Three-Dimensional Dynamics of Towed Underslung Systems Using Geometrically Exact Beam Theory

Abstract

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.