Physical and mathematical models of shafts in drives withHook´s joints

The torque of drive vehicles is transmitted at relatively large distances. When dimensioning to the torsion under static and cyclic load, shafts are in many cases long, slender, and are susceptible to bending vibrations. The shafts must be checked not only to torsion, but also to bending in terms of shaft´s modal and spectral properties. The paper formulated a mathematical model of an one-dimensional linear continuum in a state of bending-gyratory vibration. It is performed an analytical solution of natural frequencies relative lateral vibration and it is analyzed the influence of a rotating shaft to spectrum of natural frequencies section of the continuum, that form the basis of shaft´s physical model when calculating its natural and forced vibration.