Abstract
This paper investigates the near-resonance response to exogenous excitation of a class of networks of coupled linear and nonlinear oscillators with emphasis on the dependence on network topology, distribution of nonlinearities, and damping ratios. The analysis shows a qualitative transition between the behaviors associated with the extreme cases of all linear and all nonlinear oscillators, respectively, even allowing for such a transition under continuous variations in the damping ratios but for fixed topology. Theoretical predictions for arbitrary members of the network class using the multiple-scales perturbation method are validated against numerical results obtained using parameter continuation techniques. The latter include the tracking of families of quasi-periodic invariant tori emanating from saddle-node and Hopf bifurcations of periodic orbits. In networks in the class of interest with special topology, 1:1 and 1:3 internal resonances couple modes of oscillation, and the conditions to suppress the influence of these resonances are explored.
Original language | English (US) |
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Article number | 041001 |
Journal | Journal of Computational and Nonlinear Dynamics |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Apr 1 2021 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Mechanical Engineering
- Applied Mathematics