Wave dispersion and attenuation in viscoelastic polymeric bars: Analysing the effect of lateral inertia

Elementary one-dimensional wave theory is often used to describe the propagation of longitudinal stress waves in polymer rods. More accurate solutions are available, but they are mathematically difficult. A new wave equation is derived for long polymeric rods in this paper. The material properties are modelled as a Maxwell viscoelastic material acting in parallel with an elastic material. Lateral motions of the rod that result from the Poisson effect are accounted for using a new concept called the “effective density”. The effects of both the material properties and the diameter of the bar on dispersion and attenuation coefficients are highlighted. The new wave theory simplifies to the one-dimensional solution for waves in polymer rods if the Poisson ratio is set to zero. The predictions simplify to Love's equation for stress waves in elastic bars when rate dependency is removed from the material model.