Investigation of modal interactions and their effects on the nonlinear dynamics of a periodic coupled pendulums chain

• Published in: International journal of mechanical sciences 2017-07, Vol.127, p.130-141
• Main Authors: Bitar, Diala, Kacem, Najib, Bouhaddi, Noureddine
• Format: Article
• Language: English
• Subjects: Basins of attraction; Coupled pendulums; Mechanics; Modal interactions; Nonlinear dynamics; Periodic structures; Physics
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2016.11.030

The nonlinear dynamics of a weakly coupled pendulums chain is investigated under primary resonance. The coupled equations governing the nonlinear vibrations are normalized and transformed into a set of coupled complex algebraic equations using the multiple scales method coupled with standing wave decomposition. A model reduction method is proposed to calculate the dominant dynamics without significant loss of accuracy compared to the full model. The validity of the proposed semi-analytical method is verified, and its role in identifying the type of the solution branches is highlighted. The modal interactions and their effects on the nonlinear dynamics are studied in the frequency domain in order to emphasize the large number of multimode solution branches and the bifurcation topology transfer between the modal intensities. Basins of attraction analysis have been performed, showing that the distribution of the multimodal solution branches generated by all modes collectively increases by increasing the number of coupled pendulums. [Display omitted] •Modal interactions in weakly coupled periodic pendulums chain were investigated.•A model reduction method based on standing-waves is proposed to reduce the CPU time.•High number of robust multimodal solution branches for few weakly coupled pendulums.•The distribution of resonant branches increases with the number of coupled pendulums.