Love waves propagation in layered viscoelastic waveguides characterized by a Zener model

Abstract

This paper describes a theory of surface Love waves propagating in lossy waveguides consisting of a viscoelastic layer deposited on a semi-infinite elastic substrate. The Zener model to describe the viscoelastic behavior of a medium is used. This simple model captures both the relaxation and retardation. A new form of the unsteady momentum equation for viscoelastic waveguides has been established. By using appropriate boundary conditions, an analytical expression for the complex dispersion equation of Love waves has been deduced. The influence of the loss factor and the ratio of shear moduli of the surface layer on the dispersion curves of Love waves velocity and attenuation is analyzed numerically. The numerical solutions show the dependence of the velocity change and the wave attenuation in terms of the loss factor and the ratio of shear moduli. The obtained results show that the change in the ratio of shear moduli can represent a hardening or softening effect of the surface layer. These effects depend on the loss factor value of the surface layer. In addition, these results are novel, fundamental and can be applied in the characterization of the viscoelastic properties of soft biomaterials and tissues, 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 Love waves properties in viscoelastic waveguides.