Vibration model of a multi-supported guide bar and analysis on the effect of supports location

Two methods (equivalent force method and segmental mode assuming method) of calculating the natural frequencies and mode shapes of a free-free-multi-supported beam subjected to an axial load is found, considering the structure characteristic of the guide bar, which has long length but small section, and supported by many bearings. The calculation shows that these two methods are convenient for computer programing and have the same results in obtaining the natural frequencies and mode shapes of a free-free-multi-supported beam subjected to an axial load, solving the problem that the vibration function of this kind of beam is hard to deal with because it cannot be simplified with the boundary condition of two ends. Then the segmental mode assuming method is used to analyze the impact of the support location on the natural frequencies and mode shapes of the guide bar. The relation graphs of the natural frequencies with support location, as well as the support locations where the natural frequencies reached the maximum and the minimum are found, providing a reference for the support location selection for the guide bar. The changing curves of the mode shapes with support location are plotted, which show that the bending deformation is homogeneous when the length of each segment is approximately equal, avoiding the phenomenon that bending stresses concentrates at the large-amplitude segments and cause breakage while less stress exists in small-amplitude segments and hinder the exploiting of their performance, providing a reference for the structure design of the guide bar.