ON THE MODELING OF BOUNDARY CONDITIONS IN THE PROBLEM OF DETERMINING THE NATURAL FREQUENCIES OF A PIPE

The article discusses the issues of modeling boundary conditions for calculating the natural frequencies of a cylindrical straight pipe based on finite element models. For this purpose, various types of models were used, including rod (Pipe), shell (Shell) and solid (Solid). The study examines various options for implementing the conditions of hinged and rigid fastening: at two points, four points, along the middle surface of the pipe for the Shell model, along the end surface or along part of the outer surface of the pipe for the Solid model. The results of the study showed that the Pipe model provides a better approximation to the analytical solution. For the Shell and Solid models, when hinged, the best option for limit conditions to get closer to the analytical results is to fasten on each edge of the pipe at two points through which the neutral line of the cross-section of the pipe passes during bending. For rigid fastening, the results obtained from the Shell model are closest to the analytical solution if the fastening is carried out at four points or along the line of the middle surface of the pipe. For the Solid model, fastening along the end or part of the outer surface of the pipe is most effective. An analysis of the vibration modes showed that under different fastening conditions vibration modes arise that are associated with the deformation of the pipe as a shell. An assessment of the convergence of the obtained results was given, which confirmed the adequacy of the finite element models. The conclusions from the study made it possible to determine effective ways to set boundary conditions for the Shell and Solid models, which is also confirmed by the preliminary experimental studies of the authors. To obtain clearer results when determining the natural frequencies of pipeline systems, it is recommended to use experimental research methods along with numerical ones. The results obtained are of practical importance for solving problems of design and resource assessment of pipeline systems in various fields of industry.