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Errata

Erratum: “Reciprocity Theorems for Diffusion, Flow, and Waves” [Journal of Applied Mechanics, 2004, 71(1), pp. 145–150] OPEN ACCESS

[+] Author and Article Information
Kees Wapenaar, Jacob Fokkema

J. Appl. Mech 77(6), 067001 (Aug 17, 2010) (1 page) doi:10.1115/1.4002115 History: Published July 07, 2010; Online August 17, 2010
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Matrix C defined in Appendices C and D is singular and hence expressions containing the inverse of C cannot be used as such. The singularity is a consequence of the chosen organization of the matrix-vector differential equation in these appendices. The field vector u contains nine stress components of which only six are independent. By removing the three redundant stress components from u and reorganizing the matrix-vector equation accordingly, we obtain a matrix C that is invertible. The redefined matrices A=C1A¯ and B=C1B¯ in Appendices C and D obey symmetry relations (9) and (13) in the body of the paper. Hence, the unified reciprocity theorems (12) and (14) are valid for the modified matrix-vector differential equation in these appendices. Explicit expressions for the modified matrices and vectors can be found at http://geodus1.ta.tudelft.nl/PrivatePages/C.P.A.Wapenaar/4_Journals/J.Appl.Mech/AppM_04.pdf.

We take this opportunity to indicate some printing errors in the paper. The tildes below A and u in Eq. (1) should be removed. Circumflexes should be added above all vectors u and s in Eqs. (10) and (11). A right-bracket ] should be inserted after the first ûB at the right-hand side of Eq. (10). Right-parentheses ) should be inserted after ûA at the left-hand side of Eq. (11) and after the first ûB at the right-hand side of Eq. (11).

We thank Stefan Stijlen for bringing the singularity of matrix C to our attention.

Copyright © 2010 by American Society of Mechanical Engineers
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