Dynamics of a marine lash system with a flexible link

Abstract

In connection with increase in operating depths and expansion of the scope of use of marine lash systems (MLS), it is urgent to improve the theory and methods of designing their flexible links (FL) and refine the existing calculation methods. The existing calculation and design methods are either simplistic and do not take into account the actual loads and the nature of loading of the MLS FL or are rather complicated and cumbersome for design and construction kits and require considerable timing for their implementation. The mathematical model of the MLS dynamics includes not only the FL equations, but also the equations of dynamics of the tugboat and the towed UV. Their movement determines the boundary conditions at the FL nodes with the numbers i = 0 and i = N. The FL node with the number i = 0 is fixed to the tugboat, and the FL node with the number i = N is fixed to the UV. Dynamics of the tugboat and that of the towed UV differ only in their parameters, thus, the equations of their dynamics have the same form. Let us assume that the tugboat and the UV are absolutely rigid rods. Their position in space is determined by the coordinates of their center of mass (хi, yi, zi), the course angle (φk i), the trim angle (φd i) and the roll angle (φkr i). The length of the rods (Li) is equal to the length of the tugboat or the UV. The position of the center of mass is determined by the distance from the stern (Lki) to it. Based on the developed mathematical model, there has been determined a system of equations that describes the FL element dynamics as the result of impact of external forces and reactions of stretching, bending and turning. An algorithm for simulating the FL dynamics is obtained, which makes it possible to perform calculation of the dynamics of the MLS FL and further proceed to development of a computer program describing the MLS dynamics.