An application of the transfer matrix approach for a dynamic analysis of complex spatial pipelines

Abstract

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 that general solution scheme and calculation models are the same for static and dynamic calculations, the only differenceare 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 thinwalled, 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 complex 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.

Dynamics of a cantilevered fluid-conveying straight pipe with centrosymmetric rib plates installed at its fixed end

“…has come into being recently. While for pipe structure, accessories such as connector [24] and restrained clip [25], complex spatial configuration [26][27], the material is functionally gradient [28][29][30][31], altered geometric shape [32][33] etc. are some research hotspots in recent years.…”

Cause analysis of pipeline vibration in natural gas station

“…Li et al [8][9][10] established a 14 equation model to describe the fluid-structure coupling behavior of the pipeline, and then analyzed the effects of support, structural performance and fluid parameters on the dynamic response and natural frequency of the pipeline by using the transfer matrix method. Based on the transfer matrix method, Batura et al [11] proposed an effective method for calculating the static and dynamic stress and residual strength of complex space pipeline considering the internal vibration of fluid and Poisson coupling. Guidara et al [12] used the transfer matrix method and Laplace transform to calculate the natural frequencies of the system under different boundary conditions considering fluid-structure coupling.…”

Experimental and Numerical Vibration Analysis of Hydraulic Pipeline System under Multiexcitations

“…An improved MOC approach was proposed by Johnston [15] to investigate the fluid transient characteristics. For the frequency domain solution, the transfer matrix method which is abbreviated as TMM was used to investigate FSI problems of pipelines [16][17][18]. Based on the finite element method which is abbreviated as FEM, Sreejith et al [19] investigated the vibration behavior of nuclear pipeline with a sudden valve closure.…”