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Dynamical stability of a viscoelastic bar
Author(s) -
Wójcicki Zbigniew,
Brza̧kała Aneta
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610408
Subject(s) - floquet theory , ordinary differential equation , bar (unit) , viscoelasticity , mathematical analysis , differential equation , parametric statistics , stability (learning theory) , homogeneous differential equation , parametric oscillator , mathematics , partial differential equation , physics , differential algebraic equation , thermodynamics , computer science , statistics , quantum mechanics , nonlinear system , machine learning , meteorology , optics
In the paper the dynamic stability of a simply supported viscoelastic bar of the Zener material model is investigated. The bar is subjected to a parametric excitation of a periodic nature. The physical model of the system is of the continuous type. However, the proposed approach yields a transformation of the mathematical model from the partial differential equation to an ordinary one. Such a transformation is made possible by the use of an approximation function for the bending line of the bar. This way, the system is governed by a homogeneous, ordinary differential equation of the third order with periodic coefficients. For stability studies the Floquet theory is applied. A sensitivity analysis of a parametric periodic system is discussed, i.e. the influence of stiffness and damping coefficient of the Zener model on stability of the differential equation that describes the vibration of the viscoelastic bar. Furthermore the stabilization process of an unstable parametric system was realized. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)