On the problem of vibrations of non-linear-elastic electroconductive plates in transverse and longitudinal magnetic fields

Non-linear cylindrical-form vibrations of an electroconductive plate-strip in longitudinal and transverse magnetic fields are considered. For the plate material a non-linear relationship between stress and deformation is accepted. On the basis of the known hypotheses and assumptions the general system is reduced to one equation for the normal displacement of the plate. Using the Bubnov-Galerkin method and the method of asymptotic integration, the amplitude-frequency characteristics of vibrations are defined. On the basis of numerical analysis different degrees of the influence of various factors (non-linearity, magnetic field, conductivity, etc.) on the nature of vibrations are compared. Qualitative and quantitative differences between the nature of vibrations in longitudinal and transverse magnetic fields are revealed.