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

Abstract

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.