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Localization method of contact-type failure by measuring the structural intensity of low-frequency vibrations caused by frequency down-conversion of elastic vibrations

Contact-type failures, such as early-stage fatigue cracks, bolt loosening, and welding cracks, are difficult to detect with nondestructive inspection, which uses ultrasonic waves or vibrations. When a structure experiencing contact-type failure vibrates due to ultrasonic vibrations of two different frequencies, low-frequency vibrations with frequencies equal to the difference between the frequencies of the ultrasonic vibrations are generated due to local nonlinearity at the contact interface (frequency down-conversion). The detection methods of contacttype failure based on the frequency down-conversion of elastic waves or vibrations have been proposed. These detection methods can be applied using measurements with low-sampling rates. This study aims to develop a detection and localization method based on the frequency down-conversion of elastic vibrations. Low-frequency vibrations caused by frequency down-conversion are generated only if the structure has contact-type failure. Accordingly, contact-type failure can be regarded as the excitation point of low-frequency vibration caused by frequency down-conversion. Herein, a localization method of contact-type failure using the structural intensity as the localization method of the exciting location was proposed. First, an overview of the frequency downconversion phenomenon is mentioned. Second, the theoretical investigation of the proposed localization method is explained, and the parametric excitation model that uses the Euler–Bernoulli beam is suggested. The equation transformation of the proposed model clarifies that the contact-type failure can be regarded as the exciting point of low-frequency vibration. Furthermore, from the results obtained herein, the location of contact-type failure was identified as the exciting point of low-frequency vibration caused by the frequency down-conversion. Finally, the basic performance of the proposed localization method was experimentally investigated. The exciting point can be localized from the sign change point of the structural intensity. Thus, the sign change point of the structural intensity of low-frequency vibrations caused by the frequency down-conversion is the contact-type