Assessment of thermal fatigue damage in square tubes using second harmonic generation of longitudinal waves

This paper investigates nonlinear guided wave propagation in square tubes with material nonlinearity for the first time. The dispersion characteristics of guided waves in a square aluminum tube are first analyzed and presented. A pair of longitudinal wave modes is selected as fundamental waves and second harmonics. The selected mode pair is identified to meet the internal resonance condition. Then, a three-dimensional finite element model is developed to simulate the second harmonic generation and propagation in the square tube. When the fundamental waves propagate in the square tube, the second harmonics are generated due to the self-interaction of the fundamental waves and inherent material nonlinearity. The generated second harmonics are manifested to be cumulative with the almost linearly increased nonlinear acoustic parameter versus propagation distance. Subsequently, the experiment is carried out to confirm the simulated results and they are considerably consistent. Finally, the generated second harmonics are employed to evaluate different levels of thermal fatigue damage, which is introduced into the square tube by applying increasing thermal cycles. The nonlinear acoustic parameter increases with the growing thermal cycles, which indicates the induced second harmonics are sensitive to thermal fatigue damage. The findings of this study provide insights into practical applications for the detection and evaluation of early-stage damage in square tubes using second harmonic generation of longitudinal waves.