Solitary waves in magnetostrictive circular rods with temperature effect

Abstract

A simple nonlinear model is constructed in this paper to study the solitary wave in an infinite circular magnetostrictive rod. Based on the constitutive relations for transversely isotropic magnetostrictive materials, considering the coupling of multiphysics, combined with Hamilton’s principle and Euler equation, the longitudinal wave equation (LWE) of the infinite circular rod is obtained. The nonlinearity considered is geometrically associated with the nonlinear normal strain in the longitudinal rod direction. The transverse Poisson’s effect is included by introducing the effective Poisson’s ratio. Solitary wave solution, non-topological bell-type soliton and singular periodic solutions of the LWE are obtained by the [Formula: see text]-expansion method. By using the reductive perturbation method, we derive the KdV equation, furthermore, the two-solitary solution is obtained. Numerical analysis results show that the increase of the magnetic field intensity or temperature will reduce the solitary wave’s propagation velocity. As the wave velocity ratio increases, the wave amplitude gradually increases; when the coupled physics parameter and the wave velocity ratio are constant, the increase of the dispersion parameter will make the wavelength longer. The dynamic behavior of the two-soliton solution in the magnetostrictive rod exhibits nonlinear superposition and has elastic collision characteristics.