Solución ante carga arbitraria mediante el método de interpolación lineal de la carga (Nigan & Jennings)

Propiedades del osciladorm 2 Tonk 500 kN/mxi 0 Razón de amortiguamiento

0.02 su0 0.02 m Desplazamiento inicialv0 3 m/s Velocidad inicial

Cálculos auxiliareswn 15.8114 rad/swD 15.8114 rad/sc 0.0000 kN.s/mTn 0.397 s

Cálculos auxiliares y coeficientesexp1 1 xi1 0 xi4 1cos1 0.95041528 xi2 0 xi5 0sen1 0.31098359 xi3 3.16227766

Fórmula de recurrencia

A 0.95041528 A' -4.91708234B 0.01966833 B' 0.95041528C 6.60024E-05 C' 0.00487569D 3.31671E-05 D' 0.00495847

Tiempo Carga Desp. Veloc. Accel.

t [s] pi0.00 50.00 0.0200000 3.000000 20.000000.02 50.00 0.0829718 3.244612 4.257060.04 50.00 0.1476322 3.167458 -11.908050.06 50.00 0.2075690 2.776189 -26.892250.08 50.00 0.2568382 2.109607 -39.209560.10 50.00 0.2905539 1.233816 -47.638470.12 50.00 0.3053724 0.235669 -51.343110.14 50.00 0.2998243 -0.785850 -49.956080.16 50.00 0.2744597 -1.729436 -43.614930.18 50.00 0.2317941 -2.501516 -32.948520.20 50.00 0.1760585 -3.025521 -19.014620.22 50.00 0.1127802 -3.249487 -3.195040.24 50.00 0.0482345 -3.151203 12.941380.26 50.00 -0.0111776 -2.740417 27.79441

Dt

ui vi ai

0.28 50.00 -0.0595643 -2.057864 39.891080.30 50.00 -0.0921271 -1.171235 48.031780.32 50.00 -0.1056368 -0.168454 51.409200.34 50.00 -0.0987536 0.851031 49.688390.36 50.00 -0.0721601 1.786121 43.040020.38 50.00 -0.0284935 2.544082 32.123380.40 50.00 0.0279156 3.049748 18.021100.42 50.00 0.0914733 3.252972 2.131660.44 50.00 0.1558767 3.133600 -13.969160.46 50.00 0.2147387 2.703471 -28.684680.48 50.00 0.2622222 2.005241 -40.555550.50 50.00 0.2936182 1.108152 -48.404540.52 50.00 0.3058132 0.101168 -51.453290.54 50.00 0.2975978 -0.915849 -49.399450.56 50.00 0.2697867 -1.842041 -42.446680.58 50.00 0.2251380 -2.585560 -31.284510.60 50.00 0.1680795 -3.072669 -17.019860.62 50.00 0.1042695 -3.255064 -1.067370.64 50.00 0.0400361 -3.114656 14.990970.66 50.00 -0.0182507 -2.665369 29.562670.68 50.00 -0.0648106 -1.951759 41.202650.70 50.00 -0.0950264 -1.044595 48.756590.72 50.00 -0.1059015 -0.033838 51.475370.74 50.00 -0.0963575 0.980274 49.089360.76 50.00 -0.0673408 1.897174 41.835190.78 50.00 -0.0217290 2.625931 30.432250.80 50.00 0.0359546 3.094276 16.011350.82 50.00 0.0999895 3.255764 0.002620.84 50.00 0.1640255 3.094380 -16.006370.86 50.00 0.2217121 2.626127 -30.428020.88 50.00 0.2673285 1.897443 -41.832130.90 50.00 0.2963511 0.980591 -49.087780.92 50.00 0.3059017 -0.033506 -51.475420.94 50.00 0.2950331 -1.044281 -48.758280.96 50.00 0.2648232 -1.951494 -41.205800.98 50.00 0.2182679 -2.665179 -29.566961.00 50.00 0.1599840 -3.114560 -14.995991.02 50.00 0.0957515 -3.255071 1.062131.04 50.00 0.0319403 -3.072779 17.014921.06 50.00 -0.0251214 -2.585761 31.280341.08 50.00 -0.0697749 -1.842315 42.443721.10 50.00 -0.0975919 -0.916167 49.397971.12 50.00 -0.1058138 0.100836 51.453451.14 50.00 -0.0936253 1.107840 48.406331.16 50.00 -0.0622351 2.004980 40.55878

