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References

Published online by Cambridge University Press:  10 December 2009

J. D. Achenbach
J. D. Achenbach
Affiliation:
Northwestern University, Illinois
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Reciprocity in Elastodynamics , pp. 247 - 250
Publisher: Cambridge University Press
Print publication year: 2004

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References

Abramowitz, M. and Stegun, E. A., 1964. Handbook of Mathematical Functions. National Bureau of Standards, US Government Printing Office, Washington DC
Achenbach, J. D., 1973. Wave Propagation in Elastic Solids. Elsevier Science, Amsterdam
Achenbach, J. D., 1998. Lamb waves as thickness vibrations superimposed on a membrane carrier wave, J. Acoust. Soc. Am. 103, 2283–2285CrossRefGoogle Scholar
Achenbach, J. D., 2000. Calculation of surface wave motions due to a subsurface point force: an application of elastodynamic reciprocity, J. Acoust. Soc. Am. 107, 1892–1897CrossRefGoogle ScholarPubMed
Achenbach, J. D. and Kitahara, M., 1986. Reflection and transmission of an obliquely incident wave by an array of spherical cavities, J. Acoust. Soc. Am. 80, 1209–1214CrossRefGoogle Scholar
Achenbach, J. D. and Xu, X., 1999a. Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction, J. Acoust. Soc. Am. 106, 83–90CrossRefGoogle Scholar
Achenbach, J. D. and Xu, X., 1999b. Use of elastodynamic reciprocity to analyze point-load generated axisymmetric waves in a plate, Wave Motion 30, 57–68CrossRefGoogle Scholar
Achenbach, J. D., Gautesen, A. K. and McMaken, H., 1982. Ray Methods for Waves in Elastic Solids. Pitman Advanced Publishing Program, Boston, Massachusetts
Achenbach, J. D., Kitahara, M., Mikata, Y. and Sotiropoulos, D. A., 1988. Reflection and transmission of plane waves by a layer of compact inhomogeneities, PAGEOPH 128, 101–118CrossRefGoogle Scholar
Angel, Y. C., and Achenbach, J. D., 1985. Reflection and transmission of elastic waves by a periodic array of cracks, Wave Motion 7, 375–397CrossRefGoogle Scholar
Auld, B. A., 1973. Acoustic Fields and Waves in Solids, Vols. I and II. Reprinted R. E. Krieger Publ. Co. 1990, Malabar, Florida
Auld, B. A., 1979. General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients, Wave Motion 1, 3–10CrossRefGoogle Scholar
Banerjee, P. K. and Kobayashi, S. (eds.), 1992. Advanced Dynamic Analysis by Boundary Element Methods. Elsevier Applied Science, London and New York
Belousov, Y. I. and Rimskii-Korsakov, A. V., 1975. The reciprocity principle in acoustics and its applications to the sound fields of bodies, Sov. Physics – Acoustics 21, 103–109Google Scholar
Beskos, D. E., 1987. Boundary element methods in dynamic analysis, Appl. Mech. Rev. 40, 1–23CrossRefGoogle Scholar
Betti, E., 1872. Teori della elasticita, Il Nuove Ciemento (Series 2), 7–10
Bleistein, N., 1984. Mathematical Methods of Wave Phenomena. Academic Press, Orlando, Florida
Block, G., Harris, J. G. and Hayat, T., 2000. Measurement models for ultrasonic nondestructive evaluation, IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control 47, 604–611CrossRefGoogle ScholarPubMed
Blok, H. and Zeylmans, M. C. S., 1987. Reciprocity and the formulation of inverse profiling problems, Radio Science 22, 1137–1147CrossRefGoogle Scholar
Bonnet, M., 1995. Boundary Integral Equation Methods for Solids and Fluids. John Wiley and Sons, New York
