PSI - Issue 52

Carlos A. Galán Pinilla et al. / Procedia Structural Integrity 52 (2024) 20–27

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Carlos A. Gala´n-Pinilla et al. / Structural Integrity Procedia 00 (2023) 000–000

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in the in-plane direction for the viscoelastic layer is greater compared with the displacement in the elastic layer because of the energy leakage. The e ff ect of adding a viscoelastic coating to a steel plate on the wave structure can be noted in Fig. 3 for the S 0 mode at frequencies of 400 kHz (no attenuation and high dispersion), 500 kHz (high attenuation and low dispersion), and 700 kHz (low attenuation and low dispersion). In Fig. 3(a), minor displacements are observed in the metal with respect to the coating layer and considerable out-of-plane displacement at the metal-coating interface. In Fig 3(b), more noticeable out-of-plane displacements are observed in both the plate and the coating, which is undesirable for energy leakage considerations. Finally, in Fig 3(c), the displacement amplitude is reduced at high frequencies, with similar amplitudes for the two layers, with a high proportion for the out-of-plane direction.

a)

b)

c)

d)

e)

f)

Fig. 3. Wave structures of S 0 Lamb waves on a coated steel plate. Bitumen coating: a) S 0 , 400kHz. b) S 0 , 500 khz, c) S 0 , 700 khz. Single-layer fusion bonded epoxy: d) S 0 , 400kHz. e) S 0 , 500 khz, f) S 0 , 700khz.

The same wave structure study for a single-layer fusion bonded epoxy coating is presented in Fig. 3(e-f). The results show a larger amplitude di ff erence between the plate and the coating for the S 0 mode studied at the same frequencies. This was a consequence of lower values of density and attenuation coe ffi cients of the coating. Lastly, it can be concluded from Fig. 3 a larger wave displacement for in-plane and out-of-the-plane directions in the coating with respect to the metal layer due to the low acoustic impedance of the viscoelastic materials. Therefore, the selection of the suitable mode is a complex task and several criteria must be considered. The convergence of the implemented method was guaranteed using order six in the plate element and order ten in the coating element. As a result the run time to obtain the dispersion curves with a gradual increase of 1 kHz is 15 s on a current notebook PC (AMD Ryzen 5 3450U 2.10 GHz, 24 GB RAM).

5. Conclusions

This paper presents the e ff ect of viscoelastic coating on the dispersion, attenuation, and wave structure in an elastic viscoelastic (steel-bitumen) bilayer structure. The results showed the relationship of displacement amplitudes in the wave for the cases of the free and coated plates. A significantly higher amplitude is exhibited in the coating, especially