fix: lump HydroDyn filled-member ballast into deck-built floating platforms

CHANGELOG.md

@@ -81,11 +81,33 @@ The format follows [Keep a Changelog](https://keepachangelog.com/en/1.1.0/).
   `Tower.run` on a free-free floating model now warns (`UserWarning`)
   when `hydro_K + mooring_K` has a negative direction, naming the
   dominant DOFs: the platform is statically unstable there and the
-  general solver leaves those modes out of the result. The bundled
-  `08_nrel5mw_oc4semi` sample triggers it — the OC4 DeepCwind deck keeps
-  its ballast in HydroDyn filled members rather than `PtfmMass`, which
-  the platform model does not include, so its roll / pitch restoring is
-  negative and the modes labelled roll / pitch there are tower bending.
+  general solver leaves those modes out of the result.
+- **Ballast held in HydroDyn filled members was missing from floating
+  models.** Some decks keep their water ballast out of ElastoDyn's
+  `PtfmMass` and declare it as HydroDyn filled-member groups, which
+  OpenFAST applies through HydroDyn at run time. The OC4 DeepCwind semi
+  is the standard case, with 3.852e6 kg of steel in `PtfmMass` and
+  9.62e6 kg of water in two fill groups. `Tower.from_elastodyn_with_mooring`
+  and the deck-backed tier of `Tower.from_windio_floating` now read the
+  joints, cross-sections, members and fill groups of the HydroDyn deck
+  and lump the fill into the platform as the rigid, body-fixed ballast
+  HydroDyn models it as: mass, centre of mass and full 3×3 inertia about
+  the combined centre of mass. On OC4 this gives 1.3476e7 kg with the
+  centre of mass 13.460 m below MSL, against 1.3473e7 kg and 13.46 m in
+  Robertson et al. (2014), NREL/TP-5000-60601. Roll / pitch restoring
+  goes from −3.8e8 to +9.85e8 N·m/rad and all six rigid-body modes come
+  back (surge / sway 0.0088, heave 0.0579, roll / pitch 0.0390, yaw
+  0.0125 Hz); before, the modes labelled roll and pitch were tower
+  bending. Decks without fill groups are unaffected. Only cylindrical
+  filled members are supported; a rectangular one raises
+  `NotImplementedError` rather than being skipped.
+- **Bundled floating samples regenerated.** `08_nrel5mw_oc4semi` now
+  carries the ballasted platform above (its first tower FA mode moves
+  from 0.4507 to 0.4284 Hz), and `09_iea15_umainesemi`,
+  `10_iea22_semi` and `11_upscale25_centraltower` now include the weight
+  restoring in `hydro_K` (roll / pitch +3.4e8, +1.3e7 and −1.4e9
+  N·m/rad; all stay positive). Every sample README picks up the
+  corrected dense-solver frequencies.
 - **`Tower.add_point_mass` on a deck-built floater now updates the
   weight restoring.** The weight term is formed when the model is
   constructed, so a lump added afterwards reached the FEM mass matrix but

