Three-dimensional transient dynamics of a towed system is investigated in this paper. The tow cable is modeled as a geometrically exact (GE) beam, and the payload is a rigid body. The GE beam model incorporates large displacements and rotations of the cable, including cross-sectional shear, which is impossible in current models. Time-domain electromagnetic (TDEM) systems, used in mineral surveying, are selected as a specific application, and so the payload is taken as a rigid ring attached to the cable through rigid, massless links. Aerodynamic loads, including von Kármán forces, are computed by adding loads experienced by small cylindrical elements constituting the cable and the payload. The heavy aircraft remains unaffected by the underslung system’s motion. The governing equations are derived and solved using a nonlinear finite element method, which requires computationally coupling the GE beam (cable) with the rigid payload. The dynamics of a model TDEM system under several flight conditions is then simulated to investigate 1) transient oscillations driven by von Kármán effect, 2) steady-state payload configurations, and 3) von Mises stress in the cable at its point of attachment to the aircraft. Our general formulation, with straightforward modifications of the payload model, will also be useful for other such cable-towed systems.

本文研究了牵引系统的三维瞬态动力学。拖缆建模为几何精确（GE）梁，有效载荷为刚体。GE梁模型包含电缆的大位移和旋转，包括横截面剪切，这在当前模型中是不可能的。选择在矿物勘测中使用的时域电磁（TDEM）系统作为特定应用，因此有效载荷被视为通过刚性，无质量链连接到电缆的刚性环。包括冯·卡尔曼力在内的空气动力学载荷是通过将构成电缆和有效载荷的小圆柱体所承受的载荷相加而得出的。重型飞机仍然不受下悬系统运动的影响。使用非线性有限元方法推导并求解控制方程，这需要将GE梁（电缆）与刚性有效载荷进行计算耦合。然后模拟TDEM系统在几种飞行条件下的动力学特性，以研究1）由vonKármán效应驱动的瞬态振荡，2）稳态有效载荷配置，以及3）电缆在其附着点处的von Mises应力飞机。我们对一般有效载荷模型进行了简单修改的​​一般公式对于其他类似的电缆拖曳系统也将很有用。