Modelling of the Colliding Process Between
                a Viscoelastic Bar and a Rigid Barrier

                       Yuriy A. Rossikhin
                       Maxim A. Kolesnikov
                       Marina V. Shitikova

     Department of Theoretical Mechanics
     Voronezh State Academy of Construction and Architecture
     ul. Kirova 3-75, Voronezh 394018, Russia
     Tel/Fax: + 7-0732-773992,
     E-mail: MVS@vgasa.voronezh.su

     The  impact  of  a  viscoelastic  bar  moving along its axis upon a rigid
barrier   is   investigated.  The  generalized  standard  linear  solid  model
involving  fractional derivatives of two different orders is used as the model
describing  the  viscoelastic properties of the bar's material. The problem is
solved  by the Laplace integral transformation method, however, as distinct to
traditional  numerical approaches, it has been possible to obtain the solution
in  the analytical form during the transition from image to pre-image. This is
connected  with the fact that the characteristic equation involving fractional
powers  is  not  rationalized,  but  it is solved directly with the fractional
powers.  The  solution obtained is valid as long as the bar is in contact with
the  barrier,  i.e.  the  contact  stress  in  the  bar  is  nonzero. The time
dependence of the contact stress in the bar has been obtained and analyzed for
various  magnitudes  of  the  rheological parameters: the orders of fractional
derivatives,  the average time of relaxation (retardation), and the modulus of
imperfection.  The  emphasis  has been made on the influence of temperature on
the  duration  of  contact  of the viscoelastic bar with the rigid wall, in so
doing  the temperature dependence of the relaxation time has been determined
by  the  Arrenius  formula. As investigations show, the bar does not adhere to
the wall at any magnitudes of the rheological parameters, i.e. the bar bounces
back from the rigid barrier at any temperature.