B1 = [0.007664184 -2.9881 0.000406092 0.1383288248 10
0.0053322412 -3.048 0.0002825517 0.0714132532 12
0.0042969663 -3.0302 0.0002159107 0.0801274422 14
0.0031679216 -3.0999 0.0001603665 0.0499956477 16
0.0024500651 3.127 0.0001253999 0.0167884315 18
0.0018020404 -3.0564 9.5879682537E-005 0.0804556617 20
0.0016002233 -3.081 8.2650745149E-005 0.0673574656 22
0.0012999792 -3.0267 6.8012139495E-005 0.1026917201 24
0.001155153 -3.0648 0.000059505 0.0825282443 26
0.0009531787 -3.0536 4.989626375E-005 0.0895396702 28
0.0008416327 -3.0188 4.3843321828E-005 0.1143555927 30
0.0007522062 -3.0274 3.8860919031E-005 0.1103797724 32
0.0006623274 -3.0246 3.4339736398E-005 0.1144002354 34
0.0005919037 -3.0258 3.0584852036E-005 0.1163171484 36
0.0005235098 -3.0065 2.7265063479E-005 0.1304833172 38
0.0004830025 -3.0225 2.4883695857E-005 0.1239731127 40
0.0004244609 -2.9805 2.2193648751E-005 0.1494148435 42
0.0004009732 -3.0266 2.0624824753E-005 0.1276295172 44
0.000359225 -2.9564 1.858626358E-005 0.1678516957 46
0.0003261346 -3.0193 1.7063118751E-005 0.1369829386 48
0.0003120171 -2.9673 1.5915213836E-005 0.1680043239 50
0.0002693305 -2.9435 0.000014329 0.1859078099 52
0.0002812117 -3.0245 1.4041725043E-005 0.1382077591 54
0.0002116965 -2.9125 1.1677432273E-005 0.2091763157 56
0.0002642234 -2.8936 1.2746849092E-005 0.2107667695 58
0.0001898308 3.1232 1.0341119994E-005 0.0932720657 60
0.00019979 -2.7536 1.0273400016E-005 0.307157976 62
0.0001991536 -3.0709 9.952607032E-006 0.119385153 64
0.000165415 -2.8053 8.73257667E-006 0.2853994795 66
0.0001700311 -3.0214 8.714461089E-006 0.1586754338 68
0.0001540148 -2.8283 7.933818969E-006 0.2734670407 70
0.0001449999 -2.966 0.000007576 0.1979668351 72
0.0001429988 -2.9023 7.277896049E-006 0.2403375186 74
0.000125105 -2.8839 6.62244223E-006 0.2469045762 76
0.0001270686 -2.9129 6.511898157E-006 0.2398268201 78
0.0001183434 -2.8587 0.000006146 0.2668548798 80
0.0001086549 -2.9165 5.704403141E-006 0.2428620316 82
0.0001095321 -2.8379 5.614745897E-006 0.2863767016 84
0.0001003129 -2.8821 5.22477478E-006 0.2646836331 86
0.0001023633 -2.8537 5.207785332E-006 0.2838450134 88
8.9119501229E-005 -2.8941 4.689761568E-006 0.2624271574 90
8.9431208625E-005 -2.825 4.629515853E-006 0.3105181392 92
8.4029056702E-005 -2.8524 4.387228996E-006 0.2875973488 94
8.2962131609E-005 -2.8202 4.252480531E-006 0.3173761643 96
7.5837905796E-005 -2.8361 3.98837164E-006 0.3048492224 98
7.86692649E-005 -2.8183 4.015409209E-006 0.3235229867 100
7.1717695792E-005 -2.8459 3.704828221E-006 0.2961609568 102
6.6648480687E-005 -2.7984 3.513714039E-006 0.3481551587 104
6.8117625807E-005 -2.8488 3.536765484E-006 0.3009997483 106
5.8206071902E-005 -2.7251 3.073588439E-006 0.386309166 108
7.1814759805E-005 -2.7222 3.550474412E-006 0.4171148351 110
6.2015859661E-005 -3.0855 3.224419127E-006 0.1183328753 112
0.000043724 -2.268 2.351290938E-006 0.751173692 114
