Drgania Prętów na Ruchomych Podporach

A consideration of transverse vibration of a bar rotating on three supports moving with constant velocity along the axis. The solution of the equation of vibration is obtained by finding the eigenvalues and the eigenfunctions. As a result of analysis of the equation of vibration, an equation is obtained for critical velocities depending on the velocity of support displacement. From this equation it follows that with a moving intermediate support the critical velocities are less than the critical velocities of a rotating bar on two supports.
The method described may be generalized to any number of supports of which the two extreme ones are immobile.