Dynamic stability of shaft loaded with axial compression and magnetic tension

The analysis of dynamic stability of shaft loaded with magnetic tension and axial compression has been presented. In order to estimate the stability of radial motion of the shaft, the equations of its transverse vibration have been formulated. On the basis of equations of motion the differential equations, connecting the dynamic deflection of shaft with space and time, have been obtained. Partial differential equations were solved by using the method of separation of variables (Fourier’s method). Then the ordinary differential equation, describing the vibration of shaft in time, has been solved and the characteristic equation has been drawn. The analysis of solution of this equation becames the basis for estimating the free vibrations frequency of the shaft. Subsequently the critical values of magnetic tension and of axial load have been determined.