A direct approach for simplifying nonlinear systems with external periodic excitation using normal forms

<i>Theory of Ordinary Differential Equations</i>

Earl A. Coddington, Norman Levinson, T. Teichmann · Physics Today · 1956 · 6.3K citations

Natural Sciences, Mathematics, Differential Equations +6

Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures

Cyril Touzé, Marco Amabili · Journal of Sound and Vibration · 2006 · 221 citations · Full text

Engineering, Mathematics, Mechanical Engineering +14

Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes

Cyril Touzé, Olivier Thomas, A. Chaigne · Journal of Sound and Vibration · 2003 · 199 citations

Engineering, Mechanical Engineering, Structural Dynamics +15

Analysis of non-linear dynamical systems by the normal form theory

L. Jézéquel, Claude‐Henri Lamarque · Journal of Sound and Vibration · 1991 · 175 citations

Natural Sciences, Mathematics, Physics +10

Normal forms for nonlinear vector fields. I. Theory and algorithm

Leon O. Chua, Hiroshi Kokubu · IEEE Transactions on Circuits and Systems · 1988 · 81 citations

Natural Sciences, Mathematics, Differential Equations +8