Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method

Abstract

The work focuses on the effect of a general state of initial stress on the dispersion behavior of guided waves in viscoelastic waveguides. To this purpose, an extension of the Semi Analytical Finite Element (SAFE) method is proposed to formulate the wave equation and to extract the waves modal properties in viscoelastic prestressed waveguides. The wave equation is derived in linearized incremental form within an updated Lagrangian framework, where the prestressed configuration is considered to be slightly deviated from the corresponding unstressed one. Next, by using the SAFE method and the Boltzmann superposition principle, a linear algebraic system of equations is obtained in the complex wavenumber-frequency domain. Dispersive guided waves wavelengths, phase velocity, group velocity and attenuation, are extracted by solving a polynomial eigenvalue problem. A modal formula for the wave energy velocity calculation, that exploits the wave equation SAFE matrices only, is proposed. Such formula is based on the linearized incremental form of the Poynting theorem obtained by manipulating the energy balance principle expressed in material description.Numerical examples on a hysteretic 113A standard rail profile and on an ASME 1-1/2 Schedule 160 steel pipe, considering various states of initial stress and applied loadings, are presented to show the effect of prestress on the dispersive properties of mechanical waves in viscoelastic waveguides.