A New Fluid-Structure Interaction Benchmark with an Analytical Solution Describing Vibration-Driven Propulsion in a Viscous Fluid
Abstract
Abstract This paper investigates the dynamics of a vibration-driven propulsion system in a fluid, modeled as a cylindrical vibration robot whose oscillations are induced by the movement of an internal mass. The system represents an attractive combination of bio-inspired physics and tractable mathematics.The directed motion of the system arises due to two-way fluid--structure interaction, mimicking the physics of a flapping wing. Despite the richness of the underlying physics, the problem admits an analytical solution with controlled accuracy, obtained in the paper using the method of asymptotic expansions. The solution explicitly describes the steady-state self-propulsion mode, determining the body oscillation amplitudes, phase shifts, and cruising speed through simple algebraic expressions. Finally, owing to the simple cylindrical geometry and the clear physical and mathematical foundation, the problem constitutes a convenient computational case for free-body motion in a viscous fluid. To capture the full system dynamics and validate the analytical framework, numerical simulations are performed in OpenFOAM using 3 and 2.5 degrees of freedom models. A comprehensive parametric study demonstrates good agreement between the numerical and analytical results: the average relative error for kinematics (oscillation amplitudes and phase shifts) does not exceed 2\% (with average amplitude deviation about 3.5\%), while the average deviation for the cruising speed is within 6\%.…
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