SUMMARYA numerical procedure for the analysis of non-Newtonian uid ow in a longitudinally vibrating tube is developed. The formulation of the problem is presented in di erential equation form and ÿnite element model is developed leading to the ÿrst-order matrix di erential equation. A special modiÿcation of the harmonic balance procedure is proposed for this non-linear problem. Numerical validation of the harmonic balance procedure was performed by comparison of the average mass ow rate with the results of direct time integration.

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This paper presents a novel method for nonprehensile manipulation of parts on a circularly oscillating platform when the effective coefficient of dry friction between the part and the platform is being dynamically controlled. Theoretical and experimental analyses have been performed to validate the proposed method and to determine the control parameters that define the characteristics of the part’s motion. A mathematical model of the manipulation process with dynamic dry friction control was developed and solved. The modeling showed that by changing the phase shift between the function for dynamic dry friction control and the function defining the circular motion of the platform, the part can be moved in any direction as the angle of displacement can be controlled in a full range from 0 to 2π. The nature of the trajectory and the mean displacement velocity of the part mainly depend on the width of the rectangular function for dynamic dry friction control. To verify the theoretical findings, an experimental setup was developed, and experiments of manipulation were carried out. The experimental results qualitatively confirmed the theoretical findings. The presented analysis enriches the classical theories of nonprehensile manipulation on oscillating platforms, and the presented findings are relevant for mechatronics, robotics, mechanics, electronics, medical, and other industries.