Efficient Time-Domain Model for Frequency-Dependent Added Mass and Damping

Abstract

In simulation of 1st-order wave-induced motion of vessels it is sometimes necessary to express frequency-dependent added mass and damping in time-domain formulation. One way to do this is to transform the frequency dependence into retardation functions. During simulation these are convolved with the velocity history, which is time-consuming and impractical. To get a more efficient model a method for expressing the retardation function as a linear differential equation has been developed. The method calculates the coefficients of the differential equation from the damping function only, avoiding the uncertain added mass function.

Time- vs. Frequency-domain Identification of Parametric Radiation Force Models for Marine Structures at Zero Speed

“…This issue, however, is solvable by adding constraints related to the stability of the system. Kaasen and Mo (2004) addressed this problem in a different way. They made a partial-fraction expansion of (20) in terms of ω 2 :…”

“…In the sequel, we revisit the second approach, which was first proposed by Jefferys (1984) and then further analysed by Damaren (2000). Kaasen and Mo (2004) propose a variant to estimate the parameters of the approximation for K(jω), but using only the data of B(ω). This approach has the advantage that the infinite frequency added mass is not necessary; and therefore, it is useful if one has data from 2D hydrodynamic codes that in general do not compute A(∞).…”

“…This, however, should be done carefully, since the method described in the previous section can be sensitive to this value. Kaasen and Mo (2004) presented a method that resolves this problem by estimating the parameters using only the data of the computed damping B ik (ω). This is possible because the parametric models for K ik (s) are stable and proper; therefore, it follows form Bode's integrals that the real part contains all the information to reconstruct the imaginary part (Serón et al, 1997).…”

Joint Identification of Infinite-Frequency Added Mass and Fluid-Memory Models of Marine Structures

“…In these cases, we cannot form K(jω) as indicated in (6). Kaasen and Mo (2004) addressed this problem by making a partial-fraction expansion of the real part ofK ik (s) in terms of ω 2 . The poles and residuals of this expansion can be estimated using Least-squares and the damping data B ik (ω).…”

“…The model identified relates the total radiation forces to the velocities, and it allows identifying the infinite-frequency added mass together with a fluid memory model. The proposed method is motivated by the work of Kaasen and Mo (2004), but provides a simpler alternative.…”