An Analytical Expression for the Fundamental Frequency of a Long Free-Spanning Submarine Pipeline

Ty Phuor, Pavel A. Trapper, Avshalom Ganz

Research output: Contribution to journalArticlepeer-review


The DNVGL-RP-F105 guidelines provide essential techniques for the preliminary design of undersea pipelines. However, its approximations for static displacement and the natural frequency of the pipe are restricted to cases where the ratio of the pipe’s diameter to its length (L/D) is less than 140. This limitation poses challenges for longer spans, which, although rare, can sometimes be unavoidable. This study introduces a novel analytical method, rooted in the energy method and cable theory, for computing the static deformation and natural frequency of long free-span underwater pipelines. We conducted a comprehensive verification of our proposed method by comparing its outcomes with those of 212 finite element analysis simulations. The results reveal excellent predictions for long spans. However, for shorter spans, traditional methods remain more accurate. Additionally, we explored the influence of pipeline’s diameter, thickness, and boundary conditions on both static displacement and frequency, providing valuable insights for design considerations. We found that the boundary conditions’ impact on the fundamental frequency becomes negligible for long spans, with up to a 10% difference between pinned–pinned and fixed–fixed conditions. In essence, this research offers a vital enhancement to the existing DNV guidelines, becoming particularly beneficial during the preliminary design phases of pipelines with L/D ratios exceeding 140.

Original languageEnglish
Article number4481
Issue number21
StatePublished - Nov 2023


  • buoyancy
  • free spanning
  • natural frequency
  • static deformation
  • submarine pipeline
  • vortex-induced vibration (VIV)


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