A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems
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Publication:781960
DOI10.1016/j.jcp.2020.109477zbMath1437.65074OpenAlexW3021356918WikidataQ118359389 ScholiaQ118359389MaRDI QIDQ781960
Christophe Vergez, Arnaud Lazarus, Louis Guillot, Bruno Cochelin, Olivier Thomas
Publication date: 21 July 2020
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109477
Floquet multipliersbifurcationsharmonic balance methodasymptotic numerical methodHill's methodbackbone curvequadratic nonlinearities recaststability analysis of periodic solutions
Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Numerical investigation of stability of solutions to ordinary differential equations (65L07)
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Cites Work
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- A harmonic-based method for computing the stability of periodic solutions of dynamical systems
- Nonlinear vibrations of free-edge thin spherical shells: experiments on a \(1:1:2\) internal resonance
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
- Computational formulation for periodic vibration of geometrically nonlinear structures. I: Theoretical background. II: Numerical strategy and examples
- Continuation of periodic orbits in conservative and Hamiltonian systems
- Discrete dynamical stabilization of a naturally diverging mass in a harmonically time-varying potential
- On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models
- A Taylor series-based continuation method for solutions of dynamical systems
- Nonlinear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance
- Galerkin's procedure for nonlinear periodic systems
- Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances
- Spectral characteristics and eigenvalues computation of the harmonic state operators in continuous-time periodic systems
- The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
- A path-following technique via an asymptotic-numerical method
- Control of time-periodic systems
- On a periodically forced, weakly damped pendulum. Part 3: Vertical forcing
- Modal Interactions in Dynamical and Structural Systems
- Normal Modes for Non-Linear Vibratory Systems
- Non-Linear Free Vibrations of Beams By the Finite Element and Continuation Methods
- Asymptotic–numerical methods and Pade approximants for non‐linear elastic structures
- The asymptotic-numerical method: an efficient perturbation technique for nonlinear structural mechanics
- NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
- Solutions With Bifurcation Points For Free Vibration Of Beams: An Analytical Approach
- Floquet Theory as a Computational Tool
- The Nonlinear Accelerator and the Persistence of Business Cycles
- Perturbed bifurcation theory
- On monodromy matrix computation
