Nonlinear waves in thermo-magnetoelasticity I. Basic equations

Article type: Research Article

Authors: Ghaleb, A.F.^{a; *} | Ayad, M.M.^a

Affiliations: [a] Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544, USA

Correspondence: [*] Corresponding author. On leave from Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.

Abstract: A complete set of field equations, constitutive relations and boundary conditions is derived in material form, within the framework of rigorous thermodynamics, to study the nonlinear thermo‐magnetoelastic interactions in anisotropic continuous media for which the specific heat capacity depends on strain and magnetic field. The proposed model includes several other couplings as well and may be considered as a refinement of other existing models. When the medium has finite electric conductivity, it is appropriate to represent the electromagnetic field in terms of the electromagnetic potentials. This has the advantage of reducing the number of field equations. The special case of the perfect electric conductor is briefly mentioned and the linear theory for the isotropic medium of finite electric conductivity is investigated. Comparison is carried out with previous results. The bilinear theory and the propagation of surface regimes and surface magnetoacoustic waves will be dealt with separately.

DOI: 10.3233/JAEM-1998-093

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 9, no. 4, pp. 339-357, 1998