000001796 001__ 1796
000001796 005__ 20141118153454.0
000001796 04107 $$acze
000001796 046__ $$k2010-05-10
000001796 100__ $$aNáprstek, J.
000001796 24500 $$aDynamic stability and post-critical processes of pendulum related auto-parametric systems

000001796 24630 $$n16$$pEngineering Mechanics 2010
000001796 260__ $$bInstitute of Thermomechanics AS CR, v.v.i., Prague
000001796 506__ $$arestricted
000001796 520__ $$2eng$$aMany structures encountered in civil, mechanical, naval or aerospace engineering can show properties of auto-parametric systems. The general mathematical structure of the basic and generalized auto-parametric non-linear systems is formulated in the paper. Their internal structure and principal attributes are investigated. The aim of this study is to point out two special classes of auto-parametric systems, which are related on the level of mathematical analogy with spherical or inverse pendulum respectively. Very different character demonstrate both classes from the viewpoint of the semi-trivial solution and subsequent post-critical states. The existence and stability of the semi-trivial solution is analyzed. Individual types of post-critical states are discussed (limit cycles, quasi-periodic response types, chaotic processes, transition processes). General considerations are demonstrated on particular DDOF and MDOF cases in both classes mentioned above. Sensitivity of several systems to stability loss with respect to their parameters, excitation amplitudes and other factors are evaluated. Bifurcation mechanism and diagrams are developed and analyzed. Important transition effects together with physical interpretation are investigated. Some open problems and possible future research strategy are outlined.

000001796 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000001796 653__ $$a

000001796 7112_ $$aEngineering Mechanics 2010$$cSvratka (CZ)$$d2010-05-10 / 2010-05-13$$gEM2010
000001796 720__ $$aNáprstek, J.$$iFischer, C.
000001796 8560_ $$ffischerc@itam.cas.cz
000001796 8564_ $$s3464204$$uhttps://invenio.itam.cas.cz/record/1796/files/Naprstek-022-PT.pdf$$y
             Original version of the author's contribution as presented on CD, KEY.
            
000001796 962__ $$r1750
000001796 980__ $$aPAPER