kill(all);

data from the "cblade.mfd" model

from the modal analysis (no end support) loadcase
natural frequencies, and
the associated z displacement of the loaded node, according to unit modal mass normalization

fl:[  8.337e1, 5.247e2, 8.289e2,1.488e3,1.608e3,2.544e3, 2.978e3]$
ωl:2*%pi*fl$
wl:[ -863.197, -865.16,-2172.93,-870.81,      0,2281.97,-878.895]$

number of modes

m:length(fl);

damping ratio, for each mode

ζ :0.01$
ζl:makelist( ζ , i ,fl);

auxiliary quantities

rl:f/fl$
al:1-rl^2$
bl:2*ζl*rl$

load-mode coupling term

Reql: (1/*N*/) *wl; /* unit z force applied at the monitored dof, phase=0 (reference phase)*/
Imql: (0/*N*/) *wl; /* */

Real and imaginary part of the harmonic response

Reζl:1/ωl^2 * (al*Reql+bl*Imql)/(al^2+bl^2),numer;

Imζl:1/ωl^2 * (al*Imql-bl*Reql)/(al^2+bl^2),numer;

accumulation of the mode contribution in order to obtain the overall harmonic response

Rew:makelist(0,i,1,m)$
Imw:makelist(0,i,1,m)$
for j:1 thru m do (
    for i:1 thru j do(
        Rew[j]:Rew[j]+Reζl[i]*wl[i],
        Imw[j]:Imw[j]+Imζl[i]*wl[i]
    )
);

derived quantities: magnitude

wmag:sqrt(Rew^2+Imw^2)$ /*magnitude*/

plots:

Magnitude, real and Imaginary part plot

plot2d([wmag[m],abs(Rew[m]),abs(Imw[m])],[f,1,2000],logy,[legend,"mag(x)","Re(w)","Im(w)"]);

effect of mode truncation

mylegend:append([legend],makelist(concat("modes 1 to ",string(i)),i,1,m))$
wxplot2d(wmag,[f,1,2000],logy,mylegend);

FE model comparison, for control.
From the imposed force, harmonic response loadcase