1.18 50.00 -0.0147561 2.703287 28.689031.20 50.00 0.0441032 3.133510 13.974211.22 50.00 0.1085057 3.252985 -2.126421.24 50.00 0.1720647 3.049864 -18.016181.26 50.00 0.2284771 2.544289 -32.119291.28 50.00 0.2721486 1.786398 -43.037141.30 50.00 0.2987481 0.851352 -49.687021.32 50.00 0.3056379 -0.168123 -51.409471.34 50.00 0.2921347 -1.170925 -48.033671.36 50.00 0.2595776 -2.057607 -39.894401.38 50.00 0.2111953 -2.740238 -27.798821.40 50.00 0.1517858 -3.151120 -12.946451.42 50.00 0.0872408 -3.249508 3.189811.44 50.00 0.0239610 -3.025644 19.009741.46 50.00 -0.0317780 -2.501728 32.944491.48 50.00 -0.0744486 -1.729717 43.612151.50 50.00 -0.0998193 -0.786172 49.954811.52 50.00 -0.1053740 0.235338 51.343491.54 50.00 -0.0905618 1.233510 47.640461.56 50.00 -0.0568518 2.109355 39.212951.58 50.00 -0.0075869 2.776016 26.896721.60 50.00 0.0523474 3.167382 11.913151.62 50.00 0.1170073 3.244640 -4.251831.64 50.00 0.1799807 3.000129 -19.995171.66 50.00 0.2350224 2.458097 -33.755591.68 50.00 0.2766740 1.672297 -44.168501.70 50.00 0.3008049 0.720656 -50.201231.72 50.00 0.3050222 -0.302452 -51.255541.74 50.00 0.2889075 -1.295566 -47.226871.76 50.00 0.2540589 -2.160199 -38.514731.78 50.00 0.2039324 -2.810607 -25.983111.80 50.00 0.1434990 -3.182288 -10.874761.82 50.00 0.0787519 -3.238384 5.312031.84 50.00 0.0161118 -2.973331 20.972041.86 50.00 -0.0382090 -2.413414 34.552261.88 50.00 -0.0788238 -1.614160 44.705951.90 50.00 -0.1017047 -0.654831 50.426171.92 50.00 -0.1045827 0.369437 51.145671.94 50.00 -0.0871723 1.357068 46.793071.96 50.00 -0.0512001 2.210120 37.800031.98 50.00 -0.0002335 2.843995 25.058392.00 50.00 0.0606731 3.195833 9.831712.02 50.00 0.1254799 3.230742 -6.369962.04 50.00 0.1877597 2.945260 -21.939942.06 50.00 0.2413365 2.367698 -35.33414

