Effects of lateral inertia on the group velocities and specific damping capacities of viscoelastic polymeric rods

•The group velocity distributions of the polymeric rods are presented considering the lateral inertia effect.•The frequency ranges for the dispersion characteristics are determined.•Thin polymeric rods exhibit abnormal dispersion in a large frequency range.•The lateral inertia doesn't affect the maximums of specific damping capacities.•The critical value of the viscoelastic constant θ related to the specific damping capacity of the Epoxy rod is determined. This analytical study addresses in detail the group velocities and the specific damping capacities of viscoelastic polymeric rods considering the lateral inertia effect. Determination of the group velocity and the specific damping capacity in the viscoelastic rods are crucial for the subsequent various evaluations. The group velocities and the specific damping capacities are evaluated using selected viscoelastic polymeric models published in the literature. So far, there is no analytical solution including the lateral inertia effect for the group velocity and damping capacity of the viscoelastic rods. The group velocities are calculated with help of the phase velocities by using Rayleigh's formula. The specific damping capacities are determined with the help of three different formulas. The analysis reveals generally that due to the lateral inertia effect the group velocities reduce. However, the specific damping capacities are observed to increase, for relatively high-frequency values. The dispersive characteristics that describe by the ratio of the group velocity to the phase velocity are also determined.