An application of the transfer matrix approach for a dynamic analysis of complex spatial pipelines - Batura, Anatolii; Novikov, Andrii; Pashchenko, Andrii; Dubyk, Yaroslav (Nuclear engineering and design, 2019)
•Transfer matrix approach for spatial pipelines vibration analysis is presented.•With a usage of exact physical equations it provides high accuracy and flexibility.•The TMA extension for taking into account coupled liquid vibration is developed.•For effective eigenvalues search Williams-Wittrick approach is used.•Its extension is developed for coupled liquid vibration consideration. An effective method for the calculations of stress and residual strength of complex spatial pipelines at static and dynamic loading with taking into account the vibration of internal liquid and Puasson coupling is presented. It based on the well-known transfer matrix approach. The method utilizes the exact mechanical equations for the stress-strained state of straight beam with distributed mass, which connect unknown parameters of forces and displacements at the end of beam calculation element with the parameters at the beginning of the element. At a general level, the solution scheme and calculation models are the same for static and dynamic calculations, the only difference – are the equations. Two different methods are used to find natural vibration frequencies of the distributed mass system: straightforward (“brute force”) and quick, based on Williams-Wittrick frequencies counter. Within such counter a special procedure is developed for taking into account fluid vibration with consideration of volumetric balance condition at T-nozzles. The excellent accuracy of the method is demonstrated by the modeling of thin-walled, water filled pipe behavior after the rod impact. Two seismic analysis procedures are implemented on the base of developed method: standard response spectrum procedure and normal-mode summation procedure (“exact” dynamical), which uses accelerograms. These methods and procedures have been already implemented in calculation software for pipeline strength assessment with the possibility of building of arbitrary complexity models by the user-friendly, visual way. Their effectiveness is demonstrated by the seismic calculation for primary circuit pipings of Zaporizhia NPP.