Hopf Bifurcations and Hysteresis in Flow-induced Vibrations of Cylinders

Global Chaos in Flow-Induced Oscillations of Cylinders

“…These experiments indicate harmonic cylinder motions in a narrow band located at about 884 0)94 41)2. This synchronization interval is well predicted by the numerical results (1)0054 41)225) presented by Berger & Plaschko (1993). The #uid motion*as characterized by the lift coe$cient*is, however, much less regular than the harmonic cylinder oscillations (see the temporal evolution and spectral measurements revealed in "gures 6 and 7 of Khalak & Williamson).…”

“…Berger's (1988) nonlinear model has been successfully used to describe such periodic cylinder oscillations (Berger & Plaschko, 1993). Moreover, this model has the power to predict hysteresis, as found in experiments [cylinder in air: Feng (1968) and Kobayashi (1980); #exing cylinder in air: Brika & Laneville (1993); cylinder in water: Khalak & Williamson (1996)].…”

“…We refrain from giving a detailed account of the model equations and we refer the reader to the derivation given by Berger & Plaschko (1993). The decoupling of the #ow equations was discussed by Plaschko [1996;equation (4)].…”

“…A SEMI-EMPIRICAL MODEL governing #ow-induced vibrations of cylinders was developed and discussed in previous papers (Berger 1988;Berger & Plaschko 1993). A multiple-scales approach is used to show that the #ow oscillations can be described with inhomogeneous equations decoupled from the rest of the system (Plaschko 1996).…”

An Examination of Wake Oscillator Models for Vortex-Induced Vibrations

“…Corless and Parkinson ' have studied the Harden and Currie model using multiple scales perturbation techniques around the lock-in region. Using a variety of methods, Berger 13 ' 14 has studied a similar model with an additional cubic damping term in equation (2) …”