Nonlinear traveling wave propagation in a Neo-Hookean cylindrical rod with torsional eigenstrain. (April 2020) - Motaghian, Seyedemad; Rahimian, Mohammad
Abstract: This paper investigates the torsional and longitudinal traveling wave propagation through a cylindrical rod with torsional eigenstrain distribution. We derive three dynamic equilibrium equations of axisymmetric motion of a rod which is assumed to be composed of an incompressible, isotropic neo-Hookean solid and then reduce them to one nonlinear differential equation. Employing phase plane analysis, we solve and assess this equation, and accordingly determine all smooth and non-smooth waves. We also examine the effects of torsional eigenstrain on the shapes and velocities of traveling waves. We show that a new type of traveling wave, which is not seen in a normal rod, arises due to the eigentwist. Moreover, we demonstrate that in a cylindrical rod with eigentwist, a torsional traveling wave is always associated with a longitudinal one while it can propagate alone in a normal rod. Highlights: A new shape of traveling wave is generated due to the torsional eigenstrain. A torsional traveling wave is always associated with each longitudinal one. The torsional eigenstrain affects the wave velocity. A double region of eigentwist can increase the effects on the wave velocity. The waves at the limits of the torsional wave velocity are investigated.