As a nonlinear ultrasonic nondestructive testing method, vibro-acoustic modulation (VAM) uses low-frequency vibrations to stimulate a structure and an ultrasonic wave, which is modulated by vibration if the system is damaged, to detect the structure. 

However, little research has been done on the effect of the crack position and pumping excitation on the modulation distribution along the probing frequency. In addition, the optimum probing frequency selection method has not yet been determined. 

Researchers from the Institute of Acoustics (IOA) of the Chinese Academy of Sciences found that the VAM technique exhibited the best crack sensitivity when the probing frequency was selected as the sum or difference of the resonance and pumping frequency. To lock this optimum probing frequency, the minimum sweep range should be at least twice the beam longitudinal fundamental frequency. 

Researchers investigated the interactions between the ultrasound, vibration, and crack. The results demonstrated that the modulation could be affected by the crack position.

When the crack was located at the longitudinal resonance node point x0 = L m/n (where L is the beam length, n is the mode number, m is an integer, and 1 < m < n), both the modulation at the multiples of the number n-order resonance frequencies and peaks on the side of these resonances were much lower.

The modulation peak values occurred on both sides of the high-frequency structure response resonances, and the interval frequency between the peak and corresponding resonance was equal to the low vibration (pumping) frequency. 

Further analysis suggested that the nonlinear spring model was appropriate for crack simulations to predict modulation distribution and select parameters. All of the obtained results would aid in understanding the modulation mechanism and making further improvements to the reliability and efficiency of the VAM technique. 

The research was published in Mechanical Systems and Signal Processing on March 29. It was supported by the National Natural Science Foundation of China.