VALIDATION.md

@@ -129,6 +129,7 @@ by title + publisher:
 - Jonkman, Butterfield, Musial & Scott (2009). *Definition of a 5-MW Reference Wind Turbine for Offshore System Development*. NREL/TP-500-38060. [PDF](https://docs.nrel.gov/docs/fy09osti/38060.pdf).
 - Jonkman & Musial (2010). *Offshore Code Comparison Collaboration (OC3) for IEA Wind Task 23*. NREL/TP-5000-48191. [PDF](https://docs.nrel.gov/docs/fy11osti/48191.pdf).
 - Jonkman (2010). *Definition of the Floating System for Phase IV of OC3*. NREL/TP-500-47535. [PDF](https://docs.nrel.gov/docs/fy10osti/47535.pdf).
+- Robertson, Jonkman, Masciola, Song, Goupee, Coulling & Luan (2014). *Definition of the Semisubmersible Floating System for Phase II of OC4*. NREL/TP-5000-60601. [PDF](https://docs.nrel.gov/docs/fy14osti/60601.pdf).
 - Bortolotti, Tarrés, Dykes, Merz, Sethuraman, Verelst & Zahle (2019). *IEA Wind TCP Task 37: Systems Engineering in Wind Energy — WP2.1 Reference Wind Turbines*. NREL/TP-5000-73492. [PDF](https://docs.nrel.gov/docs/fy19osti/73492.pdf).
 - Gaertner et al. (2020). *IEA Wind TCP Task 37: Definition of the IEA 15-Megawatt Offshore Reference Wind Turbine*. NREL/TP-5000-75698. [PDF](https://docs.nrel.gov/docs/fy20osti/75698.pdf).
 - Allen et al. (2020). *Definition of the UMaine VolturnUS-S Reference Platform Developed for the IEA Wind 15-Megawatt Offshore Reference Wind Turbine*. NREL/TP-5000-76773. [PDF](https://docs.nrel.gov/docs/fy20osti/76773.pdf).
@@ -230,6 +231,9 @@ is behavioural / contract-style.
 | Floating weight restoring $-g \sum m_i (z_i - z_{ref})$ in roll / pitch (platform + tower + RNA) | closed form; classical $C_{44} = \rho g V (z_B - z_G) + \rho g I_{wp}$ (Faltinsen 1990, ch. 2) | 6×6 weight matrix, reference-point shift, mass scaling, point masses | `rel = 1e-9` | exact | [`tests/test_floating_weight_restoring.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_floating_weight_restoring.py) | no |
 | Negative platform restoring is reported, not silently dropped | construction (OC3 Hywind sample with the weight term removed) | `UserWarning` naming roll / pitch | always | (within tol) | [`tests/test_floating_weight_restoring.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_floating_weight_restoring.py) | no |
 | **`Tower.from_elastodyn_with_mooring` — OC3 Hywind rigid-body frequencies** (WAMIT `.hst` + weight of platform, tower and RNA) | Jonkman (2010) NREL/TP-500-47535, FAST full-system natural frequencies: surge/sway 0.0080, heave 0.0324, roll 0.0342, pitch 0.0343 Hz | six labelled rigid-body modes | surge/sway/roll/pitch 3 %, heave 2 % | surge/sway 0.8 %, heave 0.0 %, roll 1.1 %, pitch 1.4 % (roll/pitch were missing before the weight term) | [`tests/test_floating_weight_restoring.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_floating_weight_restoring.py) | yes |
+| HydroDyn filled-member ballast mass properties (body-fixed, as HydroDyn precomputes them) | closed form: solid cylinder, frustum volume / centroid / axial moment, parallel axis | mass, centre of mass, 3×3 inertia; partial / full / empty, horizontal, inclined, tapered members; both member-table layouts | `rel = 1e-12` | exact | [`tests/test_hydrodyn_ballast.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_hydrodyn_ballast.py) | no |
+| **`Tower.from_elastodyn_with_mooring` — OC4 DeepCwind ballasted platform** (steel `PtfmMass` + two HydroDyn fill groups) | Robertson et al. (2014) NREL/TP-5000-60601: platform incl. ballast 1.3473e7 kg, CM 13.46 m below SWL | platform mass, CM depth; positive roll / pitch restoring; six labelled rigid-body modes; heave vs single-DOF estimate | mass `rel = 1e-3`, CM `abs = 0.01 m`, heave `rel = 2%` | mass +0.02 %, CM 0.000 m | [`tests/test_hydrodyn_ballast.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_hydrodyn_ballast.py) | yes |
+| Bundled floating samples are statically stable | construction (samples 07-11) | six labelled rigid-body modes, no negative-restoring warning | always | (within tol) | [`tests/test_floating_samples_spectra.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_floating_samples_spectra.py) | no |
 | `MudlineFoundation.from_soil_properties` — Yu & Amdahl (2023) Table 9 DTU 10 MW flexible pile, E\_SO = 30 MPa | Yu and Amdahl (2023) Marine Structures 92, 103482, Table 9 row 2 | K\_hh, K\_hr, K\_rr via Shadlou and Bhattacharya (2016) formulas | `rel = 10%` | within 3.0 % on all three springs | [`tests/test_foundation.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_foundation.py) | no |
 | `MudlineFoundation.from_soil_properties` — Yu & Amdahl (2023) Table 9 DTU 10 MW rigid pile, E\_SO = 30 MPa | Yu and Amdahl (2023) Table 9 row 1 | K\_hh, K\_hr, K\_rr via Shadlou and Bhattacharya (2016) rigid-pile formulas | `rel = 5%` | within 2.9 % on all three springs | [`tests/test_foundation.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_foundation.py) | no |
 | `MudlineFoundation.as_mooring_K` — cross-coupling sign matches Jonkman 2010 OC3 convention | construction | K\[0,4\] < 0, K\[1,3\] > 0, K\[0,4\]·K\[1,3\] < 0 | always | (within tol) | [`tests/test_foundation.py`](https://github.com/SMI-Lab-Inha/pyBModes/blob/master/tests/test_foundation.py) | no |

