| Summary: | Many reptiles, known as ‘sand swimmers’, adapt to their specific environments by vibrating or rotating their body. To understand these type of interactions of active objects with granular media, we study a simplified model of a self-excited spherical object (SO) immersed in the granular bed, using three-dimensional discrete element method (DEM) simulations. Modelling the vibration by an oscillatory motion, we simulate the longitudinal locomotion of the SO in three modes: transverse vibration, rotation around different axes, and a combination of both. We find that the mode of oscillation in <i>y</i> direction coupled with rotation around <i>x</i>-axis is optimal in the sense that the SO rises fastest, with periodic oscillations, in the <i>z</i> direction while remaining stable at the initial <i>x</i> position. We analyze the physical mechanisms governing the meandering up or down and show that the large oscillations are caused by an asynchronous changes between the directions of oscillation and rotation. We also observed that the SO’s rising rate is sensitive to three parameters: the oscillation amplitude, the oscillation frequency, <i>f</i>, and the rotation angular velocity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>. We report the following results. 1. When the frequencies of the rotation and transverse motion are synchronised, SO rises when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Ω</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula> and sinks when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Ω</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>; the average rising/sinking rate is proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi mathvariant="sans-serif">Ω</mi><mo>|</mo></mrow></semantics></math></inline-formula>. 2. The rising rate increases linearly with the oscillation amplitude. 3. There exists a critical oscillation frequency, above and below which the rising mechanisms are different. Our study reveals the range of parameters that idealized ‘swimmers’ need to use to optimize performance in granular environments.
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