Propagation of longitudinal deformation wave along a lifting rope of variable length
Propagation of longitudinal deformation wave along a lifting rope of variable length
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DOI：
10.1016/j.ijsolstr.2011.08.005
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发表时间：
2011-12
影响因子：
3.6
通讯作者：
A. G. Razdolsky
中科院分区：
文献类型：
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作者：
A. G. Razdolsky
变长绳的运动问题是一维波动方程的变边界边值问题。绳索长度的变化是由作用在绳索上横截面上的力引起的。研究波沿绳索沿着的传播过程是基于已知的积分-微分关系。该问题被简化为求解两个带有滞后参数的常微分方程，该方程描述了绳索的可变长度及其下端的位置。方程的右侧中涉及的函数的自变量值落后于方程的左侧中的自变量值一个时间间隔，该时间间隔是变形波在整个当前绳索长度上传播所花费的。该问题的解决是通过使用一种技术的顺序延续的解决方案，在循环模式的每个方程交替。这种技术的计算机实现没有问题。为解决这一问题，已编制了一个试验性的计算机程序。在主动力随时间分段线性变化的情况下，给出了数值解的结果。
The problem of motion of the rope of variable length consists of solving the boundary value problem with a variable boundary for the one-dimensional wave equation. A change of the rope length is caused by the force acting at the upper cross section of the rope. Studying the wave propagation process along the rope is based on the known integro-differential relation. The problem is reduced to solving two ordinary differential equations with a retarded argument that describe the variable length of the rope and the position of its lower end. The value of argument for functions involved in the right-hand side of the equations lag behind the argument value in the left-hand side of the equations by a time interval it takes for a propagation of the deformation wave throughout the current rope length. The problem is solved by using a technique of the sequential continuation of solution in the cyclic mode for each of the equation alternately. A computer realization of this technique presents no problem. A pilot computer program has been developed for solving the problem. Results of the numerical solution are presented in the case that the active force varies with time according to a piecewise linear relation.