Multistability and Modal Interactions in Periodic 2D Coupled Pendulums Array

Abstract

The collective dynamics of an array of periodic two dimensional (2D) coupled pendulums under harmonic horizontal base excitation is investigated. The coupled differential equations governing the nonlinear vibrations of the considered system have been solved using an analytical-numerical solving procedure, based on the multiple scales method coupled with standing wave decomposition. It allows the identification of complex and wide variety of nonlinear phenomenon exhibited by the periodic nonlinear structure. The frequency responses for several coupled pendulums were calculated in order to analyze the stability, the modal interactions and the bifurcation topologies resulting from the collective dynamics of the coupled pendulums, while highlighting the large number of multimodal solutions for a small number of coupled pendulums. The complexity and the multivaludness of the responses were illustrated by a study of basins of attraction which display the large distribution of the multi-mode branches.