def first_order_excitation(k, draft, radius, water_depth):
"""Returns F/(rho g a^2 A) -- from Drake, but adapted by me to
integrate down to the draft depth only (not to the seabed)"""
ka = k * radius
kd = k * draft
kh = k * water_depth
# XXX check this!
f1 = -1j * (jn(1, ka) - jnd(1, ka) * hankel2(1, ka) / hankel2d(1, ka))
#f1 = -1j * (jn(1, ka) - jnd(1, ka) * hankel1(1, ka) / hankel1d(1, ka))
M = (kd * sinh(kh - kd) + cosh(kh - kd) - cosh(kh)) / (k * cosh(kh))
F = (-sinh(kh - kd) + sinh(kh)) / cosh(kh)
X = np.zeros(M.shape + (6, ), dtype=np.complex)
X[..., 0] = (-2 * pi / ka) * f1 * F
X[..., 4] = (-2 * pi / ka) * f1 * M
return X
def excitation_force(w, draft, radius, water_depth):
"""Excitation force on cylinder using Drake's first_order_excitation"""
k = w**2 / 9.81
ka = k * radius
kd = k * draft
kh = k * water_depth
rho = 1025
g = 9.81
# XXX check this!
f1 = -1j * (jn(1, ka) - jnd(1, ka) * hankel2(1, ka) / hankel2d(1, ka))
#f1 = -1j * (jn(1, ka) - jnd(1, ka) * hankel1(1, ka) / hankel1d(1, ka))
M = (kd * sinh(kh - kd) + cosh(kh - kd) - cosh(kh)) / (k**2 * cosh(kh))
F = (-sinh(kh - kd) + sinh(kh)) / (k * cosh(kh))
zs = zeros_like(F, dtype=np.complex)
X = np.c_[F, zs, zs, zs, M, zs]
X *= (-rho * g * pi * radius) * 2 * f1[:, newaxis]
return X
