P-positive definite matrices and stability of nonconservative systems

DOI10.1002/zamm.201100055zbMath1321.74029OpenAlexW2107343934MaRDI QIDQ2888897

Florent Prunier, Marwa Aldowaji, Noël Challamel, François Nicot, Jean Lerbet, Félix Darve

Publication date: 4 June 2012

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201100055

zbMATH Keywords

bifurcation problemkinematic constraintssecond-order work criterion

Mathematics Subject Classification ID

Stability of dynamical problems in solid mechanics (74H55) Positive matrices and their generalizations; cones of matrices (15B48) Dynamical bifurcation of solutions to dynamical problems in solid mechanics (74H60)

Related Items (11)

A paradigmatic minimal system to explain the Ziegler paradox ⋮ Kinematical structural stability ⋮ Second-order work criterion: from material point to boundary value problems ⋮ Standard and helical magnetorotational instability ⋮ Coordinate free nonlinear incremental discrete mechanics ⋮ On the stability of nonconservative continuous systems under kinematic constraints ⋮ 3-dimensional flutter kinematic structural stability ⋮ Divergence instability of kinematically constrained Hencky chains: Analytic results and asymptotic behavior ⋮ Variational formulation of divergence stability for constrained systems ⋮ Geometric degree of nonconservativity: set of solutions for the linear case and extension to the differentiable non-linear case ⋮ Second-order work criterion and divergence criterion: a full equivalence for kinematically constrained systems

Cites Work

• ABOUT THE STABILITY OF NONCONSERVATIVE UNDAMPED ELASTIC SYSTEMS: SOME NEW ELEMENTS
• Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?
• The Geometry of Algorithms with Orthogonality Constraints
• [https://portal.mardi4nfdi.de/wiki/Publication:5813729 Die Stabilit�tskriterien der Elastomechanik]

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