Vibrating String in A Magnetic Field

Abstract

Conventional devices in which large magnetic fields and electric currents are present include switches, motors, electromagnets and more complicated structures. Also, in certain modern technical equipment such as MHD-devices and fusion reactors, a large magnetic field is applied. In the design of these devices the problem of vibration and stability plays an important role. As an example of the behavior of these structures, a vibrating string carrying electric current and situated in a parallel uniform magnetic field is considered. In general, an electromagnto-elastic problem is governed by the Maxwell equations, the Navier equation of motion, the constitutive equations and, finally, the electromagnetic and mechanical boundary conditions. After stating the basic theory, the nonlinear set of equations is linearized with respect to an intermediae equilibrium state. The string problem, when the self-magnetic field and the changes in electric current due to motion of the string are taken into account, is investigated in detail and the results are discussed.