Reciprocal Theorem and Other Integral Relations

  • Lester W. SchmerrJr.


Chapter 5 develops reciprocal theorems for both fluids and elastic solids, then combines fundamental solutions derived in Chap. 4 with those theorems to obtain general integral representation expressions and integral equations. We also develop a more generalized electromechanical reciprocity theorem that is applicable to all elements (electrical, piezoelectric, and mechanical) of an ultrasonic measurement system. Results from this chapter serve as the foundation for many later applications, including transducer modeling (Chap. 8), flaw scattering (Chap. 10), and a general model of the entire ultrasonic measurement process (Chap. 12).


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Suggested Reading

  1. V. D. Kupradze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity (North Holland, New York, 1979).zbMATHGoogle Scholar
  2. V. D. Kupradze, Potential Methods in the Theory of Elasticity (Israel Program for Scientific Translations, Jerusalem, 1965).zbMATHGoogle Scholar
  3. V. D. Kupradze, Dynamical problems in elasticity, in Progress in Solid Mechanics, vol. 3 (I. N. Sneddon and R. Hill, eds.) (North Holland, Amsterdam, 1963).Google Scholar
  4. V. Z. Parton and P. I. Perlin, Integral Equations in Elasticity (English translation) (Mir, Moscow, 1982).zbMATHGoogle Scholar
  5. V. K. Varadan and V. V. Varadan, eds., Elastic Wave Propagation and Scattering (Ann Arbor Science, Ann Arbor, Michigan, 1982).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Lester W. SchmerrJr.
    • 1
  1. 1.Iowa State UniversityAmesUSA

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