R.H.M. Ogink, A.V. Metrikine

 

A wake oscillator with frequency dependent coupling for the modelling of vortex-induced vibration

                                               

Journal of Sound and Vibration

 

Summary. In this paper a wake oscillator for the modelling of vortex-induced vibration is presented in which the coupling term between the wake equation and the equation of structural motion is made frequency dependent. The wake behavior is modeled with a Van der Pol equation. Attention has been paid to properly include the effects of stall in the fluid forces. The relation between the in-phase and out-of-phase frequency dependent coupling coefficients is in the frequency domain given by the Kramers-Kronig relation. The frequency dependent coupling can be applied in the time domain through a convolution integral. The kernel of this convolution integral is given by the inverse Laplace transform of the frequency dependent coupling coefficients. The in-phase and out-of-phase part of these coupling coefficients have been determined on the basis of forced vibration measurements. At every amplitude of forced vibration a different set of frequency dependent coupling coefficients have been found, moreover, these sets did not seem to satisfy the Kramers-Kronig relation. This leads to the conclusion that the nonlinearities in the specific wake oscillator used are apparently not correct. Although the inclusion of frequency dependent effects did not improve the predictions of the presented wake oscillator, the proper inclusion of the stall term did have a noticeable effect on the possibilities to tune the wake oscillator to the results of free vibration experiments.