技術者教育のための工学数理の力学教材の改定(28): 変形Atwood 機械の運動解析

概要

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Atwood's machine is a representative device in mechanics, which George Atwood invented in 1784 as a laboratoryexperiment to verify the mechanical laws of uniformly accelerated motion. In the book by Nayfeh & Mook (1995),introduced is Atwood's machine in which a body of mass m1 is linked to two bodies of mass m2 with ropes through twopulleys. If m2/m1 < 1/2, it works as usual Atwood's machine. If m2/m1 > 1/2, however, it works as an oscillationmachine around its equilibrium state. We call this "Modified Atwood's Machine" and make numerical computations toreveal its typical features from equations of motion. It is found that the displacement of massm1 may move asymmetricallyaround its equilibrium point, leading to super/sub-harmonic resonance in the amplitude of response to external forcing withdamper. This mechanism is revealed using methods of singular perturbations in the following papers.
2012-01-31