TOWER FORE-AFT MODE SHAPES, coefficients of polynomial terms

[EWEMkite]

Dear @jjonkman,

I write a python code for the modal analysis of the tower, in the code I establish the mass and stiffness matrix then use eigenvalues, eigenvectors = eigh(stiffness_matrix, mass_matrix_scaled). But because the coordinates are defined as (z/L), the eigenvectors [6X6] give the coefficients of (z/L) ~ (z/L)^6 for mode 1~6 I think. As far as I know, the mode shape and eigenvector are connected by for examle: mode shape [Z] = sum(eigenvector[:, 0] · [(z/L), (z/L)^2, (z/L)^3, (z/L)^4, (z/L)^5, (z/L)^6])

I am not very sure what should I do to get the required coefficients for x^1 ~ x^6 in ElastoDyn file, should I just multiply eigenvectors with L ~ L^6, or should I just use z rather than z/L when building the matrix? I use z/L because it's an equation I found in this paper:
https://www.researchgate.net/publication/372289833_A_Rayleigh-Ritz_solution_for_high_order_natural_frequencies_and_eigenmodes_of_monopile_supported_offshore_wind_turbines_considering_tapered_towers_and_soil_pile_interactions

[jjonkman]

Dear @EWEMkite,

I'm not really sure I understand your question. If you are looking to fit the mode shape polynomial for ElastoDyn from a given mode shape, the old ModeShapePolyFitting.xls spreadsheet would compute these using a number of different methods. A MATLAB-based version of this script was provided on our forum: https://forums.nrel.gov/t/fast-tower-polynomial-mode-shapes-from-bmodes-matlab-script/1637. If you are looking for a Python-based tool, while I haven't used this myself, I found the _get_modal_coefficients() function of the bmodes_out_file.py script in the OpenFAST Toolbox: https://github.com/OpenFAST/openfast_toolbox/blob/main/openfast_toolbox/io/bmodes_out_file.py.

Best regards,

[EWEMkite]

Dear @jjonkman ,

I tried with BModes, but the outputs show a very small frequency (the first mode has a magnitude of 0.0001). I suppose there is something wrong in the input files, could you help me have a check? Thanks.
`====================== BModes v1.03 Main Input File ==================
Modes of a 82.4m tower with tip mass

--------- General parameters ---------------------------------------------------------------------
False Echo Echo input file contents to *.echo file if true.
2 beam_type 1: blade, 2: tower (-)
0. romg: rotor speed (rpm), automatically set to zero for tower modal analysis
1.0 romg_mult: rotor speed muliplicative factor (-)
82.39 radius: rotor tip radius measured along coned blade axis OR tower height (m)
0. hub_rad: hub radius measured along coned blade axis OR tower rigid-base height (m)
0. precone: built-in precone angle (deg), automatically set to zero for a tower
0. bl_thp: blade pitch setting (deg), automatically set to zero for a tower
1 hub_conn: hub-to-blade connection [1: cantilevered; other options not yet available]
20 modepr: number of modes to be printed (-)
f TabDelim (true: tab-delimited output tables; false: space-delimited tables)
f mid_node_tw (true: output twist at mid-node of elements; false: no mid-node outputs)

--------- Blade-tip or tower-top mass properties --------------------------------------------
1026410.750 tip_mass blade-tip or tower-top mass (see users' manual) (kg)
-3.3 cm_loc tip-mass c.m. offset from the tower axis measured along the tower-tip x reference axis (m)
1.1 cm_axial tip-mass c.m. offset tower tip measures axially along the z axis (m)
6.22E+09 ixx_tip blade lag or tower s-s mass moment of inertia about the tip-section x reference axis (kg-m^2)
6.22E+09 iyy_tip blade flap or tower f-a mass moment of inertia about the tip-section y reference axis (kg-m^2)
2.66E+07 izz_tip torsion mass moment of inertia about the tip-section z reference axis (kg-m^2)
0. ixy_tip cross product of inertia about x and y reference axes(kg-m^2)
-18400. izx_tip cross product of inertia about z and x reference axes(kg-m^2)
0. iyz_tip cross product of inertia about y and z reference axes(kg-m^2)

--------- Distributed-property identifiers --------------------------------------------------------
1 id_mat: material_type [1: isotropic; non-isotropic composites option not yet available]
'IEA15_CSpar_Bmodes.dat' sec_props_file name of beam section properties file (-)

Property scaling factors..............................
1.0 sec_mass_mult: mass density multiplier (-)
1.0 flp_iner_mult: blade flap or tower f-a inertia multiplier (-)
1.0 lag_iner_mult: blade lag or tower s-s inertia multiplier (-)
1.0 flp_stff_mult: blade flap or tower f-a bending stiffness multiplier (-)
1.0 edge_stff_mult: blade lag or tower s-s bending stiffness multiplier (-)
1.0 tor_stff_mult: torsion stiffness multiplier (-)
1.0 axial_stff_mult: axial stiffness multiplier (-)
1.0 cg_offst_mult: cg offset multiplier (-)
1.0 sc_offst_mult: shear center multiplier (-)
1.0 tc_offst_mult: tension center multiplier (-)

