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Stability and bifurcations of a stationary state for an impact oscillator
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.ORCID iD: 0000-0001-6016-6342
Department of Civil and Environmental Engineering, Clarkson university.
Division of Solid Mechanics, School of Engineering, Uppsala University.
1994 (English)In: Chaos, ISSN 1054-1500, E-ISSN 1089-7682, Vol. 4, no 4, p. 621-630Article in journal (Refereed) Published
Abstract [en]

The motion of a vibroimpacting one-degree-of-freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass-spring-dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe-like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations

Place, publisher, year, edition, pages
1994. Vol. 4, no 4, p. 621-630
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-4562DOI: 10.1063/1.166039ISI: 000208309000003Local ID: 2877bc10-0bb3-11dd-9b51-000ea68e967bOAI: oai:DiVA.org:ltu-4562DiVA, id: diva2:977436
Note
Godkänd; 1994; 20080416 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Aidanpää, Jan-Olov

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