An Upper bound for validity limits of asymptotic analytical approaches based on normal form theory

DOI10.1007/S11071-012-0584-YzbMath1268.34070OpenAlexW2094358046MaRDI QIDQ354550

Olivier Thomas, Claude-Henri Lamarque, Cyril Touzé

Publication date: 19 July 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0584-y

zbMATH Keywords

perturbation methodsnormal form theorynonlinear normal modesupper bound of validity limit

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (9)

A normal form analysis in a finite neighborhood of a Hopf bifurcation: on the center manifold dimension ⋮ Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect ⋮ A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness ⋮ Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators ⋮ 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 ⋮ Bifurcation of limit cycles, classification of centers and isochronicity for a class of non-analytic quintic systems ⋮ On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models ⋮ Using frequency detuning to compare analytical approximations for forced responses

Uses Software

• ManLab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A harmonic-based method for computing the stability of periodic solutions of dynamical systems
• Reduced-order models for large-amplitude vibrations of shells including in-plane inertia
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Singularities and groups in bifurcation theory. Volume I
• A simple global characterization for normal forms of singular vector fields
• Global characterization of the normal form for a vector field near a closed orbit
• Applications of centre manifold theory
• Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
• Singularities and groups in bifurcation theory. Volume II
• Nonlinear dynamics of a beam on elastic foundation
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• ON THE COMPUTATION OF THE COEFFICIENTS ASSOCIATED WITH HIGH ORDER NORMAL FORMS
• Applying the method of normal forms to second-order nonlinear vibration problems
• Amplitude Equations for Systems with Competing Instabilities
• Normal Modes for Non-Linear Vibratory Systems
• Averaging methods in nonlinear dynamical systems

This page was built for publication: An Upper bound for validity limits of asymptotic analytical approaches based on normal form theory