Dynamic modeling and performance analysis of the undulating fin considering flexible deformation and fluid-fin interactions

Biomimetic undulating fin offer significant potential for underwater robots by improving manoeuvrability and stability. However, current biomimetic fin designs often lack effective theoretical guidance, with the neglect of flexible fin deformation being one of the leading causes of inefficiency. This study proposes a dynamic model based on the Absolute Nodal Coordinate Formulation to address arbitrary deformations in undulating fins. This model not only accounts for the actual shape of the fin but also incorporates fluid dynamics to analyze the fluid-fin interaction—an aspect not sufficiently addressed in previous studies. Specifically, the model is applied to an annular sector fin with five fin rays, focusing on fin thickness, elastic modulus, and ray spacing effects on the fin's undulating waveform. Results indicate that fin thickness and elastic modulus influence the waveform by altering the fin's bending stiffness, with greater stiffness improving the waveforms. Additionally, varying fin ray spacing produces different structural waveforms. Meanwhile, a comparative analysis of the deformation and hydrodynamic performance between the annular sector fin and the rectangular fin demonstrates that the annular sector fin exhibits a more biomimetic waveform and generates greater thrust. Consequently, the proposed model offers a foundation and framework for designing and optimizing undulating fins.