9.4189895672E-005 -2.9131 4.459922748E-006 0.2350604009 116
8.290389035E-006 -2.7966 8.90285566E-007 0.3433514951 118
9.2249674793E-005 -2.5786 4.344121796E-006 0.5559203906 120
3.9738388966E-005 2.72 2.074549346E-006 -0.2200033243 122
5.8998789313E-005 -2.3305 2.883651306E-006 0.7267156446 124
5.1477934834E-005 -2.9539 2.600070394E-006 0.2345811745 126
4.3748274292E-005 -2.7037 2.24423694E-006 0.4291147854 128
4.2920889131E-005 -2.8276 2.253191761E-006 0.3528561867 130
3.8559644393E-005 -2.5697 2.100473049E-006 0.5150099106 132
0.000043419 -2.7568 2.203787217E-006 0.3891812655 134
4.190565899E-005 -2.5831 0.000002104 0.5052787063 136
3.952925812E-005 -2.8791 2.039152763E-006 0.3360007855 138
3.9843496416E-005 -2.6325 0.000002003 0.4888000918 140
3.2045134808E-005 -2.7572 1.7736334E-006 0.396859339 142
3.6704113016E-005 -2.629 1.866704567E-006 0.5043773117 144
3.8357601649E-005 -2.7105 1.908806335E-006 0.4409687994 146
3.0910109808E-005 -2.699 1.634479243E-006 0.4399326205 148
3.2924680129E-005 -2.6134 0.000001716 0.5120973974 150
3.0184550739E-005 -2.7275 1.601234163E-006 0.4459831001 152
3.2089824535E-005 -2.6144 1.641199384E-006 0.5008848223 154
2.7877088028E-005 -2.6825 0.000001469 0.4780345084 156
3.2197908273E-005 -2.5982 1.61960546E-006 0.5283030324 158
2.5788072583E-005 -2.7237 1.397532316E-006 0.4531567168 160
3.2284837605E-005 -2.5799 1.550766818E-006 0.5459171359 162
2.1808863907E-005 -2.7459 1.246598692E-006 0.4301531913 164
3.0628930935E-005 -2.4456 1.517077098E-006 0.6516454249 166
2.1691176273E-005 -2.7968 1.213655636E-006 0.3782103581 168
2.6578714264E-005 -2.6195 1.301771927E-006 0.6057001719 170
3.072133682E-005 -2.4603 1.489868588E-006 0.5728952952 172
1.8272751111E-005 -3.0865 1.006208225E-006 0.3058954546 174
2.2651672463E-005 -2.0312 1.215438312E-006 0.8646419989 176
4.014635778E-005 -2.7727 1.589648424E-006 0.408953742 178
6.520122655E-006 -2.5797 7.06921485E-007 0.6029304108 180
3.2481904908E-005 -2.4377 1.48463958E-006 0.637839553 182
1.3228797768E-005 -2.8968 0.000000798 0.4106349108 184
2.9657755476E-005 -2.4351 1.367795332E-006 0.685414901 186
1.2073478899E-005 -2.9184 7.97266381E-007 0.3846214058 188
2.4119593668E-005 -2.5032 1.158264615E-006 0.6463288249 190
1.8731266519E-005 -2.4323 0.000000962 0.6536899156 192
1.9884638894E-005 -2.5188 1.031606979E-006 0.6279863257 194
1.7212900952E-005 -2.6362 8.9455805E-007 0.5233562898 196
1.8455699579E-005 -2.3865 9.58618995E-007 0.7339303681 198
0.000018664 -2.6235 9.55731964E-007 0.5248793371 200
1.4636891657E-005 -2.3609 8.07481383E-007 0.7357536368 202
1.9713918482E-005 -2.6459 9.53156433E-007 0.5542332139 204
1.698542824E-005 -2.3546 8.7372002E-007 0.7426416207 206
1.5801808467E-005 -2.6642 8.27522618E-007 0.5313383428 208
1.5661160254E-005 -2.2473 7.98167358E-007 0.806384057 210
1.5538714935E-005 -2.5849 8.27332817E-007 0.6071133152 212
