## 1 Introduction
[PERSON] [8] developed a computational algorithm for solving problems of vibrations in composite pipelines conveying pulsating liquid. The stability and amplitude-time characteristics of vibration in composite pipelines with pulsating fluid flowing in them are studied for a wide range of changes in the parameters of deformable systems and fluid flow. [PERSON] [9] focuses on the problem of abnormal vibrations within the JYG compressor station pipeline and uses a 3D calculation model of the launcher pipeline of west-east gas pipeline III to perform simulation analysis using Fluent to find the cause of the abnormal vibrations. Our results show that the fluid pressure fluctuation in the pipeline is the main factor in the abnormal vibration of the launcher pipeline in the JYG compressor station. In [PERSON]'s [10] paper, a novel multidimensional vibration isolation and mitigation device (MVIMD) is proposed and optimized to mitigate the multidimensional vibration of pipelines. First, the dynamic characteristics and responses of pipelines with and without the devices are compared based on the modified equivalent standard solid model. Then the MVIMD is attached to a pipeline to verify its vibration mitigation effect in horizontal and vertical directions. Finally, the genetic algorithm (GA) is adopted to optimize the parameters of MVIMD. The numerical analysis results show that the novel MVIMD with parameters optimized by the genetic algorithm has better effects for controlling both horizontal and vertical vibration responses of pipelines. [PERSON] [11] finds that the unique modal frequencies of each order are applied to the elbow to obtain different exclusive mode shapes. The evolution of the flow pattern is related to the increase in wave height, and the wave amplitude often depends on the gas-liquid superficial velocity. The superficial liquid velocity is more sensitive to the influence of flow pattern formation and vibration than that of gas. The above nonlinear fluid-structure interaction vibration analysis model for curved pipelines, although considering nonlinear factors, does not comprehensively consider the fluid-structure interaction effect of the junction between the actual pipeline branch and the main pipeline, while the actual situation will cause structural and fluid vibration due to the fluid-structure interaction effect of the junction. In order to study the complex coupling situation caused by various factors at the junction of the branch and solve the problem of difficult analysis of its vibration mechanism, many scholars have made preliminary attempts to address the mechanism and modeling issues of the branch pipeline. [PERSON] [12] considered FSI (Fluid-Structure Interaction) and cavitation phenomena and conducted experimental research on T-shaped pipelines[PERSON] [PERSON] [13] conducted an experimental study on the coupling response of T-shaped pipes in the upstream region of the pipeline due to the acoustic resonance mechanism. [PERSON] and [PERSON] [14] perceived pipe systems with three-port junctions as having a global transmission matrix. Their research has solved the round-off problems[PERSON] The above research results on the branch pipeline have carried out targeted exploration of the pipeline fluid-structure interaction vibration model, and the coupling conditions considered are more complex. [PERSON] [15] provided the general steps for calculating pipeline dynamics problems using the transfer matrix method and the process of establishing the point transfer matrix for any pipeline branch component absorption transfer matrix method, achieving the solution of branch pipeline system dynamics problems, and proving its correctness through comparison with experimental results. Afterwards, based on the selected branch pipeline design basic model, the uniform design principle is used to select calculation samples, and the transfer matrix method is applied to calculate the sample model.