COMPARISON OF VIBRATION CHARACTERISTICS OF THREE TYPICAL AXIALLY MOVING STRUCTURES

The transverse vibration of the axially moving structure is always one of the hot topics in the field of dynamics. At present, most literatures are considering the study of one model. There are few researches considering the comparative analysis of several models. The vibration characteristics of three typical axially moving structures, such as the Euler beam, the panel, and the plate with two opposite sides simply supported and other two free, are compared and analyzed in this paper. In view of different structural parameters in engineering, this paper provides a reference for choosing a more reasonable model in the study of vibration theory. The governing equations of the three models are solved by the complex mode method. The corresponding natural frequencies and mode functions can be obtained. For the plate model, two rigid displacements and the coupled flexural and torsional vibration are both considered. The variations of the first four order natural frequencies of the three models with the axial velocity and the aspect ratio are given by numerical examples. At the same time, the analytical solution obtained by the complex modal method is verified by the differential quadrature method. The influence of different axial speed, damping, stiffness, and aspect ratio on the first order natural frequency of three models is analyzed by adopting the form of three-dimensional diagram for the first time. The effects of different aspect ratios and axial speed mixing on the relative errors of the first natural frequencies the first order natural frequency of the plates and beams are emphatically studied. The results show that the natural frequency of the three structures decreases gradually with the increasing axially speed. The panel is a simplified model of the plate. The damping has the least effect on the first order natural frequency when other parameters change. The complex model can be simplified into a simple model when the moving structure has a large aspect ratio and a small axial speed.