NONLINEAR MAGNETOTHERMOELASTICITY OF ANISOTROPIC PLATES IMMERSED IN A MAGNETIC FIELD

Abstract

A geometrically nonlinear theory of magnetothermoelasticity of electroconductive anisotropic plates in a magnetic field is developed. In this context, the Kirchhoff hypothesis is adopted for the plate modeling and the geometrical nonlinearities are considered in the von Kármán sense. In addition, the assumptions related to the distribution of electric and magnetic field disturbances through the plate thickness as proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e., the ones by Faraday, Ampère, Ohm, Maxwell, and Lorentz), on the modified Fourier law of heat conduction, and elastokinetic field equations, the three-dimensional coupled problem is reduced to an equivalent two-dimensional one appropriate to the theory of plates. The theory developed herein enables one to investigate the interacting effects among the magnetic, thermal, and elastic fields in orthotropic thin plates. As a special case, the problem of the free vibration of simply supported plate strips immersed in a transversal magnetic field is considered. Effects of the directionality property of the constituent material, magnetic and temperature fields, and electric conductivity, as well as thermal expansion coefficients, on the characteristics of vibrational behavior of the plate strips are investigated.