docs/conventions.rst

@@ -299,6 +299,12 @@ Common pitfalls
   a ballast-stabilised spar is negative in roll / pitch (OC3 Hywind:
   ``−5.0e9 N·m/rad``), and ``Tower.run`` warns that those rigid-body
   modes are unstable rather than returning them.
+* **Leaving out ballast declared in HydroDyn.** Water ballast given as
+  HydroDyn filled-member groups is not in ElastoDyn's ``PtfmMass``
+  (OC4 DeepCwind keeps all of it there). The deck constructors lump it
+  into ``mass_pform``, ``cm_pform`` and ``i_matrix`` as the rigid ballast
+  HydroDyn treats it as; a hand-built ``PlatformSupport`` has to include
+  it itself.
 
 * **Confusing OpenFAST's two frames.** ``PtfmCMzt`` (CM) and
   ``PtfmRefzt`` (reference) are both in the tower-base *t*-frame;

src/pybmodes/_examples/sample_inputs/reference_turbines/01_nrel5mw_land/README.md

@@ -33,13 +33,13 @@ This sample is a cantilever (`hub_conn = 1`) clamped at TowerBsHt with the RNA l
 
 ### Tower
 
-- 1st FA tower-bending: **0.3332 Hz**
+- 1st FA tower-bending: **0.3304 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 12.1 rpm`)
 
-- 1st flap: **0.7343 Hz**
-- 1st edge: **1.1083 Hz**
-- 2nd flap: **2.0177 Hz**
+- 1st flap: **0.7342 Hz**
+- 1st edge: **1.1080 Hz**
+- 2nd flap: **2.0175 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/02_nrel5mw_oc3monopile/README.md

@@ -33,13 +33,13 @@ This sample is a combined pile + tower cantilever (`hub_conn = 1`) clamped at th
 
 ### Tower
 
-- 1st FA tower-bending: **0.2856 Hz**
+- 1st FA tower-bending: **0.2869 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 12.1 rpm`)
 
-- 1st flap: **0.7343 Hz**
-- 1st edge: **1.1083 Hz**
-- 2nd flap: **2.0177 Hz**
+- 1st flap: **0.7342 Hz**
+- 1st edge: **1.1080 Hz**
+- 2nd flap: **2.0175 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/03_iea34_land/README.md

@@ -33,13 +33,13 @@ This sample is a cantilever (`hub_conn = 1`) clamped at TowerBsHt with the RNA l
 
 ### Tower
 
-- 1st FA tower-bending: **0.4172 Hz**
+- 1st FA tower-bending: **0.4179 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 5 rpm`)
 
-- 1st flap: **0.7958 Hz**
-- 1st edge: **1.0294 Hz**
-- 2nd flap: **2.3593 Hz**
+- 1st flap: **0.7960 Hz**
+- 1st edge: **1.0296 Hz**
+- 2nd flap: **2.3592 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/04_iea10_monopile/README.md

@@ -33,13 +33,13 @@ This sample is a combined pile + tower cantilever (`hub_conn = 1`) clamped at th
 
