Transition from local complexity to global spatio-temporal dynamics in a two dimensional array of fluid-elastic oscillators is examined experimentally with an apparatus comprising 90–1000 cantilevered rods in a wind tunnel. Wave-like behavior is observed which may be related to soliton solutions in nonlinear arrays of nonlinear oscillators. The 90 to 1000 steel and polycarbonate rods have gap ratios ranging from 1.0 to 2.5. As the Reynolds number (based on rod diameter) increases from 200 to 900, a pattern with characteristics of spatio-temporal chaos emerges in global behavior of the elastic-rod array. There are local and global patterns. Local patterns comprise transient rest, linear motion, and elliptical motion. In 90-rod experiments, a cluster-pattern entropy measure based on these three patterns is introduced as a quantitative measure of local complexity. No significant dynamics appear below a threshold wind velocity. Video images reveal that, at first, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave-like motion occurs at higher flow velocities. Spatial patterns in rod-density distribution appear as more rods impact with their nearest neighbors. Furthermore, these collective nonlinear motions of rods are observed and categorized into several global modes. Using accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. This phenomenon may have application to plant-wind dynamics and damage as well as heat exchangers in energy systems. This experiment may also be a two dimensional analog of impact dynamics of granular materials in a flow.
- Applied Mechanics Division
Local Complexity and Global Nonlinear Modes in Large Arrays of Fluid-Elastic Oscillators
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Kuroda, M, & Moon, FC. "Local Complexity and Global Nonlinear Modes in Large Arrays of Fluid-Elastic Oscillators." Proceedings of the ASME 2002 International Mechanical Engineering Congress and Exposition. 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise. New Orleans, Louisiana, USA. November 17–22, 2002. pp. 631-641. ASME. https://doi.org/10.1115/IMECE2002-32752
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