Modeling and parametric studies of retaining clips on pipes

As an indispensable accessory, retaining clips on pipes are usually modeled as simply supported or fixed end boundaries. In this paper, a dynamic model of a pipe without fluid, with fixed-fixed ends and restrained by a middle clip is established. Different from the previous modeling that ignores the width of a clip, the clip is modeled as a rigid body with a certain width, which is elastically connected to the base. The effects of clip width, thickness, material parameters, and connection stiffness on the natural vibration of the pipe are presented. Moreover, to illustrate the necessity of the proposed model, a dynamic model of a half pipe is extracted with a clip as one end boundary. According to the two models, the natural frequencies and modes of the pipe are calculated and compared. Some meaningful results are obtained. The clip parameters influence the natural frequencies of the pipe nonlinearly. When calculating the natural frequencies of the pipe, ignoring the clip width or modeling the clip as a boundary will cause a noticeable error. The symmetry of the modes and the numbers and locations of modal nodes change as the clip stiffness changes. Furthermore, modal shapes of the symmetric modes change noticeably as the clip thickness or width increases. The locations of the maximum modal displacements may change as the clip width varies. In summary, a novel and valuable dynamic model of the retaining clip is proposed in this study. The vibration of a pipe restrained by a clip can be more accurately described. Influence laws of clip parameters can be used to guide the design and vibration measurement of pipes with clips.