On the undamped free vibration of a mass interacting with a Hertzian contact stiffness
On the undamped free vibration of a mass interacting with a Hertzian contact stiffness
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DOI：
10.1016/j.mechrescom.2011.07.012
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发表时间：
2011-12
影响因子：
2.4
通讯作者：
Huifang Xiao;M. Brennan;Y. Shao
中科院分区：
文献类型：
--
作者：
Huifang Xiao;M. Brennan;Y. Shao
使用三种方法来确定与赫兹接触刚度相互作用的质量的无阻尼自由振动的固有频率。精确值是使用运动的第一积分确定的。调和平衡法用于变换方程的近似解，多尺度法用于近似方程。还确定了避免接触损失的最大初始位移，并通过解析获得了相应的精确固有频率。通过研究平坦刚性表面上弹性球体的自由振动来评估这些方法。
Three methods are used to determine the natural frequency of undamped free vibration of a mass interacting with a Hertzian contact stiffness. The exact value is determined using the first integral of motion. The harmonic balance method is used on a transformed equation for an approximate solution, and the multiple scales method is used on an approximate equation. The maximum initial displacement avoiding contact loss is also determined, and the corresponding exact natural frequency is also obtained analytically. The methods are evaluated by studying the free vibration of an elastic sphere on a flat rigid surface.