2.08 50.00 0.2808971 1.555333 -45.224272.10 50.00 0.3025182 0.588727 -50.629542.12 50.00 0.3040556 -0.436264 -51.013902.14 50.00 0.2853570 -1.417990 -46.339252.16 50.00 0.2482766 -2.259095 -37.069162.18 50.00 0.1964918 -2.876167 -24.122942.20 50.00 0.1351378 -3.208011 -8.784462.22 50.00 0.0702993 -3.221718 7.425172.24 50.00 0.0084062 -2.915929 22.898452.26 50.00 -0.0444036 -2.320970 36.100902.28 50.00 -0.0828930 -1.495841 45.723252.30 50.00 -0.1032450 -0.522370 50.811242.32 50.00 -0.1034413 0.502904 50.860322.34 50.00 -0.0834624 1.478305 45.865602.36 50.00 -0.0452897 2.307103 36.322422.38 50.00 0.0072913 2.907108 23.177172.40 50.00 0.0690662 3.218816 7.733452.42 50.00 0.1339088 3.211316 -8.477202.44 50.00 0.1953886 2.885351 -23.847162.46 50.00 0.2474089 2.273248 -36.852212.48 50.00 0.2848106 1.435708 -46.202662.50 50.00 0.3038848 0.455790 -50.971212.52 50.00 0.3027399 -0.569329 -50.684972.54 50.00 0.2814893 -1.537987 -45.372332.56 50.00 0.2422406 -2.354125 -35.560152.58 50.00 0.1888859 -2.936805 -22.221482.60 50.00 0.1267165 -3.228244 -6.679132.62 50.00 0.0618976 -3.199539 9.525602.64 50.00 0.0008573 -2.853539 24.785672.66 50.00 -0.0503511 -2.224554 37.587762.68 50.00 -0.0866492 -1.374962 46.662302.70 50.00 -0.1044374 -0.389015 51.109362.72 50.00 -0.1019517 0.635510 50.487942.74 50.00 -0.0794386 1.597012 44.859652.76 50.00 -0.0391306 2.400139 34.782662.78 50.00 0.0149748 2.965245 21.256292.80 50.00 0.0775122 3.236290 5.621952.82 50.00 0.1422797 3.186394 -10.569922.84 50.00 0.2028543 2.820505 -25.713582.86 50.00 0.2532289 2.174908 -38.307232.88 50.00 0.2884079 1.313626 -47.101982.90 50.00 0.3049026 0.322073 -51.225652.92 50.00 0.3010772 -0.701419 -50.269302.94 50.00 0.2773111 -1.655353 -44.327782.96 50.00 0.2359612 -2.445126 -33.99029

2.98 50.00 0.1811280 -2.992417 -20.282003.00 50.00 0.1182495 -3.242952 -4.562363.02 50.00 0.0535611 -3.171885 11.609723.04 50.00 -0.0065219 -2.786265 26.630483.06 50.00 -0.0560412 -2.124331 39.010313.08 50.00 -0.0900860 -1.251729 47.521503.10 50.00 -0.1052801 -0.254994 51.320023.12 50.00 -0.1001166 0.767029 50.029163.14 50.00 -0.0751077 1.712986 43.776933.16 50.00 -0.0327335 2.489067 33.183373.18 50.00 0.0228038 3.018309 19.299043.20 50.00 0.0859967 3.248227 3.500833.22 50.00 0.1505782 3.156020 -12.644563.24 50.00 0.2101440 2.750832 -27.535993.26 50.00 0.2587868 2.072846 -39.696693.28 50.00 0.2916828 1.189297 -47.920703.30 50.00 0.3055697 0.187806 -51.392433.32 50.00 0.2990704 -0.832310 -49.767613.34 50.00 0.2728294 -1.769886 -43.207363.36 50.00 0.2294491 -2.531943 -32.362263.38 50.00 0.1732313 -3.042909 -18.307823.40 50.00 0.1097512 -3.252111 -2.437793.42 50.00 0.0453041 -3.138804 13.673983.44 50.00 -0.0137189 -2.714223 28.429723.46 50.00 -0.0614644 -2.020474 40.366103.48 50.00 -0.0931976 -1.126355 48.299393.50 50.00 -0.1057714 -0.120537 51.442863.52 50.00 -0.0979391 0.897235 49.484773.54 50.00 -0.0704772 1.826028 42.619303.56 50.00 -0.0261092 2.573736 31.527303.58 50.00 0.0307650 3.066207 17.308763.60 50.00 0.0945051 3.254605 1.373723.62 50.00 0.1587902 3.120245 -14.697563.64 50.00 0.2172451 2.676452 -29.311283.66 50.00 0.2640729 1.967237 -41.018233.68 50.00 0.2946297 1.062932 -48.657413.70 50.00 0.3058851 0.053217 -51.471273.72 50.00 0.2967230 -0.961776 -49.180763.74 50.00 0.2680520 -1.881390 -42.013013.76 50.00 0.2227154 -2.614427 -30.678863.78 50.00 0.1652092 -3.088194 -16.302303.80 50.00 0.1012362 -3.255705 -0.309053.82 50.00 0.0371406 -3.100351 15.714843.84 50.00 -0.0207212 -2.637536 30.180313.86 50.00 -0.0666112 -1.913158 41.65281