Burridge, R. and Knopoff, L., 1964. Body force equivalents for seismic dislocations, Bull. Seismol. Soc. Am. 54, 1875–1888Google Scholar
Chao, C. C., 1960, Dynamical response of an elastic half-space to tangential surface loadings, J. Appl. Mech. 27, 559–567CrossRefGoogle Scholar
Chimenti, D. E., 1997. Guided waves in plates and their use in materials characterization, Appl. Mech. Rev. 50, 247–284CrossRefGoogle Scholar
Christensen, R. M., 1972. Theory of Viscoelasticity – An Introduction. Academic Press, New York
Cohen, J. K. and Bleistein, N., 1977. An inverse method for determining small variations in propagation speed, SIAM J. Appl. Math. 32, 784–799CrossRefGoogle Scholar
Collin, R. E., 1960. Field Theory of Guided Waves. Reprinted IEEE Press 1991, New York
Courant, R. and Hilbert, D., 1962. Methods of Mathematical Physics Vol. II. Interscience Publishers, New York
Cremer, L., Heckl, M. and Ungar, E. E., 1973. Structure-borne Sound. Springer-Verlag, New York
Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. and Leppington, F. G., 1992. Modern Methods in Analytical Acoustics. Springer-Verlag, London
d'Alembert, J.-le-Rond, 1747. Investigation of the curve formed by a vibrating string (transl.). In Lindsay R. B. (ed.), 1972, Acoustics: Historical and Philosophical Development, Dowden, Hutchinson and Ross, Stroudsbury, Pennsylvania, 119–130
de Hoop, A. T., 1995. Handbook of Radiation and Scattering of Waves. Academic Press, London
DiMaggio, F. L. and Bleich, H. H., 1959. An application of a dynamic reciprocal theorem. J. Appl. Mech. 26, 678–679Google Scholar
Dowling, A. P. and Ffowcs Williams, J. E., 1983. Sound and Sources of Sound. Ellis Horwood, Chichester, UK
Eringen, A. C. and Suhubi, E. S., 1975. Elastodynamics, Vol. II, Linear Theory. Academic Press, New York
Ewing, W. M., Jardetzky, W. S. and Press, F., 1957. Elastic Waves in Layered Media. McGraw-Hill, New York
Fahy, F., 1985. Sound and Structural Vibration. Academic Press, London
Fokkema, J. T. and van den Berg, P. M., 1993. Seismic Applications of Acoustic Reciprocity. Elsevier Science, Amsterdam
Foldy, L. L. and Primakoff, H., 1945. A general theory of passive linear electroacoustic transducers and the electroacoustic reciprocity theorem I, J. Acoust. Soc. Am. 17, 109–120CrossRefGoogle Scholar
Graff, K. F., 1975. Wave Motion in Elastic Solids. Ohio State University Press, Columbus, Ohio
Graffi, D., 1946. Sul teorema di reciprocita nella dinamica dei corpi elastici, Mem. Acad. Sci. Bologna 10, 103–111Google Scholar
Gubernatis, J. E., Domany, E., Krumhansl, J. A., and Huberman, M., 1977. The Born approximation in the theory of the scattering of elastic waves by flaws, J. Appl. Phys. 48, 2804–2811, 2812–2819CrossRefGoogle Scholar
Harris, J. G., 2001. Linear Elastic Waves. Cambridge University Press, Cambridge
Jones, D. S., 1986. Acoustic and Electromagnetic Waves. Clarendon Press, Oxford
Junger, M. C. and Feit, F., 1972. Sound, Structures and Their Interaction. MIT Press, Cambridge, Massachusetts
Keller, J. B. and Karal, F. C. Jr., 1964. Geometrical theory of elastic surface-wave excitation and propagation, J. Acoust. Soc. Am. 36, 32–40CrossRefGoogle Scholar
Kino, G. S., 1978. The application of reciprocity theory to scattering of acoustic waves by flaws, J. Appl. Phys. 49, 3190–3199CrossRefGoogle Scholar
Knopoff, L. and Gangi, A. F., 1959. Seismic reciprocity, Geophysics 24, 681–691CrossRefGoogle Scholar
