Periodic arrays of perpendicular gyroscopes
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This presentation introduces the perpendicular gyroscope model, which is formed of two perpendicular beams—with the vertical beam either clamped at the base or mounted on a flexural plate—and a gyroscope placed at the free end of the horizontal beam. The design of the perpendicular gyroscope has similarities with the structure of a wind turbine. The analytical model is studied alongside finite element simulations. Finite element simulations are also used to investigate periodic arrays of perpendicular gyroscopes on flexural plates. Boundary conditions are applied to simulate the presence of the spinners [1] and describe the connections between the beams and plates [2]. Particular attention is paid to the broken symmetries of the perpendicular gyroscope system, the coupling of flexural and torsional rotations, and the active chirality of gyroscopes. We investigate the control over the eigenfrequencies and dispersive properties of the arrays afforded by altering parameters of the system, such as the rate of spin of the gyroscopes, the length of the beams and the orientation of the gyroscope axes. This work has potential applications to modelling systems of spinning rotors where the axis of rotation is perpendicular or near perpendicular to the axis at the base, such as in wind turbines, and wind farms formed of periodic arrays of turbines. REFERENCES [1] M. J. Nieves, G. Carta, I. S. Jones, A. B. Movchan, and N. V. Movchan. Vibrations and elastic waves in chiral multi-structures. Journal of the Mechanics and Physics of Solids, 121:387–408, 2018. [2] G. Carta, D. J. Colquitt, A. B. Movchan, N. V. Movchan, and I. S. Jones. Chiral flexural waves in structured plates: Directional localisation and control. Journal of the Mechanics and Physics of Solids, 137:103866, 2020.