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added mass amplitude analysis ASCE Bessel function boundary conditions Chakrabarti circular cylinder cnoidal coefﬁcients components computed cosh cosh ks cylinder damping deﬁned deﬁnition diffraction distribution drag force dynamic energy density ﬁeld ﬁnite ﬁrst ﬁxed ﬂoating structure ﬂow ﬂuid Fourier Fourier series free surface frequency given hydrodynamic hydrodynamic coefﬁcients inertia installed integral kinematics lift force loads maximum method modiﬁed mooring Morison equation nondimensional nonlinear North Sea obtained ocean waves offshore structures oscillation parameter phase angle platform pressure probability density probability density function Rayleigh distribution response Sarpkaya satisﬁes second-order shown in Fig signiﬁcant wave height sinh solution spectral spectrum model Stokes stream function submerged tanker tension leg platform values of CM velocity potential vertical cylinder vertical force water depth water particle velocity wave forces wave length wave period wave proﬁle wave record wave theory zero