Skip to main content
SpringerLink
Log in
Book cover

Fundamentals of Ultrasonic Nondestructive Evaluation pp 69–89Cite as

Reciprocal Theorem and Other Integral Relations

  • Chapter

  • 388 Accesses

Abstract

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).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Hartmann, Introduction to Boundary Elements (Springer Verlag, New York, 1989).

    Book  MATH  Google Scholar 

  2. G. Beer and J. O. Watson, Introduction to Finite and Boundary Element Methods for Engineers (Wiley, New York, 1992).

    MATH  Google Scholar 

  3. J. H. Kane, Boundary Element Analysis (Prentice-Hall Englewood Cliffs, NJ, 1994).

    Google Scholar 

  4. Y Liu and F. J. Rizzo, Comp. Meth. in Appl. Mech. and Eng. 107 (1993) 131.

    Article  MathSciNet  MATH  Google Scholar 

Suggested Reading

  • V. D. Kupradze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity (North Holland, New York, 1979).

    MATH  Google Scholar 

  • V. D. Kupradze, Potential Methods in the Theory of Elasticity (Israel Program for Scientific Translations, Jerusalem, 1965).

    MATH  Google Scholar 

  • 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 

  • V. Z. Parton and P. I. Perlin, Integral Equations in Elasticity (English translation) (Mir, Moscow, 1982).

    MATH  Google Scholar 

  • V. K. Varadan and V. V. Varadan, eds., Elastic Wave Propagation and Scattering (Ann Arbor Science, Ann Arbor, Michigan, 1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Iowa State University, Ames, Iowa, USA

    Lester W. Schmerr Jr.

Authors
  1. Lester W. Schmerr Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Schmerr, L.W. (1998). Reciprocal Theorem and Other Integral Relations. In: Fundamentals of Ultrasonic Nondestructive Evaluation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0142-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-0142-2_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0144-6

  • Online ISBN: 978-1-4899-0142-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation