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.