The viscoelastic stress wave propagation model based on fractional derivative constitutive

Abstract

The study of stress wave propagation in viscoelastic bars is important for the dynamic mechanical property testing of low-impedance materials. For the propagation of stress waves in viscoelastic bars, it is significant to consider the lateral inertia effects and viscous effects on wave propagation. This paper establishes a viscoelastic stress wave propagation model based on fractional derivative constitutive. The analytical solution of the viscoelastic wave equation based on the fractional derivative constitutive model is obtained. The model employs fractional derivative viscoelastic constitutive relations instead of traditional standard mechanical viscoelastic models and is capable of describing the lateral inertia effects and viscoelastic effects on stress wave propagation. While the Poisson's ratio is zero, the model simplifies to a viscoelastic stress wave propagation model that does not account for lateral inertia effects. In this paper, the material parameters of polymethylmethacrylate (PMMA) are obtained by Dynamic Mechanical Analysis (DMA) test, and the attenuation coefficient and phase velocity change with frequency are calculated by this model.