--------- Finite element discretization --------------------------------------------------
20 nselt: no of blade or tower elements (-)
Distance of element boundary nodes from blade or flexible-tower root (normalized wrt blade or tower length), el_loc()
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

--------- Properties of additional tower support subsystem (read only if beam_type is 2) ------------
0 tow_support: : additional tower support [0: no additional support; 1: Tension guy wires for land-based tower; 2: offshore turbine support: floating platform or monopile] (-)
Tension-wires data
0 n_attachments: no of wire-attachment locations on tower, maxm allowable is 2; 0: no tension-wire support (-)
3 3 n_wires: no of wires attached at each location (must be 3 or higher) (-)
6 9 node_attach: node numbers of attacments location (node number must be more than 1 and less than nselt+2) (-)
1.e8 1.e8 wire_stfness: wire sifnness in each set (see users' manual) (N/m)
45. 45. th_wire: angle of tension wires (wrt a horizontal plane) at each attachment point (deg)
Tower section properties (WindPact 1.5 MW turbine)
21 n_secs: number of blade or tower sections at which properties are specified (-)

sec_loc str_tw tw_iner mass_den flp_iner edge_iner flp_stff edge_stff tor_stff axial_stff cg_offst sc_offst tc_offst
(-) (deg) (deg) (kg/m) (kg-m) (kg-m) (Nm^2) (Nm^2) (Nm^2) (N) (m) (m) (m)
0 0 0 1.03E+04 2.14E+05 2.14E+05 4.59E+12 4.59E+12 1.03E+03 2.28E+02 0 0 0
0.05 0 0 1.01E+04 1.98E+05 1.98E+05 4.25E+12 4.25E+12 9.52E+02 2.23E+02 0 0 0
0.1 0 0 9.80E+03 1.83E+05 1.83E+05 3.93E+12 3.93E+12 8.80E+02 2.17E+02 0 0 0
0.15 0 0 9.54E+03 1.69E+05 1.69E+05 3.63E+12 3.63E+12 8.12E+02 2.11E+02 0 0 0
0.2 0 0 9.28E+03 1.55E+05 1.55E+05 3.34E+12 3.34E+12 7.47E+02 2.05E+02 0 0 0
0.25 0 0 9.02E+03 1.43E+05 1.43E+05 3.06E+12 3.06E+12 6.86E+02 2.00E+02 0 0 0
0.3 0 0 8.76E+03 1.31E+05 1.31E+05 2.81E+12 2.81E+12 6.28E+02 1.94E+02 0 0 0
0.35 0 0 8.50E+03 1.19E+05 1.19E+05 2.56E+12 2.56E+12 5.74E+02 1.88E+02 0 0 0
0.4 0 0 8.24E+03 1.09E+05 1.09E+05 2.33E+12 2.33E+12 5.22E+02 1.82E+02 0 0 0
0.45 0 0 7.98E+03 9.87E+04 9.87E+04 2.12E+12 2.12E+12 4.74E+02 1.76E+02 0 0 0
0.5 0 0 7.72E+03 8.93E+04 8.93E+04 1.92E+12 1.92E+12 4.29E+02 1.71E+02 0 0 0
0.55 0 0 7.46E+03 8.06E+04 8.06E+04 1.73E+12 1.73E+12 3.87E+02 1.65E+02 0 0 0
0.6 0 0 7.20E+03 7.24E+04 7.24E+04 1.56E+12 1.56E+12 3.48E+02 1.59E+02 0 0 0
0.65 0 0 6.94E+03 6.48E+04 6.48E+04 1.39E+12 1.39E+12 3.12E+02 1.53E+02 0 0 0
0.7 0 0 6.68E+03 5.78E+04 5.78E+04 1.24E+12 1.24E+12 2.78E+02 1.48E+02 0 0 0
0.75 0 0 6.41E+03 5.13E+04 5.13E+04 1.10E+12 1.10E+12 2.47E+02 1.42E+02 0 0 0
0.8 0 0 6.15E+03 4.53E+04 4.53E+04 9.73E+11 9.73E+11 2.18E+02 1.36E+02 0 0 0
0.85 0 0 5.89E+03 3.98E+04 3.98E+04 8.54E+11 8.54E+11 1.91E+02 1.30E+02 0 0 0
0.9 0 0 5.63E+03 3.47E+04 3.47E+04 7.46E+11 7.46E+11 1.67E+02 1.25E+02 0 0 0
0.95 0 0 5.37E+03 3.01E+04 3.01E+04 6.47E+11 6.47E+11 1.45E+02 1.19E+02 0 0 0
1 0 0 5.11E+03 2.59E+04 2.59E+04 5.58E+11 5.58E+11 1.25E+02 1.13E+02 0 0 0

**Note: If this file is for a TOWER, the following section properties are read but overwritten as follows:
str_tw is set to zero
tw_iner is set to zero
cg_offst is set to zero
sc_offst is set to zero
tc_offst is set to zero
edge_iner is set equal to flp_iner
edge_stff is set equal to flp_stff
`

[jjonkman]

Dear @EWEMkite,

Are you trying to calculate the tower mode shapes for a specific reference model provided by NREL, such as the WindPACT 1.5-MW baseline, the NREL 5-MW baseline, or the IEA Wind 15-MW RWT? I see few references in your input files, but not sure which one is correct.

Best regards,