The use of normal forms for analysing nonlinear mechanical vibrations

DOI10.1098/rsta.2014.0404zbMath1353.70052OpenAlexW1733229080WikidataQ42180729 ScholiaQ42180729MaRDI QIDQ2955805

T. L. Hill, A. Cammarano, Simon A. Neild, David J. Wagg, Alan R. Champneys

Publication date: 13 January 2017

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rsta.2014.0404

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Dynamical systems in classical and celestial mechanics (37N05) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (14)

Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems ⋮ Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations ⋮ Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction ⋮ Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective ⋮ Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect ⋮ Linear and nonlinear modal analysis of the axially moving continua based on the invariant manifold method ⋮ Identifying the significance of nonlinear normal modes ⋮ Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators ⋮ Identifying phase-varying periodic behaviour in conservative nonlinear systems ⋮ Comparing the direct normal form and multiple scales methods through frequency detuning ⋮ A direct approach for simplifying nonlinear systems with external periodic excitation using normal forms ⋮ Rigorous model reduction for a damped-forced nonlinear beam model: an infinite-dimensional analysis ⋮ Using frequency detuning to compare analytical approximations for forced responses ⋮ ε 2-Order Normal Form Analysis for a Two-Degree-of-Freedom Nonlinear Coupled Oscillator

Uses Software

• AUTO
• AUTO-07P

Cites Work

• An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems
• Nonlinear vibration with control. For flexible and adaptive structures
• Henri Poincaré
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Chaos near resonance
• The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities
• A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness
• Introduction to Perturbation Methods
• Applying the method of normal forms to second-order nonlinear vibration problems
• Existence of nonlinear normal modes of symmetric Hamiltonian systems
• Normal Modes of Vibration for Non-Linear Continuous Systems
• Normal Forms and Unfoldings for Local Dynamical Systems
• Out-of-unison resonance in weakly nonlinear coupled oscillators
• Elements of applied bifurcation theory

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