Longitudinal Waves in Nonlinear Viscoelastic Rods under Initial Axial Stress

摘要

Longitudinal wave propagation in a semi-infinite rod is considered, where the medium is nonlinear viscoelastic and under constant initial axial stress, i.e., the rod is undergoing axial creep deformation. The deformation gradient is assumed to be infinitesimal, but the deformation itself may be finite. The constitutive law is taken with stress power functions in the elastic, transient creep and steady creep terms. A wave is generated by a step input in velocity or stress at one end of the rod. It is assumed that the initial stress is much greater then the increment of stress generated by the impact and a perturbation technique is employed. Closed form perturbation stress solutions are obtained for five nonlinear viscoelastic models. Numerical examples are given and discussed. (Author)