 ### Tower
 
-- 1st FA tower-bending: **0.3008 Hz**
+- 1st FA tower-bending: **0.3000 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 5 rpm`)
 
-- 1st flap: **0.4044 Hz**
-- 1st edge: **0.6496 Hz**
-- 2nd flap: **1.0430 Hz**
+- 1st flap: **0.4050 Hz**
+- 1st edge: **0.6494 Hz**
+- 2nd flap: **1.0433 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/05_iea15_monopile/README.md

@@ -33,13 +33,13 @@ This sample is a combined pile + tower cantilever (`hub_conn = 1`) clamped at th
 
 ### Tower
 
-- 1st FA tower-bending: **0.1906 Hz**
+- 1st FA tower-bending: **0.1883 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 7.55 rpm`)
 
-- 1st flap: **0.5583 Hz**
-- 1st edge: **0.7278 Hz**
-- 2nd flap: **1.5915 Hz**
+- 1st flap: **0.5585 Hz**
+- 1st edge: **0.7281 Hz**
+- 2nd flap: **1.5916 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/06_iea22_monopile/README.md

@@ -33,13 +33,13 @@ This sample is a combined pile + tower cantilever (`hub_conn = 1`) clamped at th
 
 ### Tower
 
-- 1st FA tower-bending: **0.1819 Hz**
+- 1st FA tower-bending: **0.1701 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 3 rpm`)
 
-- 1st flap: **0.3998 Hz**
-- 1st edge: **0.5381 Hz**
-- 2nd flap: **1.1032 Hz**
+- 1st flap: **0.3987 Hz**
+- 1st edge: **0.5388 Hz**
+- 2nd flap: **1.1031 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/07_nrel5mw_oc3hywind_spar/README.md

@@ -37,9 +37,9 @@ This sample is a free-free flexible-tower (`hub_conn = 2`) with a full PlatformS
 
 ### Blade  (spinning at deck `RotSpeed = 12.1 rpm`)
 
-- 1st flap: **0.7343 Hz**
-- 1st edge: **1.1083 Hz**
-- 2nd flap: **2.0177 Hz**
+- 1st flap: **0.7342 Hz**
+- 1st edge: **1.1080 Hz**
+- 2nd flap: **2.0175 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/08_nrel5mw_oc4semi/08_nrel5mw_oc4semi_tower.bmi

