On the escape from a potential well via vortex-induced vibrations: A computational approach

Abstract

The past decade witnessed a renewed interest in understanding the escape phenomenon in nonlinear oscillators. This is due to the emergence of new devices where escape of the dynamic trajectories from a potential well can be utilized as a trigger for switching and structural morphing. In this study, the basic characteristics of escape from a potential well for a circular cylinder undergoing vortex-induced vibrations is investigated via a computational model for low Reynolds number ranging between 70 and 250. The cylinder has a low mass ratio, zero structural damping, and is supported by a softening nonlinear spring. It is shown that the magnitude of the nonlinearity in the supporting spring has a substantial influence on the response behavior of the oscillator prior to escape, and that escape cannot occur for small values of the nonlinearity because the magnitude of the response in the lock-in region can never exceed the threshold amplitude necessary for escape. It is also shown that, when it happens, escape from the potential well typically occurs due to the transient trajectories overcoming the potential barrier. Thus, a steady-state analysis of the response behavior is not sufficient to accurately predict the flow speeds at which escape occurs. Finally, it is shown that escape occurs for a range of flow speeds which expands with the nonlinearity and shrinks with the mass ratio. Results presented in this study are fundamental to the design of flow-activated switches and morphing mechanisms.