| Autor: |
Rossikhin, Yu. A., Shitikova, M. V. |
| Předmět: |
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| Zdroj: |
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik; Jun2001, Vol. 81 Issue 6, p363-376, 14p, 1 Diagram, 6 Graphs |
| Abstrakt: |
The problems of longitudinal nonstationary vibrations of a viscoelastic rod of a finite length, the impact of a viscoelastic bar moving along its axis against a rigid barrier, and the stress wave propagation in a semi-infinite viscoelastic rod are investigated. The modified 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, in so doing, as distinct to traditional numerical approaches, the characteristic equation involving fractional powers is not rationalized, but it is solved directly with the fractional powers. The numerical analysis of the enumerated problems is presented. The time dependence of the stress and of the contact stress in the bar corresponding to the first and second problems, respectively, has been obtained and analyzed for various magnitudes of the rheological parameters: the orders of fractional derivatives and the relaxation time. As investigations show, the bar does not adhere to the wall at any magnitudes of the rheological parameters. The asymptotic solutions for the problem of stress wave propagation have been obtained in the vicinity of the wave front and at small magnitudes of time. It is shown that the given model can describe both diffusive and wave phenomena occurring in viscoelastic materials. All is dependent on a relation between the orders of the derivatives standing at the left hand side and right hand side of the rheological equation. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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