Abstract
Alternating or rotating magnetic fields are often used to stir, shape and support masses of liquid metal. The periodic electromagnetic force may parametrically excite growing disturbances which can be beneficial or detrimental to the process, and the aim of this paper is to develop the analysis of such effects. In many cases parametric excitation is described by a system of coupled simple harmonic oscillators with small periodic forcing and damping terms, and we use Floquet theory to derive a recursion formula for a matrix whose eigenvalues determine the growth rates. We consider two applications in detail – low-frequency magnetic stirring in a circular tank and the instability of a free-surface in the presence of an alternating field.
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