@@ -50,12 +50,12 @@ Distance of element boundary nodes from tower base (norm. by tower length), el_l
 --------- Properties of tower support subsystem ---------------------------------------------
 1          tow_support: 1 = floating-platform with optional tension wires (-)
 -10.000000    draft        : depth of tower base from MSL (m)
-8.658800    cm_pform     : distance of platform c.m. below MSL (m)
-3.852180e+06    mass_pform   : platform mass (kg)
+13.460321  0.000002  0.000000    cm_pform_xyz : platform c.m. below MSL + horizontal (x downwind, y lateral) offsets from the tower axis (m)
+1.347603e+07    mass_pform   : platform mass (kg)
 Platform mass inertia 3X3 matrix (i_matrix_pform):  [OC4 DeepCwind semi (Robertson 2014) via HydroDyn+MoorDyn]
-        2.561930e+09     0.000000e+00     0.000000e+00
-        0.000000e+00     2.561930e+09     0.000000e+00
-        0.000000e+00     0.000000e+00     4.242650e+09
+        7.099696e+09     0.000000e+00     6.165441e+01
+        0.000000e+00     7.099696e+09     0.000000e+00
+        6.165441e+01     0.000000e+00     1.280537e+10
 -0.000000    ref_msl    : distance of platform reference point below MSL (m)
 Hydrodynamic 6X6 mass matrix at platform ref point (hydro_M)  [OC4 DeepCwind semi (Robertson 2014) via HydroDyn+MoorDyn]:
         8.740059e+06     0.000000e+00    -3.871260e-01     0.000000e+00    -1.075816e+08     0.000000e+00
@@ -68,16 +68,16 @@ Hydrodynamic 6X6 stiffness matrix at platform ref point (hydro_K)  [OC4 DeepCwin
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     3.820308e+06     0.000000e+00    -1.541053e+02     0.000000e+00
-        0.000000e+00     0.000000e+00     0.000000e+00    -3.807176e+08     0.000000e+00     0.000000e+00
-        0.000000e+00     0.000000e+00    -1.541053e+02     0.000000e+00    -3.807153e+08     0.000000e+00
+        0.000000e+00     0.000000e+00     0.000000e+00     9.852074e+08     0.000000e+00     0.000000e+00
+        0.000000e+00     0.000000e+00    -1.541053e+02     0.000000e+00     9.852097e+08     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
 Mooring-system 6X6 stiffness matrix (mooring_K):  [OC4 DeepCwind semi (Robertson 2014) via HydroDyn+MoorDyn]
         7.083634e+04    -0.000000e+00     1.049534e-01    -0.000000e+00    -1.095301e+05    -0.000000e+00
        -0.000000e+00     7.083592e+04    -0.000000e+00     1.095165e+05    -0.000000e+00    -1.105049e+01
-        1.049534e-01    -0.000000e+00     1.914043e+04    -0.000000e+00    -2.706354e+02    -5.820766e-10
+        1.049534e-01    -0.000000e+00     1.914043e+04    -0.000000e+00    -2.706354e+02    -0.000000e+00
        -0.000000e+00     1.095165e+05    -0.000000e+00     8.770363e+07    -0.000000e+00     5.655611e+04
-       -1.095301e+05    -0.000000e+00    -2.706354e+02    -0.000000e+00     8.770406e+07    -2.328306e-09
-       -0.000000e+00    -1.105049e+01    -5.820766e-10     5.655611e+04    -2.328306e-09     1.180255e+08
+       -1.095301e+05    -0.000000e+00    -2.706354e+02    -0.000000e+00     8.770406e+07     2.328306e-09
+       -0.000000e+00    -1.105049e+01    -0.000000e+00     5.655611e+04     2.328306e-09     1.180255e+08
 
 Distributed (hydrodynamic) added-mass per unit length along the flexible tower:
 0           n_secs_m_distr: number of distributed-added-mass stations (-)

src/pybmodes/_examples/sample_inputs/reference_turbines/08_nrel5mw_oc4semi/README.md

@@ -33,13 +33,13 @@ This sample is a free-free flexible-tower (`hub_conn = 2`) with a full PlatformS
 
 ### Tower
 
-- 1st FA tower-bending: **0.4507 Hz**
+- 1st FA tower-bending: **0.4284 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 9 rpm`)
 
-- 1st flap: **0.7118 Hz**
-- 1st edge: **1.1043 Hz**
-- 2nd flap: **1.9913 Hz**
+- 1st flap: **0.7117 Hz**
+- 1st edge: **1.1042 Hz**
+- 2nd flap: **1.9914 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/09_iea15_umainesemi/09_iea15_umainesemi_tower.bmi

@@ -68,8 +68,8 @@ Hydrodynamic 6X6 stiffness matrix at platform ref point (hydro_K)  [UMaine Voltu
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     4.453443e+06     0.000000e+00    -4.033086e+03     0.000000e+00
-        0.000000e+00     0.000000e+00     0.000000e+00     2.193713e+09     0.000000e+00    -9.130073e+04
-        0.000000e+00     0.000000e+00    -4.033086e+03     0.000000e+00     2.193473e+09     0.000000e+00
+        0.000000e+00     0.000000e+00     0.000000e+00     2.538614e+09     0.000000e+00    -9.130073e+04
+        0.000000e+00     0.000000e+00    -4.033086e+03     0.000000e+00     2.538374e+09     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00    -9.130073e+04     0.000000e+00     0.000000e+00
 Mooring-system 6X6 stiffness matrix (mooring_K):  [UMaine VolturnUS-S semi (Allen 2020) via HydroDyn+MoorDyn]
         7.189209e+04    -0.000000e+00    -3.420710e-01    -0.000000e+00     1.146452e+06    -0.000000e+00

src/pybmodes/_examples/sample_inputs/reference_turbines/09_iea15_umainesemi/README.md

