Optimization of the Movement of a Cylindrical Vibration-Driven Robot in a Viscous Fluid, Induced by Pendulum Oscillations of the Internal Mass

The work is devoted to the study of the movement of a vibration-driven robot of a circular cross section in a viscous incompressible fluid, induced by the plane polyharmonic oscillations of the internal mass. The fluid flow is described by the system of Navier–Stokes equations, which is solved analytically by the method of asymptotic expansions for the case of small ratios of the internal mass to the total mass of the robot. For cruising regime of motion, when the average hydrodynamic force acting on the vibration-driven robot is equal to zero, the dependence of the average speed on the dimensionless oscillation parameters is found. Optimal parameters of motion are investigated.