Abstract
Ultrasonic fatigue specimens require rigorous design. The entire machine and specimen setup must vibrate in resonance at high frequencies, with the desired mode shapes that produce the intended stresses. The connection between parts must be considered too as they should allow for the desired mode shape to vibrate in free-free conditions. Most published research uses an analytical method that works only for uniaxial tension-compression or pure torsion specimens. This limits the range of experiments. In this paper, a semi-analytical formulation that can model more complex ultrasonic specimen geometries for a variety of stress states is proposed, namely multiaxial tension-torsion. Comparing numerical simulations with the analytical method show a good correlation between results. This work can help other researchers to design and conduct more varied and efficient ultrasonic fatigue experiments.