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首页> 外文期刊>Applied Mathematical Modelling >Dynamic interaction and instability of two moving proximate masses on a beam on a Pasternak viscoelastic foundation
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Dynamic interaction and instability of two moving proximate masses on a beam on a Pasternak viscoelastic foundation

机译：Pasternak粘弹性基础梁两次移动近似肿块的动态相互作用与不稳定性

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The study analyzes the dynamic interaction of proximate masses using a new form of semi-analytical results for the moving mass problem developed by the author. This paper presents the results for a particular case of two moving masses of equal value acted upon by constant forces of equal values. The interaction level was demonstrated to be substantially high, making it impossible to superimpose the results obtained for one mass unless the masses were located at a significantly large distance apart. In the undamped case, the onset of instability occurred at the critical velocity, as with one moving mass; however, the onset of instability could be shifted significantly into the subcritical velocity range in the damped case. The critical distance between the moving masses was determined as the value at which the exponential increase in the amplitudes was severe. The implementation of dimensionless parameters revealed that this distance was slightly dependent on the damping. Moreover, the limiting moving mass ratio for such unexpected instability was derived. The results were validated by eigenmode expansion analysis on long finite beams, for which computational time savings were proposed by the rearrangement of the terms involved. Excellent agreement between the results was obtained, validating the new formulae. Furthermore, extension to more general cases and additional moving masses can easily be achieved.
机译：该研究通过新形式的半分析结果分析了近似群众的动态相互作用，了解作者的移动质量问题。本文呈现了由恒定力的相等力作用的两个移动质量的特定情况的结果。相互作用水平被证明是基本上高的，这使得不可能叠加一体质量所获得的结果，除非质量群体位于相距大大距离。在无法透明的情况下，不稳定性发生在临界速度下，与一个移动质量一样;然而，不稳定性的开始可以显着转移到阻尼案例中的子临界速度范围内。移动质量之间的临界距离被确定为幅度的指数增加严重的值。无量纲参数的实施显示，该距离略微依赖于阻尼。此外，导出了这种意外不稳定性的限制运动质量比。通过长度有限梁的特征模型膨胀分析验证了结果，通过重新排列所涉及的术语来提出计算时间节省。获得了结果之间的良好协议，验证了新公式。此外，可以容易地实现更普遍的情况和额外的移动质量的扩展。

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