InterJournal Complex Systems, 586
Status: Accepted
Manuscript Number: [586]
Submission Date: 20621
Revised On: 20626
Local Complexity and Global Nonlinear Modes in Large Arrays of Elastic Rods in an Air Cross-Flow
Author(s): Masaharu Kuroda ,Francis Moon

Subject(s): CX.0, CX.11, CX.13, CX.14, CX.25, CX.6

Category: Article


The transition from local complexity to global spatio-temporal dynamics in a two dimensional array of fluid-elastic oscillators is examined experimentally consisting of 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 rods are made of steel and polycarbonate with gap ratios ranging from 1.0 to 2.5 are used. 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 are composed of transient rest, linear motion, and elliptical motion. In the 90-rod experiments, a cluster-pattern entropy measure is introduced based on these three patterns as a quantitative measure of local complexity. Below a threshold wind velocity, no significant dynamics appear. Video images reveal that, at first, each rod moves individually, then clusters consisting of several rods emerge and, finally, global wave-like motion takes place at higher flow velocities. Spatial patterns in the rod-density distribution appear as more rods suffer impacts with 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.

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