Suppressing Flow-induced Vibrations by Parametric Excitation

The possibility of suppressing self-excited vibrations of mechanical systems using parametric excitation is discussed. We consider a two-mass system of which the main mass is excited by a ow-induced, self excited force. A single mass which acts as a dynamic absorber is attached to the main mass and, by varying the stiiness between the main mass and the absorber mass, represents a parametric excitation. It turns out that for certain parameter ranges full vibration cancellation is possible. Using the averaging method the fully non-linear system is investigated producing as non-trivial solutions stable periodic solutions and tori. In the case of a small absorber mass we have to carry out a second-order calculation. 1. Introduction In this paper we solve an open problem formulated by Ecker and Tondl 1]; also we analyse their model to discover many interesting bifurcational phenomena. Suppressing ow-induced vibrations by using a conventional spring-mass absorber system has often been investigated and applied in practice. It is also well-known that self-excited vibrations can be suppressed by using diierent kinds of damping, see 2] and 3]. However, only little attention has been paid to vibration suppression by using interaction of diierent types of excitation. In the monograph by Tondl 4], some results on the investigation of synchronization phenomena by means of parametric resonances have lead to the idea to apply a parametric ex-citation for suppressing self-excited vibrations. The conditions for full vibration suppression (also called quenching) were formulated rst in 5] and 6]. Using the Harmonic Balance Method (see 7]and 8]) in Ecker and Tondl 1] a two-mass system is studied; see Figure 1. The main mass is excited by a ow-induced, self-excited force, in which the self-excitation is of Rayleigh type. This mass is connected to the absorber mass by a linear spring. The connecting stiiness between two masses is a harmonic function of time and represents a parametric excitation. The analysis in 1] shows that the interval