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

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 (ST), and declining (S4.). Three dynamic modulus variation modes are also considered, namely constant, increasing with activation intensity (DT), and decreasing with activation intensity (D4.). The results show that spatial variation mainly affects external performance. The ST mode enhances the fluid moment at the tail, leading to the highest cruising speed and power consumption but the lowest efficiency, while the S4. 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 D4. 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 DT mode can achieve a higher swimming speed without sacrificing efficiency. Combining spatial and dynamic variation affects both external and internal performance, with the S4. plus D4. configuration achieving higher efficiency at lower actuation input and the ST plus DT configuration delivering higher swimming speeds. These findings offer guidance for designing efficient and high-performance bioinspired underwater vehicles.