In recent years, many scholars have conducted in-depth research on the nonlinear vibration characteristics of the pipeline, and found some important phenomena that have never appeared in linear analysis. This paper mainly studies the motion characteristics of fixed-flow pipelines at both ends under the excitation of their basic harmonic motion. For a fixed conveying pipe at both ends, the axis will not be elongated during the deformation process. In this paper, considering the influence of this geometric nonlinear factor, the nonlinear differential equations of the system are derived and subjected to dimensionless processing. Then, the vibration mode function of the beam is used to approximate the vibration mode function of the beam under the same boundary condition. The motion equation is discretized by the method, and the motion equations of the system single mode and bimodal are obtained. For the single-mode system, this paper analyzes the static equilibrium point of the system and finds that there are three equilibrium points and one homoclinic orbit in the system within a certain parameter range. Then, the critical conditions of the chaotic motion of the system are studied by using the method, and the results are compared with the results of numerical simulation. It is found that the former has a small critical value, because the occurrence of homoclinic points is only one of the conditions that must be met by chaotic motion in the system. In order to compare the influence of modal truncation on the motion characteristics of the system, the direct numerical simulation of the single-modal and bi-modal differential equations of motion is also carried out by using the time-step history map and the map index mapping. The influence of the amplitude of the fundamental motion excitation on the motion pattern of the system is studied. It is found that with the increase of the excitation amplitude, the system will exhibit the intermittent motion of chaos and chaos in the periodical motion around different equilibrium points, and find two paths leading to chaos. The path of motion is a periodical bifurcation and an intermittent burst of chaotic motion. In addition, by comparing the results of the two modal truncated forms, it can be found that the motion patterns of the two systems are qualitatively the same, but there is a quantitative difference in the corresponding system parameter values. This indicates that for such a pipeline system, the single mode displacement pattern can reflect the main characteristics of the pipeline deformation, while other higher order modes will be quantitatively supplemented. Safety 3Ply Face Mask, Protective Face Mask, Non Woven Surgical Mask, Anti virus Surgical Mask GUANGZHOU HTD INTERNATIONAL , https://www.htdmask.com