Abstract
The accuracy of dynamic solutions of Timoshenko beam theory is not assured for higher frequencies above the critical frequency determined by the slenderness ratio and material constants of beam. In this paper, looking upon the free vibration of beams as the stationary motion of the transverse wave propagation, we discussed the accuracy of natural frequencies determined by Timoshenko beam theory by comparing with the Pochhammer-Chree theory. As the result, we have showed that the stationary waves with higher frequencies above the critical frequency, except for simple beams, are generated by the superposition of two transverse elastic waves with the phase velocities of the first and second modes, and that the accuracy of the second phase velocity governs the accuracy of Timoshenko beam theory. Consequently, we need to be careful to determine the applicable range according to the slenderness ratio of beam when we apply the Timoshenko beam theory for higher frequencies above the critical frequency.
