Published on July 2014 | Marine Salvage, Marine Hydrodynamics, Control Systems

Flexible Body Analysis of Lifting a Sunken Chemical Tanker using Multiple Controlled Gas Inflating Bags

In this paper, a mathematical model and numerical time domain approach to simulate the dynamics of a sunken chemical tanker being raised from sea floor by multiple controlled gas inflating bags is presented based on the principles of flexible body modeling & control. In this regard, the vessel or payload is modeled as an Euler-Bernoulli beam with free – free boundary conditions. Free vibration analysis or eigen value analysis of the vessel is carried out in MATLAB using finite element method to obtain the natural frequencies (eigen values) and mode shapes (eigen vectors). From the mode shape plots, the buoyant systems or lift bags are located suitably on the “nodes of a mode” of the beam. Then the eigenvectors are normalized with respect to mass and the equation of motion is developed in principal coordinates after defining the nodal forces and moments. Then the modal contributions of individual modes are analyzed according to their dc gain/peak gain value to define, which ones have greatest contribution and later several modal reduction techniques such as ‘modred-mdc’ and ‘modred-del’ are used to obtain the smallest state space model that represents the pertinent system dynamics. The full and reduced order modal responses are compared in both frequency and time domains. It is observed that ‘unsorted modred-mdc’ is the preferred choice for modal order reduction compared to the other reduction methods. Longitudinal distribution of shear force and bending moments across the tanker are also evaluated. Finally, a supervisory fuzzy logic controller is integrated with the flexible state space model of each lift bags to obtain the controlled stable responses.