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Classical Results and Modern Approaches to Nonconservative Stability

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Dynamic Stability and Bifurcation in Nonconservative Mechanics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 586))

Abstract

Stability of nonconservative systems is nontrivial already on the linear level, especially, if the system depends on multiple parameters. We present an overview of results and methods of stability theory that are specific for nonconservative applications. Special attention is given to the topics of flutter and divergence, reversible- and Hamiltonian-Hopf bifurcation, Krein signature, modes and waves of positive and negative energy, dissipation-induced instabilities, destabilization paradox, influence of structure of forces on stability and stability optimization.

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  1. Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom

    Oleg N. Kirillov

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  1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy

    Davide Bigoni

  2. Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, United Kingdom

    Oleg Kirillov

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Kirillov, O.N. (2019). Classical Results and Modern Approaches to Nonconservative Stability. In: Bigoni, D., Kirillov, O. (eds) Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences, vol 586. Springer, Cham. https://doi.org/10.1007/978-3-319-93722-9_4

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