Dynamic stability and post-critical processes of pendulum related auto-parametric systems

Abstract eng:
Many 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.

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