3.88 50.00 -0.0959785 -0.999054 48.994623.90 50.00 -0.1059107 0.014126 51.477673.92 50.00 -0.0954228 1.025906 48.855703.94 50.00 -0.0655550 1.935946 41.388743.96 50.00 -0.0192691 2.654000 29.817283.98 50.00 0.0388445 3.108859 15.288864.00 50.00 0.1030230 3.255413 -0.755744.02 50.00 0.1669016 3.079130 -16.725414.04 50.00 0.2241457 2.597492 -31.036424.06 50.00 0.2690783 1.858261 -42.269574.08 50.00 0.2972435 0.934748 -49.310874.10 50.00 0.3058481 -0.081463 -51.462034.12 50.00 0.2940390 -1.089596 -48.509744.14 50.00 0.2629871 -1.989675 -40.746764.16 50.00 0.2157718 -2.692438 -28.942954.18 50.00 0.1570755 -3.128194 -14.268894.20 50.00 0.0927191 -3.253728 1.820224.22 50.00 0.0290848 -3.056592 17.728814.24 50.00 -0.0275170 -2.556336 31.879254.26 50.00 -0.0714730 -1.802569 42.868244.28 50.00 -0.0984240 -0.870043 49.606014.30 50.00 -0.1056975 0.148766 51.424384.32 50.00 -0.0925721 1.152821 48.143034.34 50.00 -0.0603494 2.042551 40.087354.36 50.00 -0.0122250 2.729723 28.056244.38 50.00 0.0470288 3.146190 13.242804.40 50.00 0.1115357 3.250651 -2.883914.42 50.00 0.1748985 3.032747 -18.724634.44 50.00 0.2308338 2.514087 -32.708444.46 50.00 0.2737943 1.746106 -43.448574.48 50.00 0.2995197 0.804965 -49.879944.50 50.00 0.3054589 -0.216004 -51.364734.52 50.00 0.2910229 -1.215552 -47.755714.54 50.00 0.2576432 -2.094554 -39.410794.56 50.00 0.2086301 -2.765841 -27.157524.58 50.00 0.1488442 -3.162841 -12.211064.60 50.00 0.0842145 -3.246183 3.946374.62 50.00 0.0211502 -3.007603 19.712444.64 50.00 -0.0340946 -2.470761 33.523644.66 50.00 -0.0760413 -1.688895 44.010324.68 50.00 -0.1005301 -0.739543 50.132524.70 50.00 -0.1051324 0.283150 51.283104.72 50.00 -0.0893919 1.277763 47.347974.74 50.00 -0.0548695 2.145661 38.717374.76 50.00 -0.0049887 2.800775 26.24718

4.78 50.00 0.0553037 3.178138 11.174084.80 50.00 0.1200286 3.240326 -5.007154.82 50.00 0.1827673 2.981173 -20.691824.84 50.00 0.2372980 2.426379 -34.324504.86 50.00 0.2782129 1.630962 -44.553234.88 50.00 0.3014546 0.673804 -50.363654.90 50.00 0.3047181 -0.350175 -51.179534.92 50.00 0.2876799 -1.339428 -46.919974.94 50.00 0.2520295 -2.195850 -38.007384.96 50.00 0.2013025 -2.834511 -25.325624.98 50.00 0.1405293 -3.192075 -10.132335.00 50.00 0.0757369 -3.233083 6.065785.02 50.00 0.0133506 -2.953468 21.662345.04 50.00 -0.0404427 -2.380959 35.110665.06 50.00 -0.0803083 -1.572332 45.077085.08 50.00 -0.1022929 -0.607777 50.573235.10 50.00 -0.1042162 0.417050 51.054065.12 50.00 -0.0858876 1.400519 46.471895.14 50.00 -0.0491245 2.245099 37.281135.16 50.00 0.0024271 2.867034 24.393215.18 50.00 0.0636550 3.204647 9.086245.20 50.00 0.1284872 3.224456 -7.121815.22 50.00 0.1904944 2.924499 -22.623605.24 50.00 0.2435272 2.334520 -35.881815.26 50.00 0.2823266 1.513028 -45.581655.28 50.00 0.3030447 0.541490 -50.761185.30 50.00 0.3036270 -0.483747 -50.906755.32 50.00 0.2840157 -1.461011 -46.003935.34 50.00 0.2461557 -2.293388 -36.538925.36 50.00 0.1938015 -2.898331 -23.450375.38 50.00 0.1321451 -3.215847 -8.036265.40 50.00 0.0673008 -3.214450 8.174805.42 50.00 0.0056993 -2.894278 23.575175.44 50.00 -0.0465504 -2.287082 36.637615.46 50.00 -0.0842668 -1.453077 46.066715.48 50.00 -0.1037096 -0.474971 50.927405.50 50.00 -0.1029506 0.550237 50.737665.52 50.00 -0.0820651 1.520878 45.516285.54 50.00 -0.0431244 2.340695 35.781095.56 50.00 0.0100100 2.928387 22.497505.58 50.00 0.0720686 3.225672 6.982855.60 50.00 0.1368972 3.203069 -9.224295.62 50.00 0.1980666 2.862819 -24.516665.64 50.00 0.2495109 2.238665 -37.377725.66 50.00 0.2861282 1.392504 -46.53206

