Propagation of two Rayleigh waves in viscoelastic medium: Explicit expressions for complex velocities

Abstract

AbstractPropagation of Rayleigh waves is considered in an isotropic linear viscoelastic medium. Such propagation is represented through a complex velocity, which lies implicit in an irrational secular equation. A complex analysis technique is used to transform this irrational complex equation into an algebraic equation. A linear equation replaces the secular equation for propagation of the classical Rayleigh wave in viscoelastic medium. A quadratic equation replaces the secular equation for propagation of additional Rayleigh wave, which exists for appropriate value of a complex parameter. Explicit expressions are obtained for the complex velocity, which satisfy the secular equation for Rayleigh waves. Two different analytical expressions for the velocity certify the existence of second Rayleigh wave in some viscoelastic materials with specifically related elastic and dissipative parameters. Numerical examples are solved to analyse the complex velocities and particle motion for the two Rayleigh waves in viscoelastic materials.