Semi-analytical modeling and vibration analysis for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps

Abstract

In the current research on semi-analytical modeling of the pipeline systems, most objects targeted are simple straight pipelines. Here, a novel and universal semi-analytical modeling method is proposed for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps. The modeling idea can be described as follows. Firstly, the pipeline system is discretized into several characteristic elements, such as straight pipe, curved pipe, clamp and connecting springs. Then, the energy expressions of these characteristic elements are derived respectively. For straight pipe and curved pipe, a unique displacement function setting method is proposed to simulate the spatial motion of the pipeline. Finally, according to the Rayleigh-Ritz method and substituting the energy expressions of all characteristic elements into the Lagrangian energy function, the dynamic equations of the above-mentioned plane and regular spatial pipeline system are obtained for the vibration analysis. A case study is carried out, and the results show that the natural characteristics of the system solved by the developed semi-analytical method are basically consistent with those calculated by ANSYS software under different boundary conditions, thus verifying the rationality of the modeling method. In addition, taking the regular spatial pipeline as the example, the clamp layout optimization is carried out based on the developed semi-analytical model and finite element model. The superiority of the developed semi-analytical modeling method is proved by comparing the optimization results and the calculation time.