Dynamic Analysis and Design Optimization of a Drag-Based Vibratory Swimmer

Many organisms achieve locomotion via reciprocal motions. This paper presents the dynamic analysis and design optimization of a vibratory swimmer with asymmetric drag forces and fluid added mass. The swimmer consists of a floating body with an oscillatory mass inside. One-dimensional oscillations of the mass cause the body to oscillate with the same frequency as the mass. An asymmetric rigid fin attached to the bottom of the body generates asymmetric hydrodynamic forces, which drive the swimmer either backward or forward on average, depending on the orientation of the fin. The equation of motion of the system is a time-periodic, piecewise-smooth differential equation. We use simulations to determine the hydrodynamic forces acting on the fin and averaging techniques to determine the dynamic response of the swimmer. The analytical results are found to be in good agreement with vibratory swimmer prototype experiments. We found that the average unidirectional speed of the swimmer is optimized if the ratio of the forward and backward drag coefficients is minimized. The analysis presented here can aid in the design and optimization of bio-inspired and biomimetic robotic swimmers. A magnetically controlled microscale vibratory swimmer like the one described here could have applications in targeted drug delivery.