Nonlinear vibration of thermo-elastic plates in a magnetic field

Abstract

This chapter presents a geometrically nonlinear theory of electromagnetically conducting orthotropic flat plates exposed to a thermo-magnetic field. Based on the electromagnetic equations—by Faraday, Ampere, Ohm, Maxwell and Lorentz—the modified Fourier's law of heat conduction and elastokinetic field equations, the 3D coupled problem is reduced to an equivalent 2D one, appropriate to the theory of plates. In the modeling of the plate, the geometric nonlinearities are incorporated. While the elastic, thermal and electromagnetic fields can be determined from the elasticity, thermal and Maxwell equations, the superposition of these three fields generate, via their interaction, a new phenomena between each other. The electromagnetic field influences the thermo-elastic field by entering the elastic stress equations of motion as the magnetic body forces (Lorentz's ponderomotive force), whereas the elastic and thermal fields influence the electromagnetic field by modifying the Ohm's law.