Nonlinear traveling wave propagation in a Neo-Hookean cylindrical rod with torsional eigenstrain. (April 2020)

• Record Type: Journal Article
• Authors: Motaghian, Seyedemad; Rahimian, Mohammad
• Is Part Of: International journal of non-linear mechanics. Volume 120(2020)
• Publication Date: 2020-04
• Subjects: Nonlinear traveling waves -- Cylindrical rod -- Torsional eigenstrain -- Riemannian manifold; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2020.103411
• Languages: English
• ISSNs: 0020-7462

Abstract

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.