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Motion of a smooth foil in a fluid under the action of external periodic forces. I. (English) Zbl 1448.74030
Summary: A plane-parallel motion of a circular foil is considered in a fluid with a nonzero constant circulation under the action of external periodic force and torque. Various integrable cases are treated. Conditions for the existence of resonances of two types are found. In the case of resonances of the first type, the phase trajectory of the system and the trajectory of the foil are unbounded. In the case of resonances of the second type, the foil trajectory is unbounded, while the phase trajectory of the system remains bounded during the motion.
For Part II, see [the authors, Russ. J. Math. Phys. 27, No. 1, 1-17 (2020; Zbl 1465.74047)].

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
37N15 Dynamical systems in solid mechanics
35Q35 PDEs in connection with fluid mechanics
Zbl 1465.74047
Full Text: DOI
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