## 1 Introduction
[23] designed a beam-sheet resonant unit based on the configuration of a cantilever beam absorber. By flexibly designing the beam parameters, the local resonant beam can achieve the widest possible Bragg band gap and local resonant band gap, with the two types of bandgaps being close to each other to form a coupled ultra-wide bandgap. [PERSON] et al. [24] proposed a theoretical model for studying the propagation of bending waves in locally resonant cylindrical shells. The periodic gradient array technology was employed to effectively splice the bandgap of each resonant unit, thereby expanding the bandgap range. When mistuning occurs in the periodic structural parameters, vibration localization arises under certain conditions. During this time, the vibration wave propagates more readily in the local region and less readily in other parts [25; 26]. [PERSON] et al. [27] suppressed blade chattering by artificially attaching small masses to the tip of the blade disk. [PERSON] et al. [28] intentionally introduced mistuning to the blade disk to reduce the vibration problem due to machining errors and wear, which effectively enhanced the stability of the disk and reduced the output response. Some scholars consider the periodically mistuned structures as a type of mistuned metamaterials [29]. [PERSON] et al. [30] proposed a metamaterial plate that integrates mistuned T-type resonators and investigated the effects of mistuning parameters on the mode localization of the T-type resonators. The research findings indicate that by designing appropriate mistuning parameters, the metamaterial plate can generate coupled wide bandgaps and double bandgaps, which is beneficial for broadband and multi-frequency vibration control of engineering structures. The excellent low-frequency broadband vibration reduction performance of the periodic mistuned structure demonstrates its potential application value in pipeline vibration control. The introduction of mistuned parameters produces a vibration localization effect, resulting in mode localization and eigenvalue splitting of the structure. Mode localization causes vibrations to protrude in certain resonant units, thus confining energy within these units and facilitating its dissipation, which is essentially similar to the mechanism of action of DVAs. Eigenvalue splitting leads to a broadband continuous distribution of resonant frequencies, effectively expanding the vibration reduction frequency band. A cyclic structure is a special form of periodic structure. A cyclic mistuned structure (CMS) is formed by periodically installing resonant units in the circumferential direction of the pipeline with the aim to improve space utilization efficiency. This paper analyzes the influence of the frequency mistuning strength and coupling strength of the resonant units on the vibration localization characteristics of the CMS. Based on this, a pipeline-oriented CMS is proposed, which can achieve low-frequency broadband vibration control of pipelines by adjusting the frequency mistuning strength of the resonant units within the structure. The organization of each section is as follows: Section 2 derives the expressions for the eigenvectors and eigenvalues of the CMS using the parameter perturbation method. Section 3 investigates the parameter effects of mode localization and eigenvalue splitting of the CMS based on the theoretical model, then summarizes the effects of the frequency mistuning strength and coupling strength of the resonant units on the vibration reduction performance of the CMS. Section 4 establishes a numerical model to validate the parameter effects on the vibration localization characteristics. Section 5 proposes a pipeline-oriented CMS, and then conducts the FRF test and excitation test of the pipeline to verify its low-frequency broadband vibration reduction capability. Some conclusions are given in Section 6.