Branch switching at Hopf bifurcation analysis via asymptotic numerical method: application to nonlinear free vibrations of rotating beams

DOI10.1016/j.cnsns.2014.09.001zbMath1417.37273OpenAlexW2056771701MaRDI QIDQ907641

Laëtitia Duigou, J. M. Cadou, Ferhat Bekhoucha, Said Rechak

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.09.001

zbMATH Keywords

Galerkin methodfrequency domainHopf bifurcationbranch switchingnonlinear free vibration

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Bifurcations of singular points in dynamical systems (37G10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (2)

Analysis of internal resonance in a two-degree-of-freedom nonlinear dynamical system ⋮ Bifurcation analysis of the HIV-1 within host model

Cites Work

• Automatic detection and branch switching methods for steady bifurcation in fluid mechanics
• Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier-Stokes equations
• A direct method for the characterization and computation of bifurcation points with corank 2
• Bifurcation theory. An introduction with applications of PDEs
• A numerical continuation method based on Padé approximants
• Nonlinear free vibration of isotropic plates with internal resonance
• Regularization and computation of a bifurcation problem with corank 2
• On Timoshenko-like modeling of initially curved and twisted composite beams.
• A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams
• Practical bifurcation and stability analysis
• Energy-consistent, Galerkin approach for the nonlinear dynamics of beams using intrinsic equations
• The Computation of Symmetry-Breaking Bifurcation Points
• Nonlinear Vibrations and Stability of Shells and Plates
• The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
• Vibration Modes of Centrifugally Stiffened Beams
• Natural frequencies of radial rotating beams
• Méthodes asymptotiques numériques pour la plasticité
• Non-Linear Free Vibrations of Beams By the Finite Element and Continuation Methods
• Asymptotic–numerical methods and Pade approximants for non‐linear elastic structures
• Mathematical and numerical connections between polynomial extrapolation and Padé approximants: applications in structural mechanics
• Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

This page was built for publication: Branch switching at Hopf bifurcation analysis via asymptotic numerical method: application to nonlinear free vibrations of rotating beams