1.4397544326E-005 -2.4935 7.47920582E-007 0.6445859875 214
0.000017057 -2.501 0.000000836 0.6692484438 216
1.1602881072E-005 -2.2468 6.55592888E-007 0.7844653577 218
1.8474358555E-005 -2.4467 9.01869958E-007 0.6935663324 220
1.1383891732E-005 -2.6095 6.00329483E-007 0.6085541443 222
1.5753816876E-005 -2.3756 8.07438049E-007 0.7688518817 224
1.2501749107E-005 -2.7298 6.52737651E-007 0.4609734719 226
0.000013328 -1.8969 6.4438873E-007 1.0783986301 228
2.0031202311E-005 -2.6321 0.000000959 0.6351322072 230
7.434164463E-006 2.8238 0.000000423 -0.0876081536 232
2.6155788168E-005 -1.5099 1.149687243E-006 1.5067956326 234
0.000028297 2.885 1.230734851E-006 -0.1611631609 236
1.8594651733E-005 -1.036 7.97919721E-007 2.0245883201 238
0.000028714 -2.7944 1.290455603E-006 0.4081343361 240
5.781759324E-006 0.086 1.22604877E-007 2.2924759547 242
2.0303296361E-005 -2.3641 9.05487093E-007 0.7956949355 244
6.562408175E-006 -2.3678 4.20529411E-007 0.7059287778 246
1.5710055497E-005 -2.3857 7.22423213E-007 0.779339424 248
7.608412026E-006 -2.8685 4.24884228E-007 0.4972358231 250
1.3227420533E-005 -1.9391 6.36610781E-007 1.0796285422 252
5.502075479E-006 -2.4759 4.03428038E-007 0.6736835863 254
1.4832278855E-005 -2.3127 0.000000653 0.8638641066 256
0.000009448 -2.3109 4.82242059E-007 0.8066277166 258
1.180338642E-005 -2.3002 5.87770679E-007 0.8296021913 260
7.43112453E-006 -2.6061 4.09536043E-007 0.615681941 262
9.325570205E-006 -1.9936 5.02348999E-007 1.0601207339 264
1.0823665903E-005 -2.6018 5.2819906E-007 0.6222795943 266
9.656364688E-006 -2.172 0.000000472 0.9372291649 268
8.805859461E-006 -2.3985 4.54806957E-007 0.7740503526 270
6.13342145E-006 -2.0396 0.000000389 1.0133534698 272
1.2216441924E-005 -2.5762 5.47780652E-007 0.6346657284 274
5.960528776E-006 -1.6579 3.32643041E-007 1.2024667615 276
1.1091686552E-005 -2.4362 5.17658843E-007 0.7773851558 278
0.00000834 -1.7489 4.0010191E-007 1.1520900175 280
1.0438378861E-005 -2.478 5.06222158E-007 0.74706625 282
1.758843905E-006 -2.8873 1.81569793E-007 0.8570512052 284
1.6353630399E-005 -2.2829 7.19250697E-007 0.8549188529 286
1.459221766E-006 -1.474 9.6291681E-008 0.8656759059 288
1.0643940957E-005 -1.8546 5.82115167E-007 1.2408812764 290
1.2112902849E-005 -2.83 5.00833097E-007 0.345592866 292
1.753834893E-006 -1.7591 2.09433778E-007 1.3593767103 294
1.3119431306E-005 -1.5766 5.27930622E-007 1.2272426044 296
1.2307923634E-005 3.0878 4.23883417E-007 0.1954087761 298
8.78842585E-006 -0.8903 0.000000373 1.8343311991 300
1.3740395335E-005 -2.7272 5.67880363E-007 0.4898359679 302
6.887710514E-006 -0.8952 2.92685124E-007 1.8722266762 304
1.3431589531E-005 -2.5857 0.000000545 0.6706462278 306
5.710458789E-006 -1.4941 2.89400015E-007 1.2875029972 308
5.018848659E-006 -2.4952 2.90487226E-007 0.7591141636 310
4.455257909E-006 -2.1246 0.000000251 1.0687437755 312
9.706318243E-006 -2.0595 4.34869332E-007 1.0386471505 314
