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Title: Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations (English)
Author: Málek, Josef
Author: Rajagopal, Kumbakonam R.
Author: Suková, Petra
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 61
Issue: 1
Year: 2016
Pages: 79-102
Summary lang: English
Category: math
Summary: We study the vibration of lumped parameter systems whose constituents are described through novel constitutive relations, namely implicit relations between the forces acting on the system and appropriate kinematical variables such as the displacement and velocity of the constituent. In the classical approach constitutive expressions are provided for the force in terms of appropriate kinematical variables, which when substituted into the balance of linear momentum leads to a single governing ordinary differential equation for the system as a whole. However, in the case considered we obtain a system of equations: the balance of linear momentum, and the implicit constitutive relation for each constituent, that has to be solved simultaneously. From the mathematical perspective, we have to deal with a differential-algebraic system. We study the vibration of several specific systems using standard techniques such as Poincaré's surface of section, bifurcation diagrams, and Lyapunov exponents. We also perform recurrence analysis on the trajectories obtained. (English)
Keyword: chaos
Keyword: differential-algebraic system
Keyword: Poincaré's sections
Keyword: recurrence analysis
Keyword: bifurcation diagram
Keyword: implicit constitutive relations
Keyword: Duffing oscillator
Keyword: Bingham dashpot
Keyword: rigid-elastic spring
MSC: 34A09
MSC: 34C28
MSC: 70K55
idZBL: Zbl 06562148
idMR: MR3455169
DOI: 10.1007/s10492-016-0123-0
Date available: 2016-01-19T14:04:45Z
Last updated: 2018-03-05
Stable URL:
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