DAMPING OF OSCILLATIONS OF SHELLS BY WEAK MAGNETIC FIELDS.

The problem of free oscillations of thin elastic shells in a vacuum (s-problem) has a real spectrum of eigenvalues, that defines oscillations without attenuation in time. The problem of oscillations of shells made of electrically conducting materials in a stationary magnetic field (sm-problem) has a complex spectrum, and the corresponding oscillations attenuate in time. In this paper we investigate the sm-problem and we determine the effect of weak magnetic fields (the concept of weak is made more specific) on the solutions of the s-problem. Our emphasis is on the estimation of the imaginary parts of the eigenvalues, which govern the attenuation of oscillations in the sm-problem. All the general results of the paper are equally valid for shells and plates.