Dynamic divergence of circular cylindrical shells conveying airflow

Abstract

Experimental studies have shown that circular cylindrical shells, supported at both ends, conveying internal fluid flow can lose stability by dynamic divergence when the shell is highly pliable. This is an instability phenomenon starting as a divergence, with amplitude comparable to the shell radius, that largely constrains the flow. This results in pressure building up and reopening the shell, triggering a dynamic instability. The characteristics of dynamic divergence instability are studied in-depth in this paper for the first time to elucidate the nature and characteristics of this phenomenon. Experiments have been conducted on an elastomer (silicone rubber) thin circular cylindrical shell clamped at both ends and subjected to internal airflow. Bifurcation diagrams have been obtained by varying the flow velocity as the control parameter, exhibiting strong subcritical behaviour and large hysteresis in the flow velocity for the onset and cessation of dynamic instability. The possible existence of a chaotic component in the oscillations was firstly discerned by looking at high-resolution photos taken with a high-speed camera. The existence of chaos in the dynamic response following the initial divergence was then confirmed by means of several qualitative and quantitative measures and criteria for chaos, such as phase plane plots, Poincaré maps, power spectra, the largest Lyapunov exponent, autocorrelation, and probability density function. All these measures have shown that the chaotic nature of dynamic divergence may be intensified or weakened depending on the flow velocity. The results demonstrate that generally at higher flow velocities the oscillations display more complex nonlinear dynamics.