Year: 2025
Type: article
Abstract: Kirchhoff’s kinetic analogy relates the equilibrium solutions of an elastic rod or strip to the motion of a spinning top. In this analogy, time is replaced by the arc length parameter in the phase portrait to determine the equilibrium configurations of the rod. Predicted equilibrium solutions from the phase portrait for specific boundary value problems, as well as certain localized solutions, have been experimentally observed. In this study, we employ the kinetic analogy to investigate the equilibrium solutions of planar soft ferromagnetic rods subjected to transverse and longitudinal external magnetic fields. Our analysis reveals a subcritical pitchfork bifurcation in the phase portrait of a ferromagnetic rod subjected to a transverse external magnetic field as the axial load is decreased continuously from a large compressive load. Similarly, a supercritical pitchfork bifurcation is observed in the case of a longitudinal external magnetic field. We predict equilibrium configurations for a free-standing soft ferromagnetic elastic rod and the same subjected to canonical boundary conditions. Furthermore, we observe novel localized equilibrium solutions arising from homoclinic and heteroclinic orbits, which are absent in the phase portraits of purely elastic rods.
Source: Journal of Applied Mechanics
DOI: 10.1115/1.4068252
Institution: Indian Institute of Science Bangalore
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Indian Institute of Science
OpenAlex ID: W4408652268