Pipeline vibration has a serious impact on the nuclear island cooling system of nuclear power plants and even leads to major accidents. The nonlinear dynamic vibration absorber has the advantages of wide frequency band, strong vibration absorption performance and returning weak energy of the main structure, which makes the nonlinear energy vibration absorber play an important role in the vibration reduction of pipelines. The influence of structural parameters on the performance of dynamic vibration absorber is studied by establishing a multi-degree-of-freedom nonlinear dynamic vibration absorber model. For nonlinear energy sink (NES), the bifurcation structure of the system is analyzed by using the slow variable equation derived from the complex variable average method. The truncation damping and failure frequency of the system are found, and the existence interval of the stress response is determined. These analyses are then extended to the case of a two-degree-of-freedom NES to study the dynamic bifurcation of the system, with emphasis on the influence of the NES mass distribution. The amplitude-frequency response of two-degree-of-freedom NES is analyzed by incremental harmonic balance method and Floquet theory. Finally, the nonlinear dynamic vibration absorber is analyzed in the pipeline vibration reduction through the test, and good results are obtained.