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首页> 外文期刊>Nonlinear dynamics >Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism
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Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism

机译：附在刚体上的3D弹性弦摆和惯性固定卷轴机构的计算动力学

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摘要

A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be dynamically varied. The string is assumed to have distributed mass and elasticity that permits axial deformations. The rigid body is attached to the string at an arbitrary point, and the resulting string pendulum system exhibits nontrivial coupling between the elastic wave propagation in the string and the rigid body dynamics. Variational methods are used to develop coupled ordinary and partial differential equations of motion. Computational methods, referred to as Lie group variational integrators, are then developed, based on a finite element approximation and the use of variational methods in a discrete-time setting to obtain discrete-time equations of motion. This approach preserves the geometry of the configurations, and leads to accurate and efficient algorithms that have guaranteed accuracy properties that make them suitable for many dynamic simulations, especially over long simulation times. Numerical results are presented for typical examples involving a constant length string, string deployment, and string retrieval. These demonstrate the complicated dynamics that arise in a string pendulum from the interaction of the rigid body motion, elastic wave dynamics in the string, and the disturbances introduced by the reeling mechanism. Such interactions are dynamically important in many engineering problems, but tend be obscured in lower fidelity models.
机译：针对弹性弦摆开发了一种高保真度模型，其一端连接到刚体，而另一端连接到惯性固定卷轴机构，该机构可以动态改变弦的未拉伸长度。假定弦具有分散的质量和弹性，允许轴向变形。刚体在任意点处附着到弦上，并且所产生的弦摆系统在弦中的弹性波传播与刚体动力学之间表现出非平凡的耦合。变分方法被用来发展运动的耦合的常微分方程和偏微分方程。然后，基于有限元逼近和在离散时间设置中使用变分方法来获得运动的离散时间方程，从而开发了称为李群变分积分器的计算方法。这种方法保留了配置的几何形状，并导致精确有效的算法，这些算法具有保证的精度属性，使其适合于许多动态仿真，尤其是在较长的仿真时间内。针对涉及恒定长度字符串，字符串部署和字符串检索的典型示例，提供了数值结果。这些证明了由于刚体运动，弦中的弹性波动力学以及绕线机构引入的干扰的相互作用，弦摆产生了复杂的动力学。在许多工程问题中，这种交互在动态上是重要的，但在低保真度模型中往往被掩盖。

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