Large Rotatory Oscillations of Transversely Isotropic Rods: Spatio-Temporal Symmetry-Breaking Bifurcation

DOI10.1137/0152066zbMath0756.34040OpenAlexW2024289390MaRDI QIDQ4018869

Timothy J. Healey

Publication date: 16 January 1993

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0152066

zbMATH Keywords

continuum mechanicsnonlinear vibrationinitially straightnonlinearly elastic Cosserat curvetime-periodic motionstransversely isotropic cantilever rods

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear boundary value problems for ordinary differential equations (34B15) Nonlinear elasticity (74B20) Bifurcation theory for ordinary differential equations (34C23) Vibrations in dynamical problems in solid mechanics (74H45) Crystalline structure (74E15) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Nonlinear dynamics in mechanics (70K99) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

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A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell ⋮ Computation of elastic equilibria of complete Möbius bands and their stability ⋮ A group-theoretic approach to the geometry of elastic rings

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