Calculation of coupled added mass of multibody system immersed in fluids

The natural frequencies of structures submerged in a fluid are significantly influenced by fluid properties and adjacent structures, which can be expressed by added mass. Some finite element software can effectively determine the added mass matrix of arbitrary structures immersed in viscous fluids, provided the structure lengths are relatively long; however, the added mass specified in a second-order tensor cannot be used as is. Herein, we propose methods to calculate the coupled added mass as a single value for each structure using the MassInFlu code. When the x- and y-directional components of the coupled added mass are unequal, an effective added mass can be determined by rotating the structures or coordinate axes. Various examples considering different scenarios show that the coupled natural frequencies obtained using the coupled or effective added mass coincide with those obtained from fluid-structure interaction analyses.