The Influence of Local Increase of Stress on Eigenvalues for a Simply Supported Beam

Local increase of bending stress in a beam may be caused by a decrease of the cross-section (fracture) or a local increase of bending torque. The increase of stress issues from the well known interdependence between the stress, the bending torque and the sectional modulus. The work presents a derivation of differential equations for eigenfunctions in both cases. Knowing the eigenfunctions and boundary conditions we determine a system of algebraic equations for the eigenvalues that are different from the eigenvalues of the beam without local stress disturbances. Two computational models of local increase of stress were constructed: with fracture and with local increase of bending torque.