ИСТИНА

The problem of stability of elastic webs moving axially with constant velocities and performing separately different types of free vibrations (torsional, longitudinal and transverse) is studied. To this purpose, a narrow thin elastic web moving axially between rollers and modelled by a continuous one-dimensioned elastic element (rod) having rectangular cross-section of given width and thickness is considered. All considered types of free vibrations of small amplitude are described by a general second-order constant-coefficient partial differential equation. This equation is always hyperbolic for all considered cases regardless of the value of the axial velocity. This observation reflects the physical nature of the problem: the introduction of axial velocity should not change the basic vibrational nature of the mechanical response. The influence of transport phenomena on stability of the webs moving at critical velocities is discussed. It is shown that the elastic web (rod) if travelling at the critical velocity must stay in a steady-state configuration.