Instability dynamics and breather formation in a horizontally shaken pendulum chain.
Inspired by the experimental results of Cuevas et al. [Phys. Rev. Lett. 102, 224101 (2009)], we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance and near the period-3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and a critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single-pendulum dynamics and extend our analysis to consider multifrequency breathers connected to the period-3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of on-site and off-site breathers.
School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Australia 2610.
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Y
Xu
School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Australia 2610.
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TJ
Alexander
School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Australia 2610.
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Sidhu
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
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Kevrekidis