Frontiers in Applied Mathematics and Statistics · 2019 · 30 citations · 34 references
Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or non-linear systems, fluid-solid interaction, follower forces, etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler paradox on the destabilizing effect of small damping is also included.
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Ali H. Nayfeh, Dean T. Mook, Phillip Holmes · Journal of Applied Mechanics · 1980 · 4.7K citations
AUTO-07p: Continuation and bifurcation software for ordinary differential equations
Eusebius J. Doedel, Alan Champneys, Fabio Dercole et al. · 2007 · 1.6K citations
Numerical Methods for Scientists and Engineers
T H O'Beirne · Physics Bulletin · 1962 · 363 citations
Numerical Analysis, Weaker Stomachs, Computational Tools +15