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Abstract
In this paper the N−1 nonlinear modal interactions that occur in a nonlinear threedegreeoffreedom lumped mass system, where N=3,
are considered. The nonlinearity comes from springs with weakly
nonlinear cubic terms. Here, the case where all the natural frequencies
of the underlying linear system are close (i.e. ωn1:ωn2:ωn3≈1:1:1) is considered. However, due to the symmetries of the system under consideration, only N−1
modes interact. Depending on the sign and magnitude of the nonlinear
stiffness parameters, the subsequent responses can be classified using
backbone curves that represent the resonances of the underlying
undamped, unforced system. These backbone curves, which we estimate
analytically, are then related to the forced response of the system
around resonance in the frequency domain. The forced responses are
computed using the continuation software AUTO07p. A comparison of the
results gives insights into the multimodal interactions and shows how
the frequency response of the system is related to those branches of the
backbone curves that represent such interactions.
Original language  English 

Pages (fromto)  497511 
Number of pages  15 
Journal  Nonlinear Dynamics 
Volume  83 
Issue number  1 
Early online date  29 Aug 2015 
DOIs  
Publication status  Published  Jan 2016 
Keywords
 3DoF nonlinear oscillator
 Backbone curve
 Nonlinear modal interaction
 Secondorder normal form method
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Projects
 1 Finished

Dynamic design tools for understanding and exploiting nonlinearity in structures
1/02/13 → 31/07/18
Project: Research