Stability and bifurcations of a stationary state for an impact oscillator

Aidanpää, Jan-Olov (author): Luleå tekniska universitet,Material- och solidmekanik

Shen, Hayley H. (author): Department of Civil and Environmental Engineering, Clarkson university

Gupta, Ram B. (author): Division of Solid Mechanics, School of Engineering, Uppsala University

(creator_code:org_t)

AIP Publishing, 1994
1994
English.
In: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 4:4, s. 621-630

Related links:: https://urn.kb.se/re...; show more...; https://doi.org/10.1...; show less...

Abstract Subject headings

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

About the subject

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Mechanical Engin ...; and Applied Mechanic ...

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.