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Note on the Rayleigh waves properties in viscoelastic media

Le Pommellec J. Y., El Baroudi A.

Archives of Mechanics

2024

Vol. 76, nr 3

207--223

This paper describes a theory for surface Rayleigh waves propagating in a viscoelastic medium. The Zener model to describe the viscoelastic behavior of the medium is used. This simple model captures both the relaxation and retardation. An analytical expression for the complex dispersion equation of Rayleigh waves is established. The influence of the normalized frequency and the ratio of shear moduli on the dispersion curves of the Rayleigh wave velocity and attenuation is analyzed numerically. The numerical solutions show the dependence of the phase velocity change and the wave attenuation in terms of the normalized frequency and the ratio of shear moduli. As an important result, the Zener model can be used at a normalized low frequency to predict creep phenomenon as well as at a normalized high frequency to predict relaxation. The obtained results are fundamental and can be applied to characterize the viscoelastic properties of soft biomaterials and tissue, in nondestructive testing of materials, in geophysics and seismology. Thus, the obtained complex dispersion equation can be very useful to interpret the experimental measurements of Rayleigh waves propertie in a viscoelastic medium.