PSI - Issue 54

Jakub Gorski et al. / Procedia Structural Integrity 54 (2024) 264–270 J. Gorski et al. / Structural Integrity Procedia 00 (2023) 000–000

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The VAM phenomenon finds numerous applications in detecting defects in structures of di ff erent geometry. Jiao et al. (2011) present crack detection in pipeline. Wang and Song (2019) and Zhao et al. (2020) describe bolt loosnes detection. VAM is also not revealing limitations on the type of material of the structure. Li et al. (2020) show experi mental results performed on steel components. Chen et al. (2016) disclose similar tests for composite specimens. The method has also been used to localise damage by imaging the section of the structure under investigation, demon strated by Pieczonka et al. (2018) and Karve et al. (2020). The phenomenon of modulation transfer (MT), which belongs to the group of nonlinear acoustics, bears similarity to the VAM phenomenon. The phenomenon involves the transfer of modulation from one wave to another in the presence of damage occurring in the structure. The test procedure is similar to the VAM technique, with one key modification. In an experiment using the MT phenomenon, the pumping wave is amplitude-modulated. Zaitsev et al. (2002) used this method to detect defects in components made of glass, Trojniar et al. (2014) in alu minium, and Aymerich and Staszewski (2010) in composite materials. Thus, the performed research demonstrates the diagnostic potential of the MT phenomenon application in SHM. However, there is still much work to be done. There is little work that employs the MT phenomenon to localise damage. This can be attributed to insu ffi cient knowledge of the phenomenon. When a structure with damage is forced, various nonlinear e ff ects can contribute to the response. Therefore, this paper will present the use of the MT phenomenon for damage localisation. For this purpose, a procedure will be presented in which two specimens will be used: faulty and intact. During the tests, the collected signals will be processed to calculate the damage indices trends for state assessment. The article is structured as follows. Section 2 describes the measurement method and the proposed signal processing algorithm. Section 3 describes the experiments. Section 4 contains the results obtained in the form of spectra and indicator trends and their discussion. The section 5 concludes with the most important findings.

Nomenclature

f l f pumping wave carrier frequency f M modulation frequency f hf probing wave frequency R modulation intensity index A sid the amplitude of the selected sidebands A hf the amplitude of the probing wave response

2. Research methods

The diagnostic method described requires exciting the structure from two sources. One of these generates an amplitude-modulated wave called pumping, with carrier frequency f l f and modulation frequency f M . The other source generates a probing wave of a much higher frequency f hf . As a result of wave interactions with the damage, part of the energy of the modulating signal is transferred from the pumping wave to the probing wave. Figure 1 shows the idea of the modulation transfer phenomenon. When measuring the response of a structure, sidebands with frequencies f hf ± nf M surrounding the frequency of the sampling wave can be expected. Due to the presence of the two waves, the VAM phenomenon also occurs, which involves mutual modulation of the waves. Figure 1 shows schematically as frequency components f hf ± nf l f containing their own modulations (where n = 1 , 2 , 3 , ... ). The presented theoretical description of the diagnostic method based on the MT phenomenon was the starting point for the processing algorithm. The algorithm enables the calculation of indices based on the sideband amplitudes. It involves calculating the discrete spectrum of the response signal, reading the amplitude values of the components under investigation and calculating the modulation intensity index R , which is defined by the following formula. R = A sid A hf (1) where A sid is the amplitude of the selected sidebands and A hf is the amplitude of the probing wave response. The described index was used to present the MT phenomenon qualitatively.