The role of local active stiffness on the natural frequency of a flexible propulsor

This study identifies how local changes in active stiffness affect the natural frequency of a bio-inspired flexible propulsor. Biological swimmers actively change their body stiffness and natural frequency to maintain high swimming performance during steady swimming, acceleration, and maneuvering. However, it is not well understood how local active stiffness along the body affects the propulsor’s global stiffness and natural frequency. This study identifies the relationship between the propulsor’s natural frequency and the magnitude, spatial location, and application length of the active stiffness. We use a numerical kinematic model of a flexible bio-inspired propulsor with Euler–Bernoulli beam theory, inertial fluid-structure interactions, and active stiffness via co-contraction of piezoelectric artificial muscles to generate local in-plane forces. Using this numerical model, we uncover the fundamental mechanism by which the in-plane forces change the natural frequency. Local in-plane compressive forces increase the natural frequency, and there is a critical compressive force at which the propulsor’s first and second natural frequencies converge to yield a dynamic instability. We establish that the change in natural frequency is governed by the interplay between the spatial location and application length of the active stiffness. The propulsor is most sensitive to changes in natural frequency when the active stiffness is applied at the propulsor’s peduncle, but the largest changes in natural frequency occur when the active stiffness is applied with a long muscle centered along the anterior–posterior axis. We show that artificial muscles can change the natural frequency via local in-plane forcing, but practical implementation will require artificial muscles with high ratios of blocking force to passive muscle stiffness. These results serve as a framework for future studies that will identify the relationship between swimming performance (thrust and efficiency) and locally applied active stiffness.