Complex dynamics of perfect discrete systems under partial follower forces

Sophianopoulos, DS; Kounadis, AN; Vakakis, AF

dc.contributor.author	Sophianopoulos, DS	en
dc.contributor.author	Kounadis, AN	en
dc.contributor.author	Vakakis, AF	en
dc.date.accessioned	2014-03-01T01:17:39Z
dc.date.available	2014-03-01T01:17:39Z
dc.date.issued	2002	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14600
dc.subject	Boundary Value Problem	en
dc.subject	Complex Dynamics	en
dc.subject	Discrete System	en
dc.subject	Equilibrium Point	en
dc.subject	Initial Condition	en
dc.subject	Linear Algebra	en
dc.subject	Numerical Simulation	en
dc.subject	Periodic Orbit	en
dc.subject	4 dimensional	en
dc.subject.classification	Mechanics	en
dc.subject.other	Boundary value problems	en
dc.subject.other	Chaos theory	en
dc.subject.other	Computer simulation	en
dc.subject.other	Dynamics	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Discrete systems	en
dc.subject.other	Nonlinear systems	en
dc.title	Complex dynamics of perfect discrete systems under partial follower forces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0020-7462(01)00144-5	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0020-7462(01)00144-5	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Equilibrium points, primary and secondary static bifurcation branches, and periodic orbits with their bifurcations of discrete systems under partial follower forces and no initial imperfections are examined. Equilibrium points are computed by solving sets of simultaneous, non-linear algebraic equations, whilst periodic orbits are determined numerically by solving 2- or 4-dimensional non-linear boundary value problems. A specific application is given with Ziegler's 2-DOF cantilever model. Numerous, complicated static bifurcation paths are computed as well as complicated series of periodic orbit bifurcations of relatively large periods. Numerical simulations indicate that chaotic-like transient motions of the system may appear when a forcing parameter increases above the divergence state. At these forcing parameter values, there co-exist numerous branches of bifurcating periodic orbits of the system; it is conjectured that sensitive dependence on initial conditions due to the large number of co-existing periodic orbits causes the chaotic-like transients observed in the numerical simulations. (C) 2002 Elsevier Science Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.doi	10.1016/S0020-7462(01)00144-5	en
dc.identifier.isi	ISI:000175701800003	en
dc.identifier.volume	37	en
dc.identifier.issue	7	en
dc.identifier.spage	1121	en
dc.identifier.epage	1138	en