Rigid-flexible coupling dynamics for bionic body-caudal-fin propulsion based on Timoshenko beam theory
Year: 2026
Type: preprint
Abstract: Accurately predicting the rigid-flexible coupled dynamics of biomimetic body-caudal-fin (BCF) propulsors under transient hydrodynamic loads is crucial for underwater vehicle design. Classical Euler-Bernoulli theory, by neglecting transverse shear and rotary inertia, exhibits limitations under low-slenderness or high-frequency conditions. Therefore, this paper establishes a nonlinear rigid-flexible dynamic model using Timoshenko beam theory. By integrating the generalized principle of virtual work with the Morison equation, an analytical expression for transient thrust featuring a spatial slope correction is deduced, enabling accurate projection of local fluid forces onto the global coordinate system. The model is quantitatively validated through underwater oscillation experiments. Analyses reveal that flexible deformation breaks hydrodynamic symmetry, acting as the fundamental mechanism for thrust generation. Quantitatively, a 2-mm moderately flexible beam achieves a 100-mm tip deflection, producing significant asymmetric net thrust, whereas a stiffer counterpart yields an 80-mm deflection with markedly weakened thrust. Geometrically, propulsion approaches zero for excessively thick (5-mm) beams but increases linearly with beam width. Under high-frequency, small-amplitude conditions (e.g., 0.8 Hz, π/6 amplitude), the transient thrust waveform exhibits distinct nonlinear distortion and asymmetry. This originates from the dramatic amplification of transverse shear and rotary inertia effects unique to Timoshenko beams. Ultimately, this theoretical framework overcomes the limitations of classical assumptions, providing a solid foundation for the parametric design of flexible propulsors.
Source: Research Square
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220837280