A few results on the foundation of the theory and behavior of nonlinear magnetoelastic plates carrying an electrical current

Abstract

A fully nonlinear theory of electromagnetically conducting flat plates carrying an electric current and exposed to a magnetic field of an arbitrary orientation is developed. It is assumed that the electric current vector J is parallel to the plate mid-plane, and of arbitrary direction in the plane. It is also assumed that both the elastic and the electromagnetic media are homogeneous and isotropic. The geometrical nonlinearities are considered in the von-Kármán sense, and the soft ferromagnetic material of the plate is assumed to feature negligible hysteretic losses. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampère, Ohm, Maxwell and Lorentz), and on elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2-D one. In this context, by using the presently developed theory, the problem of the loss of stability of plates carrying an electric current is investigated. The possibilities of enhancing their electric current carrying capacity are discussed. In the same context, the problem of the free vibration of flat plates as influenced by the electrical current and magnetic field is also addressed.