Non-prismatic pipelines and their vibration parameters

BACKGROUND: The variety of pipeline types used in various fields of technology requires to consider their possible cross-sectional variability and supports with different rigidity. The authors set a corresponding problem to consider the influence of these factors complicating the vibration profile of such pipelines. AIM: To study the influence of non-prismatic pipelines on their vibration parameters. MATERIALS AND METHODS: The paper further develops the approaches used by the authors in previous publications on the development of a mathematical model, algorithm, and a program used to calculate the vibration parameters of a prismatic pipeline with two resilient supports and perfect liquid flowing in it. These approaches essentially provide for building a finite element pipeline model using basic elements, where each element consists of subelements that induce corresponding additional forces during vibration. To consider the influence of additional factors, we introduced additional subelements to the model. The corresponding calculation algorithm is based on additional elements and, as before, on the partial response method, allowing to implement the principle of conformity of the stability of the process under consideration and the calculation algorithm. For the developed algorithm, we developed a calculation program to determine vibration parameters of a rectilinear multi-support non-prismatic pipeline. RESULTS: To demonstrate the program’s functionality, vibration calculations were performed for several multi-support pipelines (a prismatic pipeline and those with a middle section with increased and reduced cross-sectional diameter). The calculations allowed to construct dependence graphs of parameters, including the fundamental frequency, critical speed, support reaction amplitude, and transverse displacement amplitude in the middle of the largest span, in relation to the diameter of the selected pipeline section; the calculations were performed for different fluid flow rates. CONCLUSION: Analysis of the graphs allowed to determine the influence of the specified factors on the pipeline vibration. The results are in good agreement with the concepts of physics of the process under consideration and confirm the reliability of the developed program.