Kobayashi, S., 1987. Elastodynamics. In Computational Methods in Mechanics (ed. D. E. Beskos), Handbooks in Mechanics and Mathematical Methods Vol. 3, North-Holland, Amsterdam
Kupradze, V. D., 1963. Dynamical Problems in Elasticity. In Progress in Solid Mechanics Vol. 3 (eds. I. N. Sneddon and R. Hill). North-Holland, Amsterdam
Lamb, H., 1888. On reciprocal theorems in dynamics, Proc London Math. Soc. 19, 144–151Google Scholar
Lamb, H., 1904. On the propagation of tremors over the surface of an elastic solid, Phil. Trans. Roy. Soc. LondonA 203, 1–42CrossRefGoogle Scholar
Lamb, H., 1917. Waves in an elastic plate, Proc. Roy. Soc. LondonA 93, 114–128CrossRefGoogle Scholar
Liang, K. K., Kino, G. S. and Khuri-Yakub, B. T., 1985. Material characterization by the inversion of V(z), IEEE Trans. Son. Ultrason. 32, 266–273CrossRefGoogle Scholar
Love, A. E. H., 1892. A Treatise on the Mathematical Theory of Elasticity. Dover, New York, 1944
Love, A. E. H., 1911. Some Problems of Geodynamics. Dover, New York, 1967
Lyamshev, L. M., 1959. A method for solving the problem of sound radiation by thin elastic plates and shells, Sov. Physics – Acoustics 5, 122–123Google Scholar
Lyon, R. H., 1955. Response of an elastic plate to localized driving force, J. Acoust. Soc. Am. 27, 259–265CrossRefGoogle Scholar
Mal, A. K. and Knopoff, L., 1967. Elastic wave velocities in two component systems, J. Inst. Math. Applic. 3, 376–387CrossRefGoogle Scholar
Maxwell, J. C., 1864. On the calculation of the equilibrium and stiffness of frames, Phil. Mag. 27, 294CrossRefGoogle Scholar
McLachlan, N. W., 1961. Bessel Functions for Engineers. Clarendon Press, Oxford
Mikata, Y. and Achenbach, J. D., 1988. Interaction of harmonic waves with a periodic array of inclined cracks, Wave Motion 10, 59–72CrossRefGoogle Scholar
Miklowitz, J., 1962. Transient compressional waves in an infinite elastic plate or elastic layer overlying a rigid half-space, J. Appl. Mech. 29, 53–60CrossRefGoogle Scholar
Miklowitz, J., 1978. The Theory of Elastic Waves and Waveguides. Elsevier Science, Amsterdam
Mindlin, R. D., 1960. Waves and vibrations in isotropic elastic plates. In Structural Mechanics, pp. 199–232 (eds. J. N. Goodier and N. J. Hoff), Pergamon Press, New York
Morse, P. M. and Ingard, K. U., 1968. Theoretical Acoustics. McGraw-Hill, New York
Pao, Y.-H. and Mow, C.-C., 1973. Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane Russak, New York
Payton, R. G., 1964. An application of the dynamic Betti–Rayleigh reciprocal theorem to moving-point loads in elastic media, Q. J. Appl. Math. XXI, 299–313CrossRefGoogle Scholar
Pekeris, C. L., 1955. The seismic surface pulse, Proc. Nat. Acad. Sci. USA 41, 469–480CrossRefGoogle ScholarPubMed
Pierce, A. D., 1981. Acoustics: An Introduction to its Physical Principles and Applications. Acoustic Society of America, Woodbury, New York
Primakoff, H. and Foldy, L. L., 1947. A general theory of passive linear electroacoustic transducers and the electroacoustic reciprocity theorem II, J. Acoust. Soc. Am. 19, 50–120CrossRefGoogle Scholar
Rayleigh, Lord, 1873. Some general theorems relating to vibrations, Proc. London Math. Soc. 4, 357–368Google Scholar
Rayleigh, Lord, 1877. The Theory of Sound, Vol. II. Dover reprint, Dover Publications, New York, 1945
Rayleigh, Lord, 1887. On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4–11Google Scholar
Santosa, F. and Pao, Y.-H., 1989. Transient axially asymmetric response of an elastic plate, Wave Motion 11, 271–296CrossRefGoogle Scholar
