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    Effect of spatial and dynamically varying stiffness on a flexible self-propelled swimmer

    Mengfan Xu1,2, Bowen Zhu2, Zhanzhou Hao1,2, and Bo Yin1,2,*

    • *Contact author: yinbo@imech.ac.cn

    Phys. Rev. Fluids 11, 023101 – Published 5 February, 2026

    DOI: https://doi.org/10.1103/7dnz-cpmc

    Abstract

    Spatially nonuniform structural properties in aquatic animals, together with their active stiffness-modulation behavior, have inspired bioinspired designs that can now be emulated using smart materials capable of dynamic stiffness changes. This study numerically investigates the propulsion performance of a self-propelled swimmer in which variable stiffness is achieved through spatially nonuniform modulus distributions, dynamically varying patterns, or a combination of both. Three spatial modulus distributions are examined, namely uniform, growing (S↑), and declining (S↓). Three dynamic modulus variation modes are also considered, namely constant, increasing with activation intensity (D↑), and decreasing with activation intensity (D↓). The results show that spatial variation mainly affects external performance. The S↑ mode enhances the fluid moment at the tail, leading to the highest cruising speed and power consumption but the lowest efficiency, while the S↓ mode exhibits the opposite trend. Comparisons of bending energy reliably predict the relative swimming speeds among different modes. Dynamic variation primarily influences the internal actuation requirements by altering the cycle-averaged equivalent stiffness. Under the D↓ mode, this reduction in effective stiffness lowers the intensity of the active bending-moment input and suppresses head deformation. Moreover, when the degree of variation is large, the D↑ mode can achieve a higher swimming speed without sacrificing efficiency. Combining spatial and dynamic variation affects both external and internal performance, with the S↓ plus D↓ configuration achieving higher efficiency at lower actuation input and the S↑ plus D↑ configuration delivering higher swimming speeds. These findings offer guidance for designing efficient and high-performance bioinspired underwater vehicles.

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