RESONANT CHARACTERISTIC ANALYSIS AND PARAMETRIC DESIGN OF THREE-THROAT ULTRASONIC TENSION-TORSION FATIGUE SPECIMEN BASED ON ELECTROMECHANICAL ANALOGY

Analyzing the resonant characteristics of three-throat specimens serves as an essential prerequisite for investigating the multiaxial tension-torsion fatigue performance of structural materials under ultrasonic high-frequency cyclic loading. In view of the unique symmetrical geometric configuration of the three-throat ultrasonic tension-torsion fatigue specimen, this paper separately derives the analytical expressions of longitudinal mechanical impedance and torsional mechanical impedance for three typical structural segments, including uniform cylindrical bars, diverging circular arc bars and converging circular arc bars. On the basis of the classic electromechanical analogy theory widely adopted in ultrasonic vibration system research, an equivalent circuit model corresponding to the entire ultrasonic tension-torsion fatigue specimen is constructed. After simplifying the series-parallel connection of mechanical impedance units within the equivalent circuit, the governing equations for longitudinal resonant frequency and torsional resonant frequency of the specimen are derived systematically. Meanwhile, complete analytical solution procedures for calculating vibration displacement distribution and internal stress distribution along the full length of the specimen are presented in detail. Comparison with finite element results demonstrates that the electromechanical analogy model accurately predicts the resonant characteristics of the three-throat specimen. The errors in both axial and torsional resonant frequencies are within 3.5%, while the errors in axial stress and shear stress at the critical section are below 4.5%, confirming the high precision of the model. Geometric parameters significantly influence the resonant frequencies: the throat radius exhibits a strong positive correlation and has the greatest impact, whereas all other geometric parameters show negative correlations. Finally, by simultaneously solving the axial and torsional resonant frequency equations, the geometric parameter design curves at a specified frequency were derived. The electromechanical analogy method avoids the cumbersome iterative modeling process of finite element analysis, enabling high-precision analysis of specimen resonant characteristics within seconds. Combined with design curves, it realizes one-shot matching of geometric parameters under a specified frequency, providing theoretical support for the efficient design of ultrasonic tension-torsion fatigue tests.