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Abstract
The efect of parametric excitation in self-excited has been investigated in two-degrees of freedom problems. The possibility of suppressing self-excited vibrationsby using parametric excitation and the dynamic behavior of those kind systems were discussed. In the this paper, we consider a system in three-degrees of freedom problem which by using a linear transformation the system becomes an Autoparametric. The system consists of a central mass and two external masses where those masses are conectedby springs with the same constant stiffness. The flow-generated self-excited force is actingon the external masses, it is represented by Rayleigh force. The variable stiffness isperiodically varying in time, represents a parametric excitation. It turns out that forcertain parameter ranges full vibration cancellation is possible. The analysis of linearcase of system shows that there are two conditions in order to obtain an interval ofthe parametric excitation. Using the averaging method the fully non-linear system is investigated producing as non-trivial solutions unstable periodic solutions. The behaviorof this unstable solution is studied in the full system.
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