (enlarged) edition.CrossRefGoogle Scholar
Malischewsky, P. (1987). Surface Waves and Discontinuities. Akademie-Verlag, Berlin.Google Scholar
Martin, P. A. (1996). Mapping flat cracks onto penny-shaped cracks, with applications to somewhat circular tensile cracks. Quart. Appl. Math., 54: 663–675.CrossRefGoogle Scholar
Martin, P. A. (1998). On potential flow past wrinkled discs. Proc. R. Soc. A, 454: 2209–2221.CrossRefGoogle Scholar
Martin, P. A. (2001). On wrinkled penny-shaped cracks. J. Mech. Phys. Solids, 49: 1481–1495.CrossRefGoogle Scholar
Martin, P. A. (2006). Multiple Scattering: Interaction of Time-Harmonic Waves with N Scatterers. Cambridge University Press, Cambridge, U.K.CrossRefGoogle Scholar
Maupin, V. (1988). Surface waves across 2-d structures: a method based on coupled local modes. Geophys. J., 93: 173–185.CrossRefGoogle Scholar
Mikhas'kiv, V. V. and Butrak, I. O. (2006). Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle. Int. Appl. Mech., 42: 61–66.CrossRefGoogle Scholar
Miklowitz, J. (1978). Elastic Waves and Waveguides. North-Holland, Amsterdam.Google Scholar
Miles, J. W. (1971). Scattering by a spherical cap. J. Acoust. Soc. Am., 50: 892–903.CrossRefGoogle Scholar
Morse, P. M. and Ingard, K. U. (1968). Theoretical Acoustics. McGraw-Hill, New York.Google Scholar
Naze Tjøtta, J. and Tjøtta, S. (1980). An analytical model for the nearfield of a baffled piston transducer. J. Acoust. Soc. Am., 68: 334–339.CrossRefGoogle Scholar
Nieto-Vesperinas, M. (1991). Scattering and Diffraction in Physical Optics. Wiley-Interscience, New York.Google Scholar
,NIST, (2008). Digital library of mathematical functions. http://dlmf.nist.gov, accessed August. This is an ongoing project.
Noble, B. (1988). Methods Based on the Wiener-Hopf Technique. Chelsea, New York, second edition.Google Scholar
Norris, A. N. (2008). Faxen relations in solids: a generalized approach to particle motion in elasticity and viscoelasticity. J. Acoust. Soc. Am., 123: 99–108.CrossRefGoogle ScholarPubMed
Oestreicher, H. L. (1951). Field and impedance of an oscillating sphere in a viscoelastic medium with an application to biophysics. J. Acoust. Soc. Am., 23: 707–714.CrossRefGoogle Scholar
Osipov, A. V. and Norris, A. N. (1999). The Malyuzhinets theory for scattering from wedge boundaries: a review. Wave Motion, 29: 313–340.CrossRefGoogle Scholar
Oughstun, K. E. editor (1991). Selected Papers on Scalar Wave Diffraction, volume 51. SPIE, Bellingham, WA.Google Scholar
Phillips, H. B. (1933). Vector Analysis. Wiley, New York.Google Scholar
Pierce, A. D. (1981). Acoustics. McGraw-Hill, New York.Google Scholar
Porter, D. and Stirling, D. S. G. (1990). Integral Equations. Cambridge University Press, Cambridge, U.K.CrossRefGoogle Scholar
Poruchikov, V. B. (1993). Methods of the Classical Theory of Elastodynamics. Springer-Verlag, Berlin. Translated from the Russian by V. A., Khokhryakov and G. P., Groshev.CrossRefGoogle Scholar
Pott, J. and Harris, J. G. (1984). Scattering of an acoustic Gaussian beam from a fluid-solid interface. J. Acoust. Soc. Am., 76: 1829–1838.CrossRefGoogle Scholar
Rebinsky, D. A. (1991). Asymptotic description of the acoustic microscopy of a surface-breaking crack. PhD thesis, University of Illinois, Urbana-Champaign.
