Dynamic Saint-Venant region in a semi-infinite elastic strip

This paper presents a formulation for the solution of the steady state rosponse of a semi-infinite strip with atress-free semi-infinite edges and a time-harmonie shear and normal stress applied to the end. If the end stresses form a self-equilibrated stress state, the presence or absence of a dynainic Saint-Venant region may be examined. The mathematical analysis is based on the linear equations for generalized plane stress and are solved by a biorthogonal eigenfunction expansion. The formulation is in terms of stresses and a displacement related auxiliary variable of the same differential order as the stress. Numerical solutions are presented as an indication of frequency and stress mode shape dependency.