Added mass matrix estimation of beams partially immersed in water using measured dynamic responses

An added mass matrix estimation method for beams partially immersed in water is proposed that employs dynamic responses, which are measured when the structure is in water and in air. Discrepancies such as mass and stiffness matrices between the finite element model (FEM) and real structure could be separated from the added mass of water by a series of correction factors, which means that the mass and stiffness of the FEM and the added mass of water could be estimated simultaneously. Compared with traditional methods, the estimated added mass correction factors of our approach will not be limited to be constant when FEM or the environment of the structure changed, meaning that the proposed method could reflect the influence of changes such as water depth, current, and so on. The greatest improvement is that the proposed method could estimate added mass of water without involving any water-related assumptions because all water influences are reflected in measured dynamic responses of the structure in water. A five degrees-of-freedom (dofs) mass-spring system is used to study the performance of the proposed scheme. The numerical results indicate that mass, stiffness, and added mass correction factors could be estimated accurately when noise-free measurements are used. Even when the first two modes are measured under the 5 percent corruption level, the added mass could be estimated properly. A steel cantilever beam with a rectangular section in a water tank at Ocean University of China was also employed to study the added mass influence on modal parameter identification and to investigate the performance of the proposed method. The experimental results demonstrated that the first two modal frequencies and mode shapes of the updated model match well with the measured values by combining the estimated added mass in the initial FEM.