Motions, Forces and Mode Transitions in Vortex-Induced Vibrations at Low Mass-Damping

Abstract

These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m* ), or a high mass-damping (high m* ). For our low m* , we "nd three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at high m* , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m* ), whereas the regime of synchronization (measured by the range of velocity ;*) is dependent primarily on the mass ratio, m*. At low (m* ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper}lower branches. A 1803 jump in phase angle is found only when the #ow jumps between the upper}lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m*"1}20), when plotted against (m*#C ) in the &&Gri$n'' plot, demonstrates that the use of a combined parameter is valid down to at least (m*#C ) &0)006. This is two orders of magnitude below the &&limit'' that had previously been stipulated in the literature, (m*#C ) '0)4. Using the actual oscillating frequency ( f ) rather than the still-water natural frequency ( f , ), to form a normalized velocity (;*/f* ), also called &&true'' reduced velocity in recent studies, we "nd an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratios m*. Such a collapse of response plots cannot be predicted a priori, and appears to be the "rst time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson}Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large ampli"cation of maximum, mean and #uctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*.

Suppression of vortex-induced vibration of a circular cylinder with fixed and rotating control cylinders.

“…The jumps between the tree branches were associated with changes in the phase angle between the motion and the excitation force. Khalak & Williamson (1999) concluded that the maximum vibration amplitude is related to the product m * ζ, while the width of the range U r where synchronization occurs is directly related to the value of m * for cases of the same m * ζ, as can be observed in (Vertical axes represent A * and horizontal axes represent U r ), from Khalak & Williamson (1999) The maximum amplitude achievable by a certain system is something that has captured the interest of researches working on VIV. Gri n & Ramberg (1982) published a work where the relationship between the maximum amplitude recorded for a system was plotted against a parameter called reduced damping which was based on the mass an the damping ratio of the system.…”

“…Experimental results for the dynamic response in terms of displacement amplitude and frequency of oscillation, as well as mean drag and uctuating lift coe cients were measured for a plain cylinder and the other suppressor models. The validation of the plain cylinder was based on the papers of Khalak & Williamson (1977,1999. Figure 5.1 presents the displacement amplitudes and frequencies of oscillation of a plain cylinder compared with the results obtained by Khalak & Williamson (1997).…”

Flow-induced vibration of elastically supported rectangular cylinders

“…After manipulation, the response amplitude and frequency can be formulated using nondimensional parameters (Khalak and Williamson, 1999), …”

Estudo experimental das vibrações induzidas pela emissão de vórtices em cilindros flexíveis inclinados em relação à correnteza.

“…O trabalho de Skop & Balasubramanian (1997) revisitou as equações do modelo de oscilador anteriormente apresentadas em Skop & Griffin (1975) e, com base nos estudos mais recentes, redefiniu a maneira como as predições de amplitude seriam realizadas. A partir deste trabalho e o de Khalak & Williamson (1999) o parâmetro mais aceito para a avaliação da amplitude máxima de resposta foi (m * + C P OT a )ζ (calculado de acordo com a Tabela 2.2).…”

“…Numa abordagem mais voltada ao estudo de VIV, como a utilizada em Khalak & Williamson (1999), o valor de amortecimento (ζ) é avaliado conforme o apresentado anteriormente na Tabela 2.2, ou seja:…”