Bifurcations and internal resonances in space-curved rods
DOI10.1016/S0045-7825(02)00263-3zbMath1039.74022OpenAlexW2097190034MaRDI QIDQ1858469
Publication date: 13 February 2003
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0045-7825(02)00263-3
Galerkin methodnonlinear eigenvalue problemcontinuation methodsTimoshenko modelshear effectscircular arches
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Dynamical bifurcation of solutions to dynamical problems in solid mechanics (74H60)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A finite strain beam formulation. The three-dimensional dynamic problem. I
- A three-dimensional finite-strain rod model. II. Computational aspects
- On finite deformations of space-curved beams
- Computational formulation for periodic vibration of geometrically nonlinear structures. I: Theoretical background. II: Numerical strategy and examples
- Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids. I: Beam concept and geometrically exact nonlinear formulation. II: Anisotropic and advanced beam models
- An excursion into large rotations
- Evaluation of simple bifurcation points and post-critical path in large finite rotation problems
- Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
- Rotation angles
- Application of the Ritz method to the analysis of non-linear free vibrations of beams
- The role of non-linear theories in transient dynamic analysis of flexible structures
- A POWER SERIES SOLUTION FOR THE NON-LINEAR VIBRATION OF BEAMS
- NORMAL MULTI-MODES OF NON-LINEAR EULER BEAMS
- HARMONIC BALANCE AND CONTINUATION TECHNIQUES IN THE DYNAMIC ANALYSIS OF DUFFING'S EQUATION
- Non-linear vibration of frames by the incremental dynamic stiffness method
- On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I
- A fast incremental/iterative solution procedure that handles “snap-through”
- Interpolation of rotational variables in nonlinear dynamics of 3D beams
- A three‐dimensional non‐linear Timoshenko beam based on the core‐congruential formulation
- Bifurcations and chaos in a quasi-periodically forced beam: theory, simulation and experiment
- Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
- Non‐linear dynamics of three‐dimensional rods: Exact energy and momentum conserving algorithms
- Shear flexible field-consistent curved spline beam element for vibration analysis
- Non‐linear steady state vibration of frames by finite element method
This page was built for publication: Bifurcations and internal resonances in space-curved rods