Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction

A spectral characterization of nonlinear normal modes

(2016) G.I. Cirillo et al.   JOURNAL OF SOUND AND VIBRATION

Numerical computation of nonlinear normal modes in mechanical engineering

(2016) L. Renson et al.   JOURNAL OF SOUND AND VIBRATION

Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds

(2015) J.D. Mireles James   INDAGATIONES MATHEMATICAE-NEW SERIES

Nonlinear normal modes, modal interactions and isolated resonance curves

(2015) R.J. Kuether et al.   JOURNAL OF SOUND AND VIBRATION

The use of normal forms for analysing nonlinear mechanical vibrations

(2015) Simon A. Neild et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Profits and Pitfalls of Timescales in Asymptotics

(2015) Ferdinand Verhulst   SIAM REVIEW

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

(2014) L. Renson et al.   MECCANICA

Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems

(2013) Konstantin V. Avramov et al.   Applied Mechanics Reviews

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

(2012) F. Blanc et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds

(2011) Amit P. Gabale et al.   JOURNAL OF SOUND AND VIBRATION

A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

(2008) Sangram Redkar et al.   Journal of Computational and Nonlinear Dynamics

Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques

(2008) M. Peeters et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Nonlinear normal modes, Part I: A useful framework for the structural dynamicist

(2008) G. Kerschen et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING