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Bistability and accompanying phenomena in the 1-DOF mathematical model of rolling

机译：一自由度轧制数学模型中的双稳态和伴随现象

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摘要

When medium and large amplitudes of rolling are analyzed then in most cases a mathematical model of rolling reveals nonlinear behavior. The typical phenomenon for nonlinear oscillations is the resonance frequency dependency on the amplitude. A strong shift of resonance frequency leads to bistability which means that for the same value of the excitation moment two different amplitudes of rolling are possible. A direct consequence of bistability is the possibility of roll amplitude jumps, which for some conditions are related to the bifurcation phenomenon. When jumps occur then rolling can seem chaotic. The roll spectrum used nowadays is insufficient to describe the extent and nature of these phenomena. Therefore, a novel expanded form of the roll spectrum is proposed where bistability areas and the bistability origin point are included.
机译：当分析中等和大幅度的滚动时，在大多数情况下，滚动的数学模型揭示了非线性行为。非线性振荡的典型现象是共振频率对振幅的依赖性。共振频率的强烈偏移会导致双稳态，这意味着对于相同的激励力矩值，可能会有两个不同的滚动幅度。双稳态的直接结果是侧倾幅度跳跃的可能性，其在某些情况下与分叉现象有关。当发生跳跃时，滚动可能会变得混乱。如今使用的滚动光谱不足以描述这些现象的程度和性质。因此，提出了一种新的扩展形式的侧倾频谱，其中包括了双稳态区域和双稳态起点。

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