Dynamic Stress Concentration In An Arbitrary Curved And Inhomogeneous Rod Joined With Infinite Straight Rods And Excited By A Twisting Wave

Abstract

An analysis is presented of the dynamic stress concentration problem of an inhomogeneous rod of infinite length, consisting of two infinite straight portions and one finite curved portion of arbitrary curvature. The curved portion lies between the two straight portions and its radius of cross-section varies continuously. The twisting wave propagates from one of the infinite straight portions to the other passing through the curved portion. First, according to the exact solution of the static equilibrium equations for a curved rod, the field transfer matrix for an element of the curved rod is developed. The point transfer matrix is obtained by consideration of the internal forces and moments. At the cross-sections of discontinuity, solutions of the curved and straight rods are connected by adjusting the continuity conditions. As examples, stress concentration factors in circular, elliptical and parabolic arc rods have been obtained.