3.699292713E-006 -2.6639 2.14459203E-007 0.7375254892 316
8.67943599E-006 -2.0234 3.98269784E-007 1.1278085302 318
2.924299397E-006 -2.4165 2.14829747E-007 0.7621175539 320
0.00000716 -1.9088 3.35927619E-007 1.1613845336 322
4.212314575E-006 -2.5707 2.28912396E-007 0.7907972555 324
9.18566906E-006 -1.824 4.17536751E-007 1.2508310583 326
3.419900234E-006 2.6307 1.60495871E-007 0.1321368009 328
8.018871062E-006 -1.7016 3.38506039E-007 1.3530451707 330
7.081941435E-006 -2.2957 3.37803656E-007 0.9558662867 332
4.722656605E-006 -1.9306 2.42861223E-007 1.0971235187 334
4.488737848E-006 -2.4362 2.35244239E-007 0.8174573039 336
5.689609198E-006 -1.1327 2.6819541E-007 1.7115747223 338
1.2064541348E-005 -2.8936 4.66269296E-007 0.404874798 340
6.887166497E-006 -0.8228 2.5415424E-007 2.1374545798 342
7.394881116E-006 -2.5931 3.60101907E-007 0.7181101298 344
8.75387789E-007 -0.2298 6.4121702E-008 0.9749830247 346
1.1121777122E-005 -1.4762 4.3805539E-007 1.7056081494 348
8.894631845E-006 -2.8821 4.29263201E-007 0.4159642551 350
6.283099793E-006 1.0055 0.000000208 -2.3005489154 352
1.7799785341E-005 -1.8186 7.79574468E-007 1.3011761687 354
9.392865455E-006 1.8037 4.01604695E-007 -1.1856335755 356
0.000016486 -1.2487 7.10447045E-007 1.8966258261 358
1.3494150641E-005 2.7656 5.2375032E-007 -0.2458406085 360
8.351336007E-006 -0.8948 3.37462869E-007 2.065870512 362
5.539729163E-006 -2.7317 2.315833E-007 0.6026373148 364
4.451278397E-006 -1.6249 2.10170439E-007 1.4429104734 366
6.363722976E-006 -1.9255 0.000000272 1.1420744287 368
2.252051027E-006 0.6629 4.1343358E-008 2.4484718085 370
6.325909873E-006 -2.6676 2.69822239E-007 0.639841853 372
6.838703112E-006 -1.1936 2.70726408E-007 1.8016261392 374
4.83651144E-006 -2.9666 1.9538832E-007 0.5162131277 376
4.979062672E-006 -1.5176 1.97230459E-007 1.4887693573 378
3.863484298E-006 -1.3957 2.00687549E-007 1.531723542 380
3.911791321E-006 2.8706 1.50493776E-007 0.0748857973 382
6.923337622E-006 -1.5772 2.98689429E-007 1.5132497853 384
9.49065862E-007 -1.9694 7.4925983E-008 1.218950613 386
5.464949547E-006 -2.1377 2.40118949E-007 0.9724919305 388
9.52184462E-007 0.3495 4.2740823E-008 2.2537681205 390
5.152416646E-006 -1.4567 0.000000242 1.5662591999 392
5.950209074E-006 -3.1172 2.17198303E-007 0.2244800244 394
6.406053833E-006 -0.5764 2.07660203E-007 2.3164964266 396
5.128158871E-006 2.8905 1.60639235E-007 0.1968500085 398
1.1097145935E-005 -1.5137 3.89831892E-007 1.6384495586 400
4.078769645E-006 2.8555 1.84583969E-007 -0.0642371008 402
5.785767181E-006 0.0376 2.38062482E-007 2.8094212509 404
1.1984450851E-005 -2.4232 4.78846843E-007 0.6564397539 406
6.097598213E-006 0.8115 2.45694643E-007 -2.5043194333 408
7.013639537E-006 -1.4874 3.31815371E-007 1.4224320133 410
0.000003506 -3.0229 1.0889822E-007 0.0810547744 412
5.007804743E-006 1.153 6.879255E-008 -2.5191594139 414
1.2574704206E-005 -1.8316 3.99111597E-007 1.2662444202 416
