Analytical Solution of the Resonance Length for Ultrasonic Torsional Fatigue Samples

A method for analytical calculation of the resonance length for ultrasonic torsional fatigue samples is recommended. The angular displacement amplitude and torsional stress/strain amplitude on the surface of samples are derived. Analysis for the stress magnification factor of sample with various cross-sections shows that when the ratio of the minimum section radius to the maximum section radius is 0.5, there is the maximum stress magnification. The sample profile defined by the analytical solution may be approximated by a circular profile, with the error in the frequency and stress being neglectable.