Schenk, H. A., 1968. Improved integral formulations for acoustic radiation problems, J. Acoust. Soc. Am. 44, 41–58CrossRefGoogle Scholar
Stokes, G. G., 1849. On the dynamical theory of diffraction, Trans. Cambridge Phil. Soc. 9, 1Google Scholar
Tan, T. H., 1977. Reciprocity relations for scattering of plane elastic waves, J. Acoust. Soc. Am. 61, 928CrossRefGoogle Scholar
Thompson, R. B., 1994. Interpretation of Auld's electromechanical reciprocity relation via a one-dimensional example, Res. Nondestr. Ev. 5, 147–156CrossRefGoogle Scholar
Vasudevan, N. and Mal, A. K., 1985. Response of an elastic plate to localized transient sources, J. Appl. Mech. 52, 356–362CrossRefGoogle Scholar
Helmholtz, H. L., 1860. Theory des Luftschalls in Rohren mit offenen Enden, Borchardt-Crelle's J. 57, 1–70Google Scholar
Helmholtz, H. L., 1886. Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung, Borchardt-Crelle's J. 100, 137–166, 213–222Google Scholar
Weaver, R. L. and Pao, Y.-H., 1982. Axisymmetric elastic waves excited by a point source in a plate, J. Appl. Mech. 49, 821–836CrossRefGoogle Scholar
Weston, V. H., 1984. Multifrequency inverse problem for the reduced wave equation with sparse data, J. Math. Phys. 25, 1382–1390CrossRefGoogle Scholar
Zhang, Ch. and Gross, D., 1998. On Wave Propagation in Elastic Solids with Cracks. Computational Mechanics Publications, Southampton, UK
Zhang, M. and Achenbach, J. D., 1999. Simulation of self-focusing by an array on a crack in an immersed specimen, Ultrasonics 37, 9–18CrossRefGoogle Scholar
Abramowitz, M. and Stegun, E. A., 1964. Handbook of Mathematical Functions. National Bureau of Standards, US Government Printing Office, Washington DC
Achenbach, J. D., 1973. Wave Propagation in Elastic Solids. Elsevier Science, Amsterdam
Achenbach, J. D., 1998. Lamb waves as thickness vibrations superimposed on a membrane carrier wave, J. Acoust. Soc. Am. 103, 2283–2285CrossRefGoogle Scholar
Achenbach, J. D., 2000. Calculation of surface wave motions due to a subsurface point force: an application of elastodynamic reciprocity, J. Acoust. Soc. Am. 107, 1892–1897CrossRefGoogle ScholarPubMed
Achenbach, J. D. and Kitahara, M., 1986. Reflection and transmission of an obliquely incident wave by an array of spherical cavities, J. Acoust. Soc. Am. 80, 1209–1214CrossRefGoogle Scholar
Achenbach, J. D. and Xu, X., 1999a. Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction, J. Acoust. Soc. Am. 106, 83–90CrossRefGoogle Scholar
Achenbach, J. D. and Xu, X., 1999b. Use of elastodynamic reciprocity to analyze point-load generated axisymmetric waves in a plate, Wave Motion 30, 57–68CrossRefGoogle Scholar
Achenbach, J. D., Gautesen, A. K. and McMaken, H., 1982. Ray Methods for Waves in Elastic Solids. Pitman Advanced Publishing Program, Boston, Massachusetts
Achenbach, J. D., Kitahara, M., Mikata, Y. and Sotiropoulos, D. A., 1988. Reflection and transmission of plane waves by a layer of compact inhomogeneities, PAGEOPH 128, 101–118CrossRefGoogle Scholar
Angel, Y. C., and Achenbach, J. D., 1985. Reflection and transmission of elastic waves by a periodic array of cracks, Wave Motion 7, 375–397CrossRefGoogle Scholar
Auld, B. A., 1973. Acoustic Fields and Waves in Solids, Vols. I and II. Reprinted R. E. Krieger Publ. Co. 1990, Malabar, Florida
Auld, B. A., 1979. General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients, Wave Motion 1, 3–10CrossRefGoogle Scholar
