Dynamic stability study of velocity time lag feedback control of axially moving viscoelastic beams

Abstract

In engineering fields, such as in deep space processing, paper industry, steel making industry and aerospace field etc., transverse vibration caused by axial motion not only affects the service life of the structure, but also may cause major accidents. Therefore, it is necessary to control the vibration. However, time lag is unavoidable in the process of vibration control because of the time lag in the signal transmission. On the one hand, it not only affects the robustness of the system and produces a very complex dynamic response; on the other hand, the amount of time lag can be used as a parameter to control the vibration. In this paper, a new model of time lag feedback is established, considering the effect of mechanical properties of the linear vibration model of an axially moving viscoelastic beam. The direct multi-scale analysis is applied to analyze the parameter stability of the beam with and without the addition of time lag feedback control model. The subharmonic parameters are obtained by solvability conditions and the Routh-Hurwitz criterion.