The eigenvalue problem and Saint-Venant decay rate for a nonhomogeneous semi-infinite strip

The eigenvalue problem about a nonhomogeneous semi-infinite strip is investigated using the methodology proposed by Papkovich and Fadle for homogeneous plane problems. Two types of nonhomogeneity are considered: (i) the elastic modulus varying with the thickness coordinate x exponentially, (ii) it varying with the length coordinate y exponentially. The eigenvalues for the two cases are obtained numerically in plane strain and plane stress states, respectively. By considering the smallest positive eigenvalue, the Saint-Venant Decay rates are estimated, which indicates material nonhomogeneity has a significant influence on the Saint-Venant end effect.