Abstract: Structural vibration-induced failure is one of the primary causes of malfunction and even breakdown in pipe systems. Investigating the natural vibration characteristics is therefore not only fundamental for understanding the dynamic behavior of pipes, but also essential for improving their structural performance, ensuring long-term stability, and enhancing operational reliability. Previous studies have primarily focused on pipes with relatively simple geometries, such as horizontal or vertical straight pipes. In these cases, the dominant dynamic features can be effectively captured through two-dimensional models, which provide sufficient accuracy for straight configurations. However, non-straight planar pipes such as L-shaped and S-shaped configurations, composed of straight and curved segments, exhibit far more complex geometries and pronounced three-dimensional vibration characteristics. Traditional two-dimensional models fail to capture their actual dynamic behavior, while the complexity of three-dimensional modeling has hindered further investigations. In this study, the Absolute Nodal Coordinate Formulation (ANCF) is employed to establish a theoretical three-dimensional pipe element model. Based on different geometric features, representative models of straight pipes, L-shaped pipes, and S-shaped pipes were developed for systematic comparison. The modal frequencies and corresponding vibration mode shapes of the three types of pipes under fixed-fixed boundary conditions were comparatively analyzed. Prior to the analysis, the accuracy of the proposed theoretical model was validated using finite element simulation software ANSYS, demonstrating good agreement. The results indicate that the straight-bend composite pipes possess more complex natural frequency distributions and vibration patterns than straight pipes, showing an obvious separation between in-plane and out-of-plane frequencies. Furthermore, when the internal fluid velocity increases, the natural frequencies of all modes decrease, and this trend remains consistent for different geometric configurations. In addition, under the same outer diameter, increasing the wall thickness raises the overall natural frequencies, with greater enhancement observed in higher-order modes. In summary, this study provides a reference for analyzing and understanding the three-dimensional dynamic characteristics of straight-bend composite pipes.