Energetics and conserved functional of axially moving materials undergoing transverse nonlinear vibration
Energetics and conserved functional of axially moving materials undergoing transverse nonlinear vibration
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DOI：
10.1115/1.1760557
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发表时间：
2004-07
期刊：
影响因子：
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通讯作者：
Liqun Chen;J. Zu
中科院分区：
文献类型：
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作者：
Liqun Chen;J. Zu
轴向运动的材料可以代表许多工程设备，如传动带、电梯电缆、塑料薄膜、磁带、纸张、纺织纤维、带锯、架空电缆索道和起重机起重电缆等。轴向运动材料的能量学在轴向运动材料的研究中有相当大的兴趣。当材料在两个支承之间移动时，与轴向运动的材料相关的总机械能不是恒定的。这是轴向运动材料自由横向振动的一个基本特征，而对于无阻尼非平移的弦或梁，总能量是恒定的。Chubachi@4#首先讨论了轴向运动弦线中能量传递的周期性。Miranker@5#分析了轴向运动弦的能量学，并推导出弦能量变化率的时间表达式。Barakat@6#考虑了轴向运动的梁的能量学，发现在足够高的传输速度下，通过支承的能量流动可以使轴向运动的弦和梁的线性理论失效。Tabarrok、Leech和Kim@7表明，无张力行波光束的总能量在时间上是周期性的。Wickert和Mote@8#指出，Miranker表达式只表示局部变化率，因为它忽略了支撑处的能量通量，他们通过应用一维输运定理给出了总能量随局部变化率的时间变化。他们还计算了与运动弦和光束的模式相关的能量的时间变化。Renshaw@9#研究了两个典型绞车问题的总机械能的变化，这两个问题提供了轴向运动系统固定孔处的能量通量的显著不同的例子。Lee和Mote@10，11#提出了平移连续体，包括轴向运动的弦和梁的能量学的一般处理方法。他们考虑了在两个边界上存在非保守力的情况。Renshaw，Rahn，Wickert和Mote@12#从拉格朗日和欧拉两个角度研究了轴向运动的弦和梁的能量。他们的研究表明，对于轴向运动的连续体，拉格朗日和欧拉能量泛函是不守恒的。朱和倪@13#研究了任意长度变化的轴向运动弦和梁的能量学。尽管轴向运动材料的总机械能的欧拉泛函和拉格朗日泛函一般都不是常数，但确实存在替代泛函，它们是连续的。
Axially moving materials can represent many engineering devices such as power transmission belts, elevator cables, plastic films, magnetic tapes, paper sheets, textile fibers, band saws, aerial cable tramways, and crane hoist cables @1–3#. Energetics of axially moving materials is of considerable interest in the study of axially moving materials. The total mechanical energy associated with axially moving materials is not constant when the materials travel between two supports. It is a fundamental feature of free transverse vibration of axially moving materials, while the total energy is constant for an undamped non-translating string or beam. Chubachi @4# first discussed periodicity of the energy transfer in an axially moving string. Miranker @5# analyzed energetics of an axially moving string, and derived an expression for the time rate of change of the string energy. Barakat @6# considered the energetics of an axially moving beam and found that energy flux through the supports can invalidate the linear theories of both the axially moving string and beam at sufficiently high transporting speed. Tabarrok, Leech and Kim @7# showed that the total energy of a travelling beam without tension is periodic in time. Wickert and Mote @8# pointed out that Miranker’s expression represents the local rate of change only because it neglected the energy flux at the supports, and they presented the temporal variation of the total energy related to the local rate of change through the application of the onedimensional transport theorem. They also calculated the temporal variation of energy associated with modes of moving strings and beams. Renshaw @9# examined the change of the total mechanical energy of two prototypical winching problems, which provided strikingly different examples of energy flux at a fixed orifice of an axially moving system. Lee and Mote @10,11# presented a generalized treatment of energetics of translating continua, including axially moving strings and beams. They considered the case that there were nonconservative forces acting on two boundaries. Renshaw, Rahn, Wickert and Mote @12# examined the energy of axially moving strings and beams from both Lagrangian and Eulerian views. Their studies indicated that Lagrangian and Eulerian energy functionals are not conserved for axially moving continua. Zhu and Ni @13# investigated energetics of axially moving strings and beams with arbitrarily varying lengths. Although both the Eulerian and Lagrangian functionals for the total mechanical energy of axially moving materials are generally not constant, there do exist alternative functionals that are con-