Banerjee, P. K. and Kobayashi, S. (eds.), 1992. Advanced Dynamic Analysis by Boundary Element Methods. Elsevier Applied Science, London and New York
Belousov, Y. I. and Rimskii-Korsakov, A. V., 1975. The reciprocity principle in acoustics and its applications to the sound fields of bodies, Sov. Physics – Acoustics 21, 103–109Google Scholar
Beskos, D. E., 1987. Boundary element methods in dynamic analysis, Appl. Mech. Rev. 40, 1–23CrossRefGoogle Scholar
Betti, E., 1872. Teori della elasticita, Il Nuove Ciemento (Series 2), 7–10
Bleistein, N., 1984. Mathematical Methods of Wave Phenomena. Academic Press, Orlando, Florida
Block, G., Harris, J. G. and Hayat, T., 2000. Measurement models for ultrasonic nondestructive evaluation, IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control 47, 604–611CrossRefGoogle ScholarPubMed
Blok, H. and Zeylmans, M. C. S., 1987. Reciprocity and the formulation of inverse profiling problems, Radio Science 22, 1137–1147CrossRefGoogle Scholar
Bonnet, M., 1995. Boundary Integral Equation Methods for Solids and Fluids. John Wiley and Sons, New York
Burridge, R. and Knopoff, L., 1964. Body force equivalents for seismic dislocations, Bull. Seismol. Soc. Am. 54, 1875–1888Google Scholar
Chao, C. C., 1960, Dynamical response of an elastic half-space to tangential surface loadings, J. Appl. Mech. 27, 559–567CrossRefGoogle Scholar
Chimenti, D. E., 1997. Guided waves in plates and their use in materials characterization, Appl. Mech. Rev. 50, 247–284CrossRefGoogle Scholar
Christensen, R. M., 1972. Theory of Viscoelasticity – An Introduction. Academic Press, New York
Cohen, J. K. and Bleistein, N., 1977. An inverse method for determining small variations in propagation speed, SIAM J. Appl. Math. 32, 784–799CrossRefGoogle Scholar
Collin, R. E., 1960. Field Theory of Guided Waves. Reprinted IEEE Press 1991, New York
Courant, R. and Hilbert, D., 1962. Methods of Mathematical Physics Vol. II. Interscience Publishers, New York
Cremer, L., Heckl, M. and Ungar, E. E., 1973. Structure-borne Sound. Springer-Verlag, New York
Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. and Leppington, F. G., 1992. Modern Methods in Analytical Acoustics. Springer-Verlag, London
d'Alembert, J.-le-Rond, 1747. Investigation of the curve formed by a vibrating string (transl.). In Lindsay R. B. (ed.), 1972, Acoustics: Historical and Philosophical Development, Dowden, Hutchinson and Ross, Stroudsbury, Pennsylvania, 119–130
de Hoop, A. T., 1995. Handbook of Radiation and Scattering of Waves. Academic Press, London
DiMaggio, F. L. and Bleich, H. H., 1959. An application of a dynamic reciprocal theorem. J. Appl. Mech. 26, 678–679Google Scholar
Dowling, A. P. and Ffowcs Williams, J. E., 1983. Sound and Sources of Sound. Ellis Horwood, Chichester, UK
Eringen, A. C. and Suhubi, E. S., 1975. Elastodynamics, Vol. II, Linear Theory. Academic Press, New York
Ewing, W. M., Jardetzky, W. S. and Press, F., 1957. Elastic Waves in Layered Media. McGraw-Hill, New York
Fahy, F., 1985. Sound and Structural Vibration. Academic Press, London
Fokkema, J. T. and van den Berg, P. M., 1993. Seismic Applications of Acoustic Reciprocity. Elsevier Science, Amsterdam
Foldy, L. L. and Primakoff, H., 1945. A general theory of passive linear electroacoustic transducers and the electroacoustic reciprocity theorem I, J. Acoust. Soc. Am. 17, 109–120CrossRefGoogle Scholar
Graff, K. F., 1975. Wave Motion in Elastic Solids. Ohio State University Press, Columbus, Ohio