1.127869296E-006 1.0188 3.4533157E-008 -3.014061121 418
1.869863792E-006 -1.4785 1.4135974E-007 1.375744977 420
3.749873819E-006 1.9782 1.17321248E-007 -1.0726557324 422
1.0551359061E-005 -1.331 3.74342765E-007 1.7822827891 424
6.633458318E-006 2.517 0.000000206 -0.3604341888 426
0.000006707 -1.1462 2.51648916E-007 2.0234067621 428
2.067602753E-006 2.5321 8.8668841E-008 -0.254796319 430
0.000001201 -0.1343 6.3710371E-008 2.0381924487 432
3.897734972E-006 -1.7923 1.54179314E-007 1.3708710291 434
7.48415348E-007 -2.0337 4.5275535E-008 1.3912065081 436
2.744615983E-006 -1.9139 1.20942413E-007 1.2212614114 438
2.624117705E-006 0.1431 8.4087737E-008 2.942845635 440
6.135401988E-006 -2.6151 0.000000234 0.5901757188 442
3.935795807E-006 -0.1999 1.60313028E-007 2.8120648586 444
3.863540495E-006 -2.398 1.73680733E-007 0.7484449575 446
2.08454968E-006 1.8483 6.1380357E-008 -1.3647109585 448
3.931825441E-006 -0.8476 1.66785219E-007 2.2057137563 450
4.225780405E-006 -2.6071 1.55429739E-007 0.5525774683 452
3.633622862E-006 -0.5307 0.000000117 2.4065539759 454
3.372449764E-006 1.7792 8.630293E-008 -1.4241322891 456
6.494593504E-006 -1.5887 2.4019241E-007 1.5221149197 458
3.474665472E-006 2.1382 1.17626052E-007 -0.9709264962 460
0.000007232 -1.0498 2.8129828E-007 2.0521377225 462
1.1818252792E-005 2.5662 3.89783207E-007 -0.4861364836 464
9.568793776E-006 0.0102 3.12271593E-007 -2.9829549922 466
1.1766667984E-005 -1.4549 4.49251152E-007 1.7525012817 468
1.4291251655E-005 2.3253 5.21693095E-007 -0.6838189242 470
1.0472060918E-005 -0.1845 4.64662377E-007 3.0480823613 472
1.371861287E-005 -2.2595 0.00000058 0.8398224636 474
1.4397354045E-005 1.0176 5.49714913E-007 -2.0623098959 476
8.786846515E-006 -1.9533 3.68596505E-007 1.3324951543 478
2.71985022E-006 2.7559 1.00123507E-007 -0.6986463378 480
4.458059261E-006 0.1599 1.25218426E-007 -2.983360104 482
9.00256221E-007 2.1841 8.051437E-009 0.0746998832 484
6.437818289E-006 -1.8849 2.21579318E-007 1.2568096554 486
6.586071395E-006 1.7864 2.33291414E-007 -1.3845408378 488
6.429549502E-006 -1.3521 2.31333354E-007 1.824521562 490
3.801872684E-006 1.8345 1.26291034E-007 -1.1256720697 492
2.877081954E-006 0.2587 1.08556401E-007 -2.9370846728 494
4.233417424E-006 -2.2972 1.53570863E-007 0.7917154803 496
3.325266172E-006 1.1931 1.22486161E-007 -1.9902205157 498
1.34388887E-007 0 4.18172E-009 3.1415926536 500];
Fx = B1(:,1);
Fx_Pi=B1(:,2);
Mx = B1(:,3);
Mx_Pi=B1(:,4);
freq=B1(:,5);
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% Initial Conditions %%%%%%%%%%%%
IC=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%% Time Span (Seconds) %%%%%%%%
t0=0; tf=5; art=0.1;
tspan=[t0:art:tf];
t_step=0.01;
ts=1/t_step;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[t,u] = ode15s(@(t,y)Huang(t,y,Fx,Fx_Pi,Mx,Mx_Pi,freq),tspan,IC); %[t,y] = ode45(@(t,y) myode(t,y,ft,f,gt,g), tspan, ic, opts);
