The analysis of underwater towed systems attracted the interest of many researchers because of the recent years utilization of remotely-operated underwater vehicle (ROV) and towed array in offshore and military applications. The purpose of this work is to show, by experimental validation, that towed cable configurations may be computed effectively and accurately by discretizing the towing cable rather than using a continuous modeling approach. Two mathematical models have been developed to predict the stationary configuration of an underwater towed system loaded by hydrodynamic forces. The system is composed of a towed inextensible cable, with no bending stiffness, and a depressor that is fixed at the cable free end. This configuration is currently used for underwater remotely-operated vehicle. This work investigates the comparison between continuous and discrete models of the 2D static equations of the steady-state towing problem in a vertical plane at different towing speeds. The results of the models have been validating using experimental trials. In the first part of this paper, a continuous model is presented, which is based on geometric compatibility relations, equilibrium equation. A set of nonlinear differential equations has been derived and solved using Runge-Kutta iterative procedure. In the second part, a discrete rod model is proposed to determinate the cable shape, which is based on a system of nonlinear algebraic equations that are solved numerically. This two models are both suitable for analyzing an underwater towed system having a known top tension and inclination angle obtained from experiments. The third part of the paper describes the experiments, which have been in a towing tank basin (CNR-INSEAN). In the fourth and last part of this study it is demonstrated the effort and cost of numerically integrating the continuous model do not compare favorably with the relative ease and efficiency of solving the discrete model, which yields the same results.
Dynamic behavior analysis of the nonlinear aeroelastic system is one of the interesting topics among researchers that have been studied in recent years. Nonlinear airfoil instability and behavior analysis in subsonic flow are one of the main parts in this field. Aeroelastic systems are characterized by complex nonlinear phenomena due to structural oscillations coupled with the fluid dynamic. The coexistence of phenomena, such as limit cycle oscillation and chaotic vibrations induced by the fluid, can lead the dynamic systems to instability such as flutter which can decrease the system performance, as well as the damage of the structure itself.Historically, the main approach to analyze the dynamic instability of nonlinear aeroelastic systems has been developed by Theodorsen [1] in the frequency domain. His theory aimed to model the aerodynamic loads on an airfoil when the wake releasing is considered as a memory effect on the global fluid-structure interaction dynamic. Wagner proposed a time-domain analysis where the memory effects are represented by convolution Volterra integrals [2]. Both these traditional models are linear, but, in many cases, the dynamic equations of an airfoil became nonlinear due to the presence of nonlinear elements (dampers, stiffness) or for the instabilities generated from the fluid-structure interaction. The nonlinear aerodynamic model in the time domain can be solved by numerical techniques or analytical methods. In the first case, the solutions such as the finite difference method, Runge-Kutta,
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