Erratum: “On the Analysis of Periodically Heterogenous Beams” [ASME J. Appl. Mech., 2016, 83(9), p. 091001; DOI: 10.1115/1.4033721]

Abstract

This erratum corrects errors in the originally published paper.The equations listed in the original manuscript have been found to include several typographical errors that make it impossible to understand the proofs presented in the paper. In Eq. (18), appearing on page 4, matrix M should readM=[Ψ6×6O6×6O6×6O6×6]Similarly, matrix N defined in Eq. (19) should beN=[ZαCr−1α−αCr−1]With these two corrections, identity (17) is proved easily(1)MNCr−1Cr−1+GNCr−1+EN=[ΓZαCr−1+ΨZCr−1αCr−1+ΨTZα+ΘZCr−1αZTΨTZα+ZTΘZCr−1α]=Owhere negative and positive terms cancel out to yield the first equality and identities (16a) and (16b) are introduced to yield the second equality.