@@ -33,13 +33,13 @@ This sample is a free-free flexible-tower (`hub_conn = 2`) with a full PlatformS
 
 ### Tower
 
-- 1st FA tower-bending: **0.5255 Hz**
+- 1st FA tower-bending: **0.5256 Hz**
 
 ### Blade  (spinning at deck `RotSpeed = 7.55 rpm`)
 
-- 1st flap: **0.5583 Hz**
-- 1st edge: **0.7278 Hz**
-- 2nd flap: **1.5915 Hz**
+- 1st flap: **0.5585 Hz**
+- 1st edge: **0.7281 Hz**
+- 2nd flap: **1.5916 Hz**
 
 ## Comparison with published values
 

src/pybmodes/_examples/sample_inputs/reference_turbines/10_iea22_semi/10_iea22_semi_tower.bmi

@@ -68,16 +68,16 @@ Hydrodynamic 6X6 stiffness matrix at platform ref point (hydro_K)  [IEA-22 semi
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00     0.000000e+00
         0.000000e+00     0.000000e+00     4.837443e+06     0.000000e+00    -3.755001e+02     0.000000e+00
-        0.000000e+00     0.000000e+00     0.000000e+00     4.182874e+09     0.000000e+00     4.600509e+04
-        0.000000e+00     0.000000e+00    -3.755001e+02     0.000000e+00     4.182872e+09     0.000000e+00
+        0.000000e+00     0.000000e+00     0.000000e+00     4.196176e+09     0.000000e+00     4.600509e+04
+        0.000000e+00     0.000000e+00    -3.755001e+02     0.000000e+00     4.196174e+09     0.000000e+00
         0.000000e+00     0.000000e+00     0.000000e+00     4.600509e+04     0.000000e+00     0.000000e+00
 Mooring-system 6X6 stiffness matrix (mooring_K):  [IEA-22 semi (Bortolotti 2024) via HydroDyn+MoorDyn]
-        1.287829e+05    -0.000000e+00     6.722716e-02    -0.000000e+00     1.740192e+06    -0.000000e+00
+        1.287829e+05    -0.000000e+00     6.722721e-02    -0.000000e+00     1.740192e+06    -0.000000e+00
        -0.000000e+00     1.287828e+05    -0.000000e+00    -1.740195e+06    -0.000000e+00    -3.233520e+00
-        6.722716e-02    -0.000000e+00     9.519838e+04    -0.000000e+00     8.539450e+02    -0.000000e+00
-       -0.000000e+00    -1.740195e+06    -0.000000e+00     4.882500e+08    -0.000000e+00     2.892178e+04
+        6.722721e-02    -0.000000e+00     9.519838e+04    -4.656613e-09     8.539450e+02    -4.656613e-09
+       -0.000000e+00    -1.740195e+06    -4.656613e-09     4.882500e+08    -0.000000e+00     2.892178e+04
         1.740192e+06    -0.000000e+00     8.539450e+02    -0.000000e+00     4.882518e+08    -0.000000e+00
-       -0.000000e+00    -3.233520e+00    -0.000000e+00     2.892178e+04    -0.000000e+00     4.879339e+08
+       -0.000000e+00    -3.233520e+00    -4.656613e-09     2.892178e+04    -0.000000e+00     4.879339e+08
 
 Distributed (hydrodynamic) added-mass per unit length along the flexible tower:
 0           n_secs_m_distr: number of distributed-added-mass stations (-)

src/pybmodes/_examples/sample_inputs/reference_turbines/10_iea22_semi/README.md

@@ -37,9 +37,9 @@ This sample is a free-free flexible-tower (`hub_conn = 2`) with a full PlatformS
 
 ### Blade  (spinning at deck `RotSpeed = 3 rpm`)
 
-- 1st flap: **0.3998 Hz**
-- 1st edge: **0.5381 Hz**
-- 2nd flap: **1.1032 Hz**
+- 1st flap: **0.3987 Hz**
+- 1st edge: **0.5388 Hz**
+- 2nd flap: **1.1031 Hz**
 
 ## Comparison with published values