Double eigenvalues for the uniform Timoshenko beam

Abstract

In this paper, a necessary and sufficient condition is given for determining if a uniform Timoshenko beam with free ends has an eigenvalue for which there exist two linearly independent eigenfunctions. Such eigenvalues are called double. Two examples are given of beams with double eigenvalues. The first example gives a physically realistic set of beam parameters which give rise to a beam with a double eigenvalue. The second example shows that there exist choices for beam parameters which give rise to beams with two double eigenvalues.