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Goldman, Daniel I.

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    Mechanics of undulatory swimming in a frictional fluid
    (Georgia Institute of Technology, 2012-12) Ding, Yang ; Sharpe, Sarah S. ; Masse, Andrew ; Goldman, Daniel I.
    The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a ‘‘granular frictional fluid’’ and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.
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    Lift-off dynamics in a simple jumping robot
    (Georgia Institute of Technology, 2012-10-26) Aguilar, Jeffrey ; Lesov, Alex ; Wiesenfeld, Kurt ; Goldman, Daniel I.
    We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot’s resonant frequency f0. Two distinct jumping modes emerge: a simple jump, which is optimal above f0, is achievable with a squat maneuver, and a peculiar stutter jump, which is optimal below f0, is generated with a countermovement. A simple dynamical model reveals how optimal lift-off results from nonresonant transient dynamics.
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    Entangled granular media
    (Georgia Institute of Technology, 2012-05-17) Gravish, Nick ; Franklin, Scott V. ; Hu, David L. ; Goldman, Daniel I.
    We study the geometrically induced cohesion of ensembles of granular“u particles” that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relationτ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement
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    Drag induced lift in granular media
    (Georgia Institute of Technology, 2011-01-14) Ding, Yang ; Gravish, Nick ; Goldman, Daniel I.
    Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at a constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.