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Metastability and chaoslike phenomena in nonlinear dynamic buckling of a simple two-mass system under step load

Metastabilität und chaosähnliche Phänomene des nichtlinearen dynamischen Knickens eines einfachen Zwei-Masse-Systems unter Treppenlast

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Summary

The nonlinear dynamic buckling based on the global response of a nonlinear autonomous dissipative or non-dissipative system with two degrees of freedom is studied in detail. Attention is focused on the unstable branch of the complementary path whose significant role on the mechanism of dynamic buckling is revealed for the first time in the literature. Theoretical results associated with distinct properties of the Jacobian matrix, verified and supplemented numerically, brought into light various new phenomena for certain values of the control parameter such as dynamic buckling of statically stable systems, metastability phenomena for loads much higher than the dynamic buckling loads, and sensitivity to initial conditions and to damping.

Übersicht

Anhand der globalen Antwort eines autonomen, dissipativen oder nicht-dissipativen Systems mit zwei Freiheitsgraden auf eine stufenförmige Last werden detaillierte Studien zum nichtlinearen dynamischen Knicken angestellt. Die Betrachtung richtet sich besonders auf den instabilen Zweig des komplementären Lastpfades, dessen Bedeutung für das dynamische Knicken hier zum ersten Mal aufgezeigt wird. Die theoretischen und numerischen Ergebnisse, die mit bestimmten Eigenschaften der Jacobi-Matrix verknüpft sind, enthüllen für bestimmte Werte des Kontrollparameters verschiedene neue Phänomene wie das dynamische Knicken von statisch stabilen Systemen, Metastabilität für Lasten weit über der dynamischen Knicklast und Empfindlichkeit auf Anfangsbedingungen und Dämpfung.

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Authors and Affiliations

  1. Structural Analysis and Steel Bridges, National Technical University of Athens, 42, Patission Str., 10682, Athens, Greece

    N. Kalathas (Graduate student)

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  1. N. Kalathas
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Kalathas, N. Metastability and chaoslike phenomena in nonlinear dynamic buckling of a simple two-mass system under step load. Arch. Appl. Mech. 61, 162–173 (1991). https://doi.org/10.1007/BF00788050

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