5.68 50.00 0.3042874 0.408250 -51.071845.70 50.00 0.3021874 -0.616491 -50.546865.72 50.00 0.2800367 -1.580095 -45.009175.74 50.00 0.2400318 -2.387001 -35.007945.76 50.00 0.1861400 -2.957190 -21.535005.78 50.00 0.1237058 -3.234116 -5.926455.80 50.00 0.0589207 -3.190317 10.269835.82 50.00 -0.0017906 -2.830136 25.447665.84 50.00 -0.0524074 -2.189291 38.101855.86 50.00 -0.0879100 -1.331336 46.977515.88 50.00 -0.1047777 -0.341353 51.194435.90 50.00 -0.1013377 0.682482 50.334435.92 50.00 -0.0779312 1.638635 44.482795.94 50.00 -0.0368793 2.432286 34.219825.96 50.00 0.0177468 2.984729 20.563295.98 50.00 0.0805300 3.241177 4.867516.00 50.00 0.1452439 3.176200 -11.310986.02 50.00 0.2054711 2.796241 -26.367776.04 50.00 0.2552387 2.138980 -38.809686.06 50.00 0.2896114 1.269598 -47.402856.08 50.00 0.3051804 0.274310 -51.295116.10 50.00 0.3004019 -0.748180 -50.100466.12 50.00 0.2757495 -1.696474 -43.937386.14 50.00 0.2336682 -2.476530 -33.417066.16 50.00 0.1783311 -3.010990 -19.582786.18 50.00 0.1152259 -3.246851 -3.806496.20 50.00 0.0506108 -3.160724 12.347296.22 50.00 -0.0091064 -2.761150 27.276606.24 50.00 -0.0580036 -2.087754 39.50090

Solución ante carga arbitraria mediante el método de interpolación lineal de la carga (Nigan & Jennings)

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.000.00

10.00

20.00

30.00

40.00

50.00

60.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-0.1500000

-0.1000000

-0.0500000

0.0000000

0.0500000

0.1000000

0.1500000

0.2000000

0.2500000

0.3000000

0.3500000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-0.1500000

-0.1000000

-0.0500000

0.0000000

0.0500000

0.1000000

0.1500000

0.2000000

0.2500000

0.3000000

0.3500000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-4.000000

-3.000000

-2.000000

-1.000000

0.000000

1.000000

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3.000000

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0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-60.00000

-40.00000

-20.00000

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20.00000

40.00000

60.00000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.000.00

10.00

20.00

30.00

40.00

50.00

60.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-0.1500000

-0.1000000

-0.0500000

0.0000000

0.0500000

0.1000000

0.1500000

0.2000000

0.2500000

0.3000000

0.3500000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-0.1500000

-0.1000000

-0.0500000

0.0000000

0.0500000

0.1000000

0.1500000

0.2000000

0.2500000

0.3000000

0.3500000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-4.000000

-3.000000

-2.000000

-1.000000

0.000000

1.000000

2.000000

3.000000

4.000000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

-60.00000

-40.00000

-20.00000

0.00000

20.00000

40.00000

60.00000