The added mass for two-dimensional floating structures

The diagonal terms in the added mass matrix for a two-dimensional surface-piercing structure, which satisfies a geometric condition known as the John condition, are proven to be non-negative. It is also shown that the heave coefficient, associated with a symmetric system of two such structures, is non-negative when the length of the free surface connecting the structures lies between an odd, and the next higher even, number of half-wavelengths. The sway and roll coefficients, associated with antisymmetric motion of the system, are non-negative in the complementary intervals. For a specific geometry these intervals are equivalent to frequency ranges. Negative added mass is associated with rapid variations with frequency, due to complex resonances that correspond to simple poles of the associated radiation potential in the complex frequency domain. Approximate techniques are used to show that, for systems of two structures, complex resonances are located at frequencies consistent with the intervals in which negative added mass is able to occur.