fe_freq:makelist(i/2,i,2,2000)$
fe_wmag:[3.01054,3.01103,3.01171,3.01259,3.01367,3.01494,3.01642,3.01809,3.01996,3.02203,3.0243,3.02677,3.02944,3.03232,3.0354,3.03869,3.04219,3.0459,3.04982,3.05395,3.05829,3.06286,3.06764,3.07264,3.07787,3.08332,3.089,3.09491,3.10106,3.10744,3.11406,3.12092,3.12804,3.1354,3.14301,3.15088,3.15901,3.16741,3.17607,3.18501,3.19423,3.20373,3.21352,3.2236,3.23399,3.24467,3.25567,3.26698,3.27861,3.29058,3.30288,3.31552,3.32851,3.34186,3.35558,3.36967,3.38414,3.39901,3.41428,3.42995,3.44605,3.46258,3.47956,3.49699,3.51488,3.53325,3.55212,3.57149,3.59137,3.6118,3.63277,3.65431,3.67642,3.69914,3.72248,3.74645,3.77108,3.79639,3.8224,3.84914,3.87662,3.90487,3.93392,3.9638,3.99454,4.02616,4.0587,4.0922,4.12668,4.16219,4.19877,4.23646,4.2753,4.31535,4.35664,4.39923,4.44318,4.48855,4.53539,4.58378,4.63378,4.68547,4.73893,4.79424,4.85149,4.91078,4.97221,5.03589,5.10194,5.17048,5.24165,5.31559,5.39246,5.47243,5.55568,5.6424,5.7328,5.82712,5.92561,6.02853,6.13619,6.24889,6.367,6.4909,6.62102,6.75781,6.9018,7.05354,7.21368,7.38291,7.562,7.75184,7.9534,8.16777,8.3962,8.6401,8.90106,9.18093,9.48179,9.80608,10.1566,10.5367,10.9501,11.4014,11.8961,12.4406,13.0428,13.7123,14.4608,15.3032,16.2581,17.3494,18.6081,20.0757,21.8077,23.8816,26.4073,29.5466,33.5453,38.7945,45.9443,56.1252,71.3299,94.5121,124.37,134.071,107.894,79.9397,61.0363,48.6342,40.1403,34.0385,29.4721,25.9385,23.1288,20.844,18.9514,17.3589,16.0009,14.8296,13.8093,12.9126,12.1186,11.4106,10.7755,10.2026,9.68331,9.21041,8.778,8.38112,8.01559,7.67786,7.36489,7.07406,6.80313,6.55012,6.31333,6.09126,5.88259,5.68614,5.50088,5.32589,5.16034,5.0035,4.8547,4.71334,4.57889,4.45085,4.32878,4.21228,4.10097,3.99453,3.89264,3.79502,3.70141,3.61156,3.52527,3.44233,3.36254,3.28573,3.21175,3.14044,3.07165,3.00527,2.94116,2.87922,2.81934,2.76141,2.70535,2.65107,2.59849,2.54753,2.49811,2.45017,2.40365,2.35848,2.31461,2.27198,2.23055,2.19025,2.15106,2.11291,2.07579,2.03963,2.00441,1.9701,1.93665,1.90404,1.87224,1.84121,1.81093,1.78138,1.75252,1.72434,1.69681,1.66991,1.64363,1.61792,1.59279,1.56822,1.54417,1.52064,1.49762,1.47508,1.45301,1.4314,1.41023,1.38949,1.36917,1.34926,1.32973,1.31059,1.29183,1.27342,1.25536,1.23765,1.22027,1.20321,1.18646,1.17003,1.15389,1.13804,1.12247,1.10718,1.09215,1.07739,1.06288,1.04863,1.03461,1.02083,1.00728,0.993961,0.980858,0.96797,0.955292,0.942818,0.930544,0.918465,0.906578,0.894876,0.883357,0.872016,0.86085,0.849854,0.839024,0.828357,0.81785,0.807499,0.7973,0.787251,0.777348,0.767589,0.757969,0.748487,0.73914,0.729924,0.720837,0.711877,0.703041,0.694326,0.68573,0.677251,0.668886,0.660634,0.652492,0.644457,0.636529,0.628704,0.620981,0.613358,0.605833,0.598405,0.59107,0.583829,0.576679,0.569618,0.562645,0.555758,0.548956,0.542237,0.5356,0.529043,0.522565,0.516165,0.509841,0.503591,0.497415,0.491311,0.485279,0.479316,0.473422,0.467596,0.461836,0.456141,0.450511,0.444944,0.439439,0.433995,0.428612,0.423287,0.418021,0.412812,0.40766,0.402563,0.397521,0.392533,0.387598,0.382715,0.377883,0.373102,0.368371,0.363688,0.359054,0.354468,0.349928,0.345435,0.340987,0.336584,0.332225,0.32791,0.323637,0.319407,0.315218,0.31107,0.306963,0.302895,0.298867,0.294878,0.290926,0.287013,0.283136,0.279296,0.275492,0.271724,0.267991,0.264292,0.260628,0.256997,0.253399,0.249834,0.246302,0.242801,0.239332,0.235894,0.232486,0.229109,0.225761,0.222443,0.219154,0.215894,0.212661,0.209457,0.206281,0.203131,0.200008,0.196912,0.193843,0.190798,0.18778,0.184787,0.181818,0.178874,0.175955,0.173059,0.170187,0.167339,0.164513,0.161711,0.158931,0.156173,0.153437,0.150723,0.14803,0.145359,0.142709,0.140079,0.13747,0.134881,0.132312,0.129763,0.127233,0.124723,0.122232,0.11976,0.117307,0.114872,0.112455,0.110056,0.107676,0.105313,0.102967,0.100639,0.0983282,0.0960343,0.0937571,0.0914966,0.0892525,0.0870248,0.0848133,0.0826178,0.0804382,0.0782744,0.0761262,0.0739934,0.0718761,0.0697741,0.0676872,0.0656155,0.0635587,0.0615169,0.05949,0.057478,0.0554807,0.0534983,0.0515307,0.049578,0.0476402,0.0457175,0.0438099,0.0419177,0.0400412,0.0381806,0.0363363,0.034509,0.0326991,0.0309076,0.0291355,0.0273841,0.0256551,0.0239505,0.0222733,0.0206271,0.0190167,0.0174487,0.0159319,0.0144784,0.0131052,0.0118354,0.0107009,0.00974379,0.0090148,0.00856646,0.00843772,0.00863721,0.00913826,0.00989042,0.0108373,0.0119289,0.0131258,0.0143987,0.0157266,0.0170941,0.0184903,0.0199071,0.0213386,0.0227803,0.0242289,0.0256817,0.0271368,0.0285925,0.0300475,0.031501,0.0329521,0.0344,0.0358444,0.0372848,0.0387208,0.0401521,0.0415785,0.0429998,0.0444159,0.0458266,0.0472318,0.0486315,0.0500256,0.0514139,0.0527966,0.0541736,0.0555448,0.0569102,0.05827,0.0596239,0.0609722,0.0623147,0.0636515,0.0649827,0.0663082,0.0676281,0.0689424,0.0702512,0.0715545,0.0728523,0.0741446,0.0754316,0.0767132,0.0779894,0.0792604,0.0805262,0.0817868,0.0830422,0.0842925,0.0855378,0.086778,0.0880133,0.0892437,0.0904692,0.0916898,0.0929057,0.0941168,0.0953232,0.0965249,0.0977221,0.0989146,0.100103,0.101286,0.102465,0.10364,0.104811,0.105977,0.1071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wxplot2d(
    [wmag[1],wmag[m],[discrete,fe_freq,fe_wmag]],
    [f,1,2000],
    [y,0,10],
    [legend,"mag(x), mode 1","mag(x), modes 1-7","FE"]
);

the static response is non correctly predicted by resorting to mode 1 alone