Experimental study on vortex-induced vibrations of a circular cylinder elastically supported by realistic nonlinear springs: Vibration response

Abstract

This study presents an experimental investigation into the vortex-induced vibrations (VIV) of a single circular cylinder supported by various nonlinear springs. Unlike previous studies focused on systems satisfying the Duffing equation, this study explores a realistic scenario with nonlinear restoring forces derived from different magnet configurations. Experiments were conducted in a low-speed circulating water flume across a Reynolds number range of Re = 232-20930, a mass ratio (m*) ranging from 3.39 to 5.55, and a nonlinear strength coefficient (λ) from -1.48 to 1.70. The results demonstrated that predicted nonlinear VIV amplitudes using linear VIV data align well with experimental observations, validating the applicability of the prediction theory (Mackowski and Williamson, PoF, 2013) to general nonlinear systems. An equivalent reduced velocity (U_eq) was introduced to rescale vibration responses, effectively collapsing the envelopes for linear and hardening nonlinear systems, although shifts to higher U_eq values were observed for softening systems. A detailed analysis of the nonlinear coefficient's impact on VIV characteristics, including amplitude, frequency, phase lag, and displacement history, identified four distinct VIV response groups: softening, weak hardening, intermediate hardening, and strong hardening nonlinear VIV. A notable finding is the presence of two lock-in regions in nonlinear VIV responses, characterized by superharmonic synchronization, and multiple-value sections and gaps in vibration envelopes at specific transitions. These behaviors are attributed to variations in the natural frequency (f_n(A*)) with vibration amplitude. This study provides valuable insights into the complex dynamics of general nonlinear VIV, offering a foundation for future research and practical applications.