Chaotic Vibrations of Nonlinearly Supported Tubes in Crossflow

Abstract

Chaotic vibrations associated with the fluidelastic instability of nonlinearly supported tubes in a crossflow is studied theoretically on the basis of the unsteady-flow theory and a bilinear mathematical model. Effective tools, including phase portraits, power spectral density, Poincare maps, Lyapunov exponent, fractal dimension, and bifurcation diagrams, are utilized to distinguish periodic and chaotic motions when the tubes vibrate in the instability region. The results show periodic and chaotic motions in the region corresponding to fluid-damping-controlled instability. Nonlinear supports, with symmetric or asymmetric gaps, significantly affect the distribution of periodic, quasi-periodic, and chaotic motions of a tube exposed to various flow velocities in the instability region of the tube-support-plate-inactive mode.