Response Spectrum Method for Submerged Structures

A submerged structure has virtual mass matrix in the inertial term and wet mass matrix in the driving term in the equation of motion, whereas a dry structure has the same mass matrix in these two terms. If a finite element code for dry structures is used to analyze a submerged structure, the results should be adjusted. Result for a Single Degree of Freedom (SDOF) system is scaled by the ratio of wet mass to virtual mass. Results for a Multiple Degree of Freedom (MDOF) system are adjusted by scaling the Floor Response Spectra (FRS) at each modal frequency by a ratio of modal work done in that mode by the wet mass matrix to that by the virtual mass matrix. The adjustment factor can be estimated as a product of a ratio of participation factors and a ratio of modal masses. Both the participation factors and the modal masses are computed by using the wet mass matrix, and then by using the virtual mass matrix, respectively. This method provides an alternative way to assess the margin in the design based on the current FRS method that does not distinguish the difference between the two mass matrices. More studies should be carried out to implement this method in specific practical applications.