Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect

General perturbation schemes for nonlinear problems in mechanics (70K60) Nonlinear resonances for nonlinear problems in mechanics (70K30) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (1)

Model reduction of a cyclic symmetric structure exhibiting geometric nonlinearity with a normal form approach

Cites Work

The parameterization method for invariant manifolds. From rigorous results to effective computations
An Upper bound for validity limits of asymptotic analytical approaches based on normal form theory
A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems
Resonantly forced motion of two quadratically coupled oscillators
Nonlinear dynamics of a shallow arch under periodic excitation. I: 1:2 internal resonance
A nonlinear vibration absorber for flexible structures
Free oscillations in conservative and dissipative symmetric cubic two-degree-of-freedom systems with closed natural frequencies
On the reconstitution problem in the multiple time-scale method
Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification
Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
A Taylor series-based continuation method for solutions of dynamical systems
Nonlinear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance
Resolving controversies in the application of the method of multiple scales and the generalized method of averaging
The use of normal forms for analysing nonlinear mechanical vibrations
Applying the method of normal forms to second-order nonlinear vibration problems
Nonlinear Vibrations and Stability of Shells and Plates
The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION
Normal Forms and Unfoldings for Local Dynamical Systems
COMPLEX NORMAL FORM FOR STRONGLY NON-LINEAR VIBRATION SYSTEMS EXEMPLIFIED BY DUFFING–VAN DER POL EQUATION
1:1 internal resonance in a two d.o.f. complete system: a comprehensive analysis and its possible exploitation for design
Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item

This page was built for publication: Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect