On the valid frequency range of Timoshenko beam theory

The frequency equation of Timoshenko beam theory factorises for hinged–hinged end conditions, leading to a first and second spectrum of natural frequencies; the latter is largely inaccurate and can be isolated and disregarded. For the majority of other end conditions, when the frequency equation does not factorise, one may think in terms of pseudo-second spectrum contributions arising when evanescent waves become propagating above the cut-off frequency ωco=κAG/ρI, and it is conjectured that these may have a corrupting effect on the frequency predictions. Comparisons with measured and simulated frequencies lead to the conclusion that Timoshenko predictions above the cut-off frequency should be disregarded for those end conditions for which the frequency equation does not factorise.