Reciprocity in Elastodynamics

1. Introduction 2. Some elastodynamic theory 3. Wave motion in an unbounded elastic solid 4. Some simple applications of reciprocity 5. Wave motion guided by a carrier wave 6. Waves in an elastic layer 7. Reciprocity considerations for the elastic layer 8. Forced motion of an elastic layer 9. Integral representations and integral equations 10. Scattering waveguides and bounded bodies Bibliography Index.

[1]  J. Achenbach,et al.  Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction , 1999 .

[2]  R. D. Mindlin.  Waves and Vibrations in Isotropic, Elastic Plates , 1989 .

[3]  Norman Bleistein,et al.  Mathematical Methods for Wave Phenomena , 1984 .

[4]  J. Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: On the Calculation of the Equilibrium and Stiffness of Frames , 1864 .

[5]  E. Betti.  Teoria della elasticita , 1872 .

[6]  Vaughan H. Weston.  Multifrequency inverse problem for the reduced wave equation with sparse data , 1984 .

[7]  B. Khuri-Yakub,et al.  Material Characterization by the Inversion of V(z) , 1985, IEEE Transactions on Sonics and Ultrasonics.

[8]  J. Achenbach,et al.  Reflection and transmission of an obliquely incident wave by an array of spherical cavities , 1986 .

[9]  Ajit K. Mal,et al.  Elastic Wave Velocities in Two-component Systems , 1967 .

[10]  L. Rayleigh.  On Waves Propagated along the Plane Surface of an Elastic Solid , 1885 .

[11]  Miguel C. Junger,et al.  Sound, Structures, and Their Interaction , 1972 .

[12]  R. Collin.  Field theory of guided waves , 1960 .

[13]  R. B. Thompson.  Interpretation of Auld's electromechanical reciprocity relation via a one-dimensional example , 1994 .

[14]  V. D. Kupradze,et al.  Dynamical problems in elasticity , 1963 .

[15]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[16]  B. Khuri-Yakub,et al.  Precise Phase Measurements with the Acoustic Microscope , 1985, IEEE Transactions on Sonics and Ultrasonics.

[17]  G. Kino.  The application of reciprocity theory to scattering of acoustic waves by flaws , 1978 .

[18]  Jan Drewes Achenbach,et al.  Acoustic and Electromagnetic Waves , 1986 .

[19]  R. G. Payton.  An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media , 1964 .

[20]  Jan Drewes Achenbach,et al.  Use of elastodynamic reciprocity to analyze point-load generated axisymmetric waves in a plate , 1999 .

[21]  Jan Drewes Achenbach,et al.  Reflection and transmission of elastic waves by a periodic array of cracks: Oblique incidence , 1985 .

[22]  T. Hayat,et al.  Measurement models for ultrasonic nondestructive evaluation , 2000, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[23]  M. Bonnet.  Boundary Integral Equation Methods for Solids and Fluids , 1999 .

[24]  Jan Drewes Achenbach,et al.  REFLECTION AND TRANSMISSION OF ELASTIC WAVES BY A PERIODIC ARRAY OF CRACKS. , 1985 .

[25]  Eytan Domany,et al.  The Born approximation in the theory of the scattering of elastic waves by flaws , 1977 .

[26]  C. Chao,et al.  Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings , 1960 .

[27]  Achenbach.  Calculation of surface wave motions due to a subsurface point force: an application of elastodynamic reciprocity , 2000, The Journal of the Acoustical Society of America.

[28]  F. G. Leppington,et al.  Modern Methods in Analytical Acoustics , 1992 .

[29]  Jan Drewes Achenbach,et al.  Lamb waves as thickness vibrations superimposed on a membrane carrier wave , 1998 .

[30]  Jack K. Cohen,et al.  An Inverse Method for Determining Small Variations in Propagation Speed , 1977 .

[31]  Horace Lamb,et al.  On Reciprocal Theorems in Dynamics , 1887 .

[32]  L. B.,et al.  Bessel Functions for Engineers , 1935, Nature.

[33]  Stefan Hurlebaus,et al.  Linear Elastic Waves , 2001 .

[34]  Jan Drewes Achenbach,et al.  Ray methods for waves in elastic solids : with applications to scattering by cracks , 1982 .

[35]  John G. Harris.  Linear Elastic Waves: Frontmatter , 2001 .

[36]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[37]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[38]  Ann P. Dowling,et al.  Sound and Sources of Sound , 1983 .

[39]  Prasanta Kumar Banerjee,et al.  Advanced dynamic analysis by boundary element methods , 1992 .

[40]  J. Achenbach,et al.  Interaction of harmonic waves with a periodic array of inclined cracks , 1988 .

[41]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis , 1987 .

[42]  W. M. Ewing,et al.  Elastic Waves in Layered Media , 2015 .

[43]  C. Pekeris,et al.  THE SEISMIC SURFACE PULSE. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[44]  A. T. Hoop.  Handbook of radiation and scattering of waves , 1995 .

[45]  G. G. Stockes.  ON THE DYNAMICAL THEORY OF DIFFRACTION , 1849 .

[46]  Fadil Santosa,et al.  Transient axially asymmetric response of an elastic plate , 1989 .

[47]  B. Auld.  General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients , 1979 .

[48]  Richard L. Weaver,et al.  Axisymmetric Elastic Waves Excited by a Point Source in a Plate , 1982 .

[49]  John William Strutt,et al.  Some General Theorems relating to Vibrations , 1871 .

[50]  Joseph B. Keller,et al.  Geometrical Theory of Elastic Surface‐Wave Excitation and Propagation , 1964 .

[51]  A. Mal,et al.  Response of an Elastic Plate to Localized Transient Sources , 1985 .

[52]  E. E. Ungar,et al.  Structure-borne sound , 1974 .

[53]  J. Achenbach,et al.  Simulation of self-focusing by an array on a crack in an immersed specimen , 1999 .

[54]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

[55]  J. Miklowitz.  Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space , 1962 .

[56]  H. Lamb.  On waves in an elastic plate , 1917 .

[57]  J. Miklowitz,et al.  The Theory of Elastic Waves and Waveguides , 1979 .

[58]  Richard H. Lyon,et al.  Response of an Elastic Plate to Localized Driving Forces , 1955 .

[59]  F. S. Lamb,et al.  On the Propagation of Tremors over the Surface of an Elastic Solid , 1904 .

[60]  Dietmar Gross,et al.  On Wave Propagation in Elastic Solids with Cracks , 1997 .

[61]  F. Fahy.  Sound and structural vibration , 1985 .

[62]  L. Foldy,et al.  A General Theory of Passive Linear Electroacoustic Transducers and the Electroacoustic Reciprocity Theorem. I , 1945 .

[63]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[64]  J. Achenbach,et al.  Reflection and transmission of plane waves by a layer of compact inhomogeneities , 1988 .

[65]  P. M. van den Berg,et al.  Seismic applications of acoustic reciprocity , 1993 .

[66]  Allan D. Pierce,et al.  Acoustics , 1989 .

[67]  Yih-Hsing Pao,et al.  Diffraction of elastic waves and dynamic stress concentrations , 1973 .

[68]  Leon Knopoff,et al.  Body Force Equivalents for Seismic Dislocations , 1964 .

[69]  D. Chimenti.  Guided Waves in Plates and Their Use in Materials Characterization , 1997 .

[70]  A. Eringen,et al.  Elastodynamics, Vol. II, Linear Theory , 1978 .

[71]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[72]  Eytan Domany,et al.  Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials , 1977 .