(The) dynamic stability analysis of a circular paate with moving passive damping elements

Abstract

An investigation of the stability characteristics of a circular disk with moving passive damping elements is presented. Three models for passive damping elements are suggested. They are Model-I, Model-II and Model-III. Model-II and Model-III are fundamentally equal. In case of Model-I, the mass of passive damping element has no degree of freedom, while in case of Model-III, mass has another degree of freedom. The number of passive damping elements were varied from one up to three. In the present stability analysis of the system, an eigenfunction expansion is employed. All these searches are performed by one and two modes approximation except finding the optimal angular position of two passive damping elements, which is obtained by six modes approximation. Model-III is proved better than Model-I in the view point of stability characteristics, even though two are equal in critical speed point of view. If damping is present, the critical speed is not increased for both two and three passive damping elements cases at any condition. But the stability characteristics over the whole region of rotation speed is improved regardless of the presence of damping by adding one more passive damping element. In case of two passive damping elements system, the optimal angle is obtained as 5$^\circ$ and the optimal radial position is obtained at the disk periphery. If damping is not present the critical speed has greatly increased. Mass, spring, damping effects are studied in some details. In case of three passive-damping elements, the optimal angle is obtained by two modes approximation. The stability characteristics over the whole region of rotation speed is not improved in comparision with two passive damping elements system. Mass, spring, damping effects are also included.