Rebinsky, D. A. and Harris, J. G. (1992a). The acoustic signature for a surface-breaking crack produced by a point focus microscope. Proc. R. Soc. A, 438: 47–65.CrossRefGoogle Scholar
Rebinsky, D. A. and Harris, J. G. (1992b). An asymptotic calculation of the acoustic signature of a cracked surface for the line focus scanning acoustic microscope. Proc. R. Soc. A, 436: 251–265.CrossRefGoogle Scholar
Rose, J. L. (1999). Ultrasonic Waves in Solids. Cambridge University Press, Cambridge, U.K.Google Scholar
Schmerr, L. W. Jr. and Song, S. J. (2007). Ultrasonic Nondestructive Evaluation Systems: Models and Measurements. Springer-Verlag, New York.CrossRefGoogle Scholar
Skudrzyk, E. (1971). The Foundations of Acoustics. Springer-Verlag, Vienna.CrossRefGoogle Scholar
Sneddon, I. N. (1951). Fourier Transforms. McGraw-Hill, New York.Google Scholar
Somekh, M. G., Bertoni, H. L., Briggs, G. A. D. and Burton, N. J. (1985). A two-dimensional imaging theory of surface discontinuities with the scanning acoustic microscope. Proc. R. Soc. A, 401: 29–51.CrossRefGoogle Scholar
Sommerfeld, A. (1967). Optics: Lectures on Theoretical Physics, Vol. 4. Academic Press, New York. Translated from the German by O., Laporte and P. A., Moldauer.Google Scholar
Sommerfeld, A. (2004). Mathematical Theory of Diffraction. Birkhäuser, Boston. Translated from the German by R. J., Nagem, M., Zampolli, and G., Sandri. An introduction and translators' notes are provided.CrossRefGoogle Scholar
Spies, M. (1994). Elastic waves in homogeneous and layered transversely isotropic media: plane waves and Gaussian wave packets. A general approach. J. Acoust. Soc. Am., 95: 1748–1760.CrossRefGoogle Scholar
Spies, M. (1999). Transducer field modeling in anisotropic media by superposition of Gaussian base functions. J. Acoust. Soc. Am., 105: 633–638.CrossRefGoogle Scholar
Stamnes, J. J. (1986). Waves in Focal Regions. Adam Hilger, Bristol, U.K.Google Scholar
Tada, T., Fukuyama, E. and Madariaga, R. (2000). Non-hypersingular boundary integral equations for 3-D non-planar crack dynamics. Comput. Mech., 25: 613–626.CrossRefGoogle Scholar
Thomas, D. P. (1963). Diffraction by a spherical cap. Proc. Camb. Phil. Soc., 59: 197–209.CrossRefGoogle Scholar
Thurston, R. N. (1974). Waves in solids. In C., Truesdell, editor, Mechanics of Solids, volume 4, pages 109–308. Springer-Verlag, New York.CrossRefGoogle Scholar
Ti, B. W., O'Brien, W. D. and Harris, J. G. (1997). Measurement of coupled wave propagation in an elastic plate. J. Acoust. Soc. Am., 102: 1528–1531.CrossRefGoogle Scholar
Titchmarsh, E. C. (1939). The Theory of Functions. Clarendon Press, Oxford, second edition.Google Scholar
Titchmarsh, E. C. (1948). Introduction to the Theory of Fourier Integrals. Clarendon Press, Oxford, second edition.Google Scholar
Ufimtsev, P. Ya. (1989). Theory of acoustical edge waves. J. Acoust. Soc. Am., 86: 463–474.CrossRefGoogle Scholar
Visscher, W. M. (1983). Theory of scattering of elastic waves from flat cracks of arbitrary shape. Wave Motion, 5: 15–32.CrossRefGoogle Scholar
Weinstein, L. A. (1969). The Theory of Diffraction and the Factorization Method. The Golem Press, Boulder, CO. Translated from the Russian by P., Beckmann.Google Scholar
Wen, J. J. and Breazeale, M. A. (1988). A diffraction beam field expressed as the superposition of Gaussian beams. J. Acoust. Soc. Am., 83: 1752–1756.CrossRefGoogle Scholar
Zhang, Ch. and Gross, D. (1998). On Wave Propagation in Elastic Solids with Cracks. Computational Mechanics Publications, Southampton, U.K.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • John G. Harris, University of Illinois, Urbana-Champaign
  • Book: Elastic Waves at High Frequencies
  • Online publication: 05 October 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511781094.012
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • John G. Harris, University of Illinois, Urbana-Champaign
  • Book: Elastic Waves at High Frequencies
  • Online publication: 05 October 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511781094.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • John G. Harris, University of Illinois, Urbana-Champaign
  • Book: Elastic Waves at High Frequencies
  • Online publication: 05 October 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511781094.012
Available formats
×