Journal or Book Title
PHYSICAL REVIEW E
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.
Xu, Y.; Alexander, T. J.; Sidhu, H.; and Kevrekidis, Panayotis G., "Instability Dynamics and Breather Formation in a Horizontally Shaken Pendulum Chain" (2014). PHYSICAL REVIEW E. 1259.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1259