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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

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 $A=C−1A¯$ and $B=C−1B¯$ 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.

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