Elastic-Plastic Wave Propagation of Combined Generalized Forces in a Timoshenko Beam

Summary

The propagation of elastic and plastic waves of combined generalized forces in a Timoshenko beam under symmetrical bending and tension or compression is investigated for isotropic work-hardening materials. The governing system of differential equations has the same structure as that of a certain class of problems dealing with the elastic-plastic wave propagation of stresses in a two or three dimensional medium. In contrast to the latter problem, however, the compliance matrix associated with the wave propagation in a Timosiienko beam is unsymmetrical. The eigenvalues and the eigenvectors are determined. The eigenvalues represent the velocities of the waves, whereas the eigenvectors yield the corresponding jumps of the generalized forces.