x1 = u(:,1); x2 = u(:,2); x3 = u(:,3); x4 = u(:,4); x5 = u(:,5);
%x1 yönü thrustbearing %x5 yönü pervane
th1 = u(:,6); th2 = u(:,7); th3 = u(:,8); th4 = u(:,9); th5 = u(:,10);
%th1= yönü thrustbearing %th5= yönü pervane %detrend(y1);
figure (1),clf
plot(tspan,x1),xlabel('Frequency (Hz)'), ylabel('y (m) ');
title('Vertical Displacement (m)')
function [du] = Huang(t,u,Fx,Fx_Pi,Mx,Mx_Pi,freq)
%%%%%% Shaft Speed %%%%%%%%%%
rpm=525; %rpm
w=rpm*2*pi/60; % rad/s
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
Fx = sum(Fx(:).*sin(2*pi*freq(:)*t + Fx_Pi(:)));
Mt =sum(Mx(:).*sin(2*pi*freq(:)*t + Mx_Pi(:)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
p=7750; %%%Kg/m^3;
g=9.81;
G=77*10^9; %%% N/m^2
E=193*10^9; %%% N/m^2
L=[0.1479 0.22034 0.3957 0.17262]; %%%m
D=[0.02 0.02 0.02 0.02]; %%m
Sh=0.02;
m(p)=0.3144;
J(p)=0.54; %0.5*10^-4;
for j=1:4
m(j)=pi*(D(j)/2)^2*L(j)*p;
A(j)=pi*D(j)^2/4 ; %%m2
J(j)=m(j)*D(j)^2/32; %%Kg*m^2
Ip(j)=pi*D(j)^4/32 ; %% m^4
dt(j)=0.05*m(j)*w;
dx(j)=0.08*J(j)*w;
kt(j)=G*Ip(j)/L(j);
kx(j)=E*A(j)/L(j);
ktx(j)=Sh*kt(j);
kxt(j)=Sh*kx(j);
end
m(1)=m(1)/2; m(2)=m(1)/2+m(2)/2; m(3)=m(2)/2+m(3)/2; m(4)=m(3)/2+m(4)/2; m(5)=m(4)/2+m(p);
J(1)=J(1)/2; J(2)=J(1)/2+J(2)/2; J(3)=J(2)/2+J(3)/2; J(4)=J(3)/2+J(4)/2; J(5)=J(4)/2+J(p);
A = [m(1) 0 0 0 0 0 0 0 0 0
0 m(2) 0 0 0 0 0 0 0 0
0 0 m(3) 0 0 0 0 0 0 0
0 0 0 m(4) 0 0 0 0 0 0
0 0 0 0 m(5) 0 0 0 0 0
0 0 0 0 0 J(1) 0 0 0 0
0 0 0 0 0 0 J(2) 0 0 0
0 0 0 0 0 0 0 J(3) 0 0
0 0 0 0 0 0 0 0 J(4) 0
0 0 0 0 0 0 0 0 0 J(5)];
D = [dx(1) -dx(1) 0 0 0 0 0 0 0 0
-dx(1) dx(1)+dx(2) -dx(2) 0 0 0 0 0 0 0
0 -dx(2) dx(2)+dx(3) -dx(3) 0 0 0 0 0 0
0 0 -dx(3) dx(3)+dx(4) -dx(4) 0 0 0 0 0
0 0 0 -dx(4) dx(4) 0 0 0 0 0
0 0 0 0 0 dt(1) -dt(1) 0 0 0
0 0 0 0 0 -dt(1) dt(1)+dt(2) -dt(2) 0 0
0 0 0 0 0 0 -dt(2) dt(2)+dt(3) -dt(3) 0
0 0 0 0 0 0 0 -dt(3) dt(3)+dt(4) -dt(4)
0 0 0 0 0 0 0 0 -dt(4) dt(4)] ;
K = [kx(1) -kx(1) 0 0 0 0 0 0 0 0
-kx(1) kx(1)+kx(2) -kx(2) 0 0 0 0 0 0 0
0 -kx(2) kx(2)+kx(3) -kx(3) 0 0 0 0 0 0
0 0 -kx(3) kx(3)+kx(4) -kx(4) 0 0 0 0 0
0 0 0 -kx(4) kx(4) 0 0 0 0 0
0 0 0 0 0 kt(1) -kt(1) 0 0 0
0 0 0 0 0 -kt(1) kt(1)+kt(2) -kt(2) 0 0
0 0 0 0 0 0 -kt(2) kt(2)+kt(3) -kt(3) 0
0 0 0 0 0 0 0 -kt(3) kt(3)+kt(4) -kt(4)
0 0 0 0 0 0 0 0 -kt(4) kt(4)] ; % K matrix
KTX = [0 0 0 0 0 kxt(1) -kxt(1) 0 0 0
0 0 0 0 0 -kxt(1) kxt(1)+kxt(2) -kxt(2) 0 0
0 0 0 0 0 0 -kxt(2) kxt(2)+kxt(3) -kxt(3) 0
0 0 0 0 0 0 0 -kxt(3) kxt(3)+kxt(4) -kxt(4)
0 0 0 0 0 0 0 0 -kxt(4) kxt(4)
ktx(1) -ktx(1) 0 0 0 0 0 0 0 0
-ktx(1) ktx(1)+ktx(2) -ktx(2) 0 0 0 0 0 0 0
0 -ktx(2) ktx(2)+ktx(3) -ktx(3) 0 0 0 0 0 0
0 0 -ktx(3) ktx(3)+ktx(4) -ktx(4) 0 0 0 0 0
0 0 0 -ktx(4) ktx(4) 0 0 0 0 0] ; % K matrix
F = [0
0
0
0
Fx
0
0
0
0
Mt];
u1 = u(1:10); % [x1 x2 x3 x4 x5 t1 t2 t3 t4 t5]
du1 = u(11:20); % [dx1 dx2 dx3 dx4 dx5 dt1 dt2 dt3 dt4 dt5]
dx1 = u(11); % dtheta
B = -D*du1 -K*u1 + KTX*u1 + F ;
du = zeros(10,1);
du(1:10) = u(11:20);
du(11:20) = A\B;
end
