Abstract <p>Low-frequency vibration in fluid-conveying pipes remains a critical challenge in engineering applications. To address this issue, this paper designs a locally resonant double-layered pipe (LR-DLP) structure constructed by periodically inserting cylindrical ring units between two concentric pipes with different diameters. The proposed cylindrical ring unit incorporates a triple-layered cylindrical ring comprising an outer rubber layer, a middle metal layer, and an inner rubber layer. For torsional vibration analysis, a double-layered shaft torsional equivalent model (DLS-TEM) is established by equivalently representing cylindrical rings as a torsional spring-inertial disk-torsional spring system. While a double layered beam bending equivalent model (DLB-BEM) with radial spring-mass-radial spring system is established for bending vibration analysis. The differential equation governing bending vibration of fluid-conveying pipes are derived based on Hamilton’s variational principle. The Transfer Matrix Method (TMM) and Plane Wave Expansion (PWE) method are further developed for characterizing both torsional and flexural bandgaps in the LR-DLP structure, with particular emphasis on the flexural wave attenuation performance under fluid-conveying conditions within the inner pipe. Finite element numerical simulations are systematically performed in COMSOL Multiphysics for the finite-periodic locally resonant double-layered pipe (LR-DLP) structure. The results demonstrate excellent agreement with theoretical analysis in both torsional and flexural bandgap characteristics. Parametric studies reveal the influence of structural dimensions properties on bandgap characteristics, demonstrating the effectiveness of the proposed design in suppressing low-frequency vibrations.</p>