Dynamics of elastic electrically conducting shells in constant and non- stationary magnetic fields (Q581115)

A system of nonlinear equations of the electromechanics of thin elastic shells of finite conductivity is obtained by the asymptotic integration of Maxwell equations (in the quasistationary approximation) and the equations of the theory of elasticity by using the relative half- thickness \(\eta\) as a small parameter. It is shown how two of their fundamental linear limit forms corresponding to two known classes of problems: 1) determining the influence of a permanent magnetic field on the free vibrations of elastic shells, and 2) the determination of the shell deformation due to ponderomotive forces caused by eddy currents indiced by alternating magnetic fields, can be obtained from these equations by neglecting asymptotically small terms. A system of boundary conditions is given, and initial conditions for certain of the problems. Deductions are made from an analysis of the asymptotic accuracy about the limit of applicability of the equations obtained. It is shown that the accuracy of any linear equations corresponding to problems 1 or 2 cannot be greater than O(\(\eta)\).