Pipelines are crucial elements in various engineering applications. However, unexpected vibrations from different sources can jeopardize the operational performance and potentially damage the piping structures and other connected units. This study explores flexural wave propagation and attenuation characteristics of the pipes supported periodically on a rack. Also, a specific case of a rack with infinite stiffness (simple support) is investigated. The dispersion relations pertinent to pipe rack scenario is obtained through transfer matrix method (TMM) in conjunction with Floquet-Bloch’s theorem, and the accuracy of ensuing band gaps (BGs) are confirmed through finite element (FE) models. Following this, the modal analysis is performed to ascertain the minimum number of unit-cells necessary for the FE model to accurately mimic the attenuation and propagation characteristics of the corresponding infinite structure. The findings indicate that a pipe supported on rack displays resonance and Bragg-type BGs, arising from local resonance and spatial periodicity, respectively, while the pipe on simple support exhibits only Bragg-type BGs. To control low-frequency vibrations in dual pipelines placed on the rack, a novel configuration using interconnected dynamic vibration absorbers (DVAs) is proposed. The DVA consisting of two spring-damper units along with a mass is connected across the center of each span of the two pipelines. The proposed DVA is designed via genetic algorithm-based optimization. It was found that the designed DVA significantly reduces the vibration of the two pipelines. The performance of DVAs improves with an increase in the mass ratio. Additionally, the performance of pipes connected with conventional tuned mass damper (TMD) is evaluated and compared with the proposed DVA. The effectiveness of DVAs is also verified by employing a white Gaussian noise as input. The proposed DVAs are efficient in scenarios involving multiple pipes within a rack, leveraging other pipe’s mass, stiffness, and damping properties to mitigate vibrations in the considered pipes.