Graffi, D., 1946. Sul teorema di reciprocita nella dinamica dei corpi elastici, Mem. Acad. Sci. Bologna 10, 103–111Google Scholar
Gubernatis, J. E., Domany, E., Krumhansl, J. A., and Huberman, M., 1977. The Born approximation in the theory of the scattering of elastic waves by flaws, J. Appl. Phys. 48, 2804–2811, 2812–2819CrossRefGoogle Scholar
Harris, J. G., 2001. Linear Elastic Waves. Cambridge University Press, Cambridge
Jones, D. S., 1986. Acoustic and Electromagnetic Waves. Clarendon Press, Oxford
Junger, M. C. and Feit, F., 1972. Sound, Structures and Their Interaction. MIT Press, Cambridge, Massachusetts
Keller, J. B. and Karal, F. C. Jr., 1964. Geometrical theory of elastic surface-wave excitation and propagation, J. Acoust. Soc. Am. 36, 32–40CrossRefGoogle Scholar
Kino, G. S., 1978. The application of reciprocity theory to scattering of acoustic waves by flaws, J. Appl. Phys. 49, 3190–3199CrossRefGoogle Scholar
Knopoff, L. and Gangi, A. F., 1959. Seismic reciprocity, Geophysics 24, 681–691CrossRefGoogle Scholar
Kobayashi, S., 1987. Elastodynamics. In Computational Methods in Mechanics (ed. D. E. Beskos), Handbooks in Mechanics and Mathematical Methods Vol. 3, North-Holland, Amsterdam
Kupradze, V. D., 1963. Dynamical Problems in Elasticity. In Progress in Solid Mechanics Vol. 3 (eds. I. N. Sneddon and R. Hill). North-Holland, Amsterdam
Lamb, H., 1888. On reciprocal theorems in dynamics, Proc London Math. Soc. 19, 144–151Google Scholar
Lamb, H., 1904. On the propagation of tremors over the surface of an elastic solid, Phil. Trans. Roy. Soc. LondonA 203, 1–42CrossRefGoogle Scholar
Lamb, H., 1917. Waves in an elastic plate, Proc. Roy. Soc. LondonA 93, 114–128CrossRefGoogle Scholar
Liang, K. K., Kino, G. S. and Khuri-Yakub, B. T., 1985. Material characterization by the inversion of V(z), IEEE Trans. Son. Ultrason. 32, 266–273CrossRefGoogle Scholar
Love, A. E. H., 1892. A Treatise on the Mathematical Theory of Elasticity. Dover, New York, 1944
Love, A. E. H., 1911. Some Problems of Geodynamics. Dover, New York, 1967
Lyamshev, L. M., 1959. A method for solving the problem of sound radiation by thin elastic plates and shells, Sov. Physics – Acoustics 5, 122–123Google Scholar
Lyon, R. H., 1955. Response of an elastic plate to localized driving force, J. Acoust. Soc. Am. 27, 259–265CrossRefGoogle Scholar
Mal, A. K. and Knopoff, L., 1967. Elastic wave velocities in two component systems, J. Inst. Math. Applic. 3, 376–387CrossRefGoogle Scholar
Maxwell, J. C., 1864. On the calculation of the equilibrium and stiffness of frames, Phil. Mag. 27, 294CrossRefGoogle Scholar
McLachlan, N. W., 1961. Bessel Functions for Engineers. Clarendon Press, Oxford
Mikata, Y. and Achenbach, J. D., 1988. Interaction of harmonic waves with a periodic array of inclined cracks, Wave Motion 10, 59–72CrossRefGoogle Scholar
Miklowitz, J., 1962. Transient compressional waves in an infinite elastic plate or elastic layer overlying a rigid half-space, J. Appl. Mech. 29, 53–60CrossRefGoogle Scholar
Miklowitz, J., 1978. The Theory of Elastic Waves and Waveguides. Elsevier Science, Amsterdam
Mindlin, R. D., 1960. Waves and vibrations in isotropic elastic plates. In Structural Mechanics, pp. 199–232 (eds. J. N. Goodier and N. J. Hoff), Pergamon Press, New York
Morse, P. M. and Ingard, K. U., 1968. Theoretical Acoustics. McGraw-Hill, New York
Pao, Y.-H. and Mow, C.-C., 1973. Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane Russak, New York
