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Abstract
When a nonlinear system is expressed in terms of the modes of the equivalent
linear system, the nonlinearity often leads to modal coupling terms between
the linear modes. In this paper it is shown that, for a system to exhibit
an internal resonance between modes, a particular type of nonlinear coupling
term is required. Such terms impose a phase condition between linear
modes, and hence are denoted phase-locking terms. The effect of additional
modes that are not coupled via phase-locking terms is then investigated by
considering the backbone curves of the system. Using the example of a two-mode
model of a taut horizontal cable, the backbone curves are derived for
both the case where phase-locked coupling terms exist, and where there are
no phase-locked coupling terms. Following this, an analytical method for
determining stability is used to show that phase-locking terms are required
for internal resonance to occur. Finally, the effect of non-phase-locked modes
is investigated and it is shown that they lead to a stiffening of the system.
Using the cable example, a physical interpretation of this is provided.
Original language | English |
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Pages (from-to) | 135-149 |
Number of pages | 15 |
Journal | Journal of Sound and Vibration |
Volume | 379 |
Early online date | 6 Jun 2016 |
DOIs | |
Publication status | Published - 29 Sept 2016 |
Keywords
- internal resonance
- nonlinear normal modes
- backbone curves
- nonlinear dynamics
- cable dynamics
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Dive into the research topics of 'The influence of phase-locking on internal resonance from a nonlinear normal mode perspective'. Together they form a unique fingerprint.Projects
- 1 Finished
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Dynamic design tools for understanding and exploiting nonlinearity in structures
1/02/13 → 31/07/18
Project: Research