Nonclassical Modes of Unrestrained Shear Beams

This paper considers the effect that a rotational motion has on the normal modes of a shear beam that is free to rotate, either because it is free in space or it is pivoted at one end. It is shown that the classical solutions for these two cases violate the principle of conservation of angular momentum, and that this is true even when the rotational inertia of the beam vanishes or is neglected.