Payton, R. G., 1964. An application of the dynamic Betti–Rayleigh reciprocal theorem to moving-point loads in elastic media, Q. J. Appl. Math. XXI, 299–313CrossRefGoogle Scholar
Pekeris, C. L., 1955. The seismic surface pulse, Proc. Nat. Acad. Sci. USA 41, 469–480CrossRefGoogle ScholarPubMed
Pierce, A. D., 1981. Acoustics: An Introduction to its Physical Principles and Applications. Acoustic Society of America, Woodbury, New York
Primakoff, H. and Foldy, L. L., 1947. A general theory of passive linear electroacoustic transducers and the electroacoustic reciprocity theorem II, J. Acoust. Soc. Am. 19, 50–120CrossRefGoogle Scholar
Rayleigh, Lord, 1873. Some general theorems relating to vibrations, Proc. London Math. Soc. 4, 357–368Google Scholar
Rayleigh, Lord, 1877. The Theory of Sound, Vol. II. Dover reprint, Dover Publications, New York, 1945
Rayleigh, Lord, 1887. On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4–11Google Scholar
Santosa, F. and Pao, Y.-H., 1989. Transient axially asymmetric response of an elastic plate, Wave Motion 11, 271–296CrossRefGoogle Scholar
Schenk, H. A., 1968. Improved integral formulations for acoustic radiation problems, J. Acoust. Soc. Am. 44, 41–58CrossRefGoogle Scholar
Stokes, G. G., 1849. On the dynamical theory of diffraction, Trans. Cambridge Phil. Soc. 9, 1Google Scholar
Tan, T. H., 1977. Reciprocity relations for scattering of plane elastic waves, J. Acoust. Soc. Am. 61, 928CrossRefGoogle Scholar
Thompson, R. B., 1994. Interpretation of Auld's electromechanical reciprocity relation via a one-dimensional example, Res. Nondestr. Ev. 5, 147–156CrossRefGoogle Scholar
Vasudevan, N. and Mal, A. K., 1985. Response of an elastic plate to localized transient sources, J. Appl. Mech. 52, 356–362CrossRefGoogle Scholar
Helmholtz, H. L., 1860. Theory des Luftschalls in Rohren mit offenen Enden, Borchardt-Crelle's J. 57, 1–70Google Scholar
Helmholtz, H. L., 1886. Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung, Borchardt-Crelle's J. 100, 137–166, 213–222Google Scholar
Weaver, R. L. and Pao, Y.-H., 1982. Axisymmetric elastic waves excited by a point source in a plate, J. Appl. Mech. 49, 821–836CrossRefGoogle Scholar
Weston, V. H., 1984. Multifrequency inverse problem for the reduced wave equation with sparse data, J. Math. Phys. 25, 1382–1390CrossRefGoogle Scholar
Zhang, Ch. and Gross, D., 1998. On Wave Propagation in Elastic Solids with Cracks. Computational Mechanics Publications, Southampton, UK
Zhang, M. and Achenbach, J. D., 1999. Simulation of self-focusing by an array on a crack in an immersed specimen, Ultrasonics 37, 9–18CrossRefGoogle Scholar

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  • References
  • J. D. Achenbach, Northwestern University, Illinois
  • Book: Reciprocity in Elastodynamics
  • Online publication: 10 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511550485.016
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  • References
  • J. D. Achenbach, Northwestern University, Illinois
  • Book: Reciprocity in Elastodynamics
  • Online publication: 10 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511550485.016
Available formats
×

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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
  • J. D. Achenbach, Northwestern University, Illinois
  • Book: Reciprocity in Elastodynamics
  • Online publication: 10 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511550485.016
Available formats
×