Dispersion and spurious reflections of viscoelastic wave

Abstract: This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes, with a consistent and lumped mass model for spatial integration is considered, and the Newmark average acceleration method of the two-step version for integration over time is adopted. The resulting system of the difference equation is then analytically integrated in non-finite terms (numerical solution of waves) using complex notation. The numerical results reveal that, even for a refined mesh, the dispersion and spurious reflections are significant.