As described in Wind, the wind speed generally consists of a mean velocity over a given period of time (usually 1 hour) at a standard height above the water surface (usually 10m), and a turbulent time-varying wind speed about the mean speed in a constant direction with respect to the fixed reference axes, as expressed in Equation 2–67. In a frequency domain analysis we assume that the displacement response of a structure from its equilibrium position is small, and that the turbulent time-varying wind speed is small compared to the mean wind speed. Based on these assumptions, and by substituting Equation 2–71 into Equation 7–2, for the wind hull drag force:

(12–1)

where the subscript j (j = 1, 3) represents the force components in the local structure x-, y- and z-directions respectively, the subscript j (j = 4, 6) represents the moment components about the local structure x-, y- and z-directions respectively, is the relative angle between the wind direction and the structure at its equilibrium position, (j = 1, 6) are the wind hull drag coefficients at , and is the velocity of the structure in the wind direction.

The first term of Equation 12–1 involves the signed square of the mean wind velocity, the components of which will not directly affect the frequency-dependent response. However, this term does contribute to the stiffness due to small yaw motion. In the local structure axis system (LSA), the additional stiffness matrix components due to the constant wind drag forces and yaw motion are

(12–2)

From Equation 12–1, the amplitude of the linear frequency-dependent wind force at a frequency point (k = 1, ) is

(12–3)

Finally, the linear wind drag damping force is

(12–4)