Dinamica

Fuerzas Empleadas
Nombre completo: Cesar Garrido Chávez
Código: 20090217I
El método a emplear será el de Newmark β=1/4
El tipo de fuerza será constante de 7 ton

Integral de Duhamel
Xt=1m.ωd0tFt.e-ε.ωn.t-T.sin(ωd(t-T))dT
Resolviendo la integral
Xt=P0K1-e-ε.ωn.tcos(ωdt)+ε1-ε2sin(ωdt)
Derivando para encontrar la velocidad y la aceleración:
Vt=P0m.ωde-ε.ωn.tsin(ωdt)at=P0m.ωde-ε.ωn.tcosωdtωd-ε.ωn.sin(ωdt)

Para T=0.1
t | x(t) | v(t) | a(t) |
0 | 0 | 0 | 7000 |
0.01 | 0.33170014 | 63.469709 | 5291.70901 |
0.02 | 1.17683499 | 99.5768095 | 1728.38421 |
0.03 | 2.19125609 | 96.6202806 | -2257.8117 |
0.04 | 2.98910097 | 58.0735913 | -5165.37978 |
0.05 | 3.28818523 | 0.37466718 | -5983.58367 |
0.06 | 3.00815742 | -53.9491815 | -4536.75191 |
0.07 | 2.28795494 |-84.9920269 | -1498.45975 |
0.08 | 1.42101305 | -82.6791439 | 1909.55595 |
0.09 | 0.73722225 | -49.8981114 | 4403.08342 |
0.1 | 0.47857804 | -0.64040326 | 5114.6742 |

Para T=1
t | x(t) | v(t) | a(t) |
0 | 0 | 0 | 7000 |
0.01 | 0.3491529 | 69.7346439 | 6942.40044 |
0.02 | 1.3923212 | 138.758158 | 6857.84908 |
0.03 | 3.12105395 | 206.803447 | 6746.84737 |
0.04 | 5.52425601 | 273.608936 |6609.99768 |
0.05 | 8.58824825 | 338.919566 | 6448.00029 |
0.06 | 12.2968375 | 402.487757 | 6261.65005 |
0.07 | 16.6313963 | 464.074335 | 6051.83262 |
0.08 | 21.5709508 | 523.449419 | 5819.52045 |
0.09 | 27.0922787 | 580.393271 | 5565.76838 |
0.1 | 33.1700142 | 634.69709 | 5291.70901 |

Para T=1
t | x(t) | v(t) | a(t) |
0 | 0 | 0 | 7000 |
0.1 | 34.9152897 | 697.346439 |6942.40044 |
0.2 | 139.23212 | 1387.58158 | 6857.84908 |
0.3 | 312.105395 | 2068.03447 | 6746.84737 |
0.4 | 552.425601 | 2736.08936 | 6609.99768 |
0.5 | 858.824825 | 3389.19566 | 6448.00029 |
0.6 | 1229.68375 | 4024.87757 | 6261.65005 |
0.7 | 1663.13963 | 4640.74335 | 6051.83262 |
0.8 | 2157.09508 | 5234.49419 | 5819.52045 |
0.9 | 2709.22787 | 5803.93271 | 5565.76838 |
1 | 3317.00142 |6346.9709 | 5291.70901 |
Para T=0.1
Condiciones tomadas para este periodo con ξ=0.05
T | Wn | WD | m/k | m | k | p | c |
0.1 | 62.83184 | 62.7532511 | 0.0002533 | 1 | 3947.84012 | 7000 | 6.283184 |

P ara Newmark los datos serán:
γ | β | Δt | k1 | a | b | u0 | v0 | a0 |
0.5 | 0.25 | 0.005 | 166461.114 | 812.566368 | 2 | 0 | 0 | 7000 |

t | u | v | a | Δp1 | Δu | Δv | Δa |
0 | 0| 0 | 7000 | 14000 | 0.08410373 | 33.6414906 | -543.403742 |
0.005 | 0.08410373 | 33.6414906 | 6456.59626 | 40249.1364 | 0.24179303 | 29.4342291 | -1139.50089 |
0.01 | 0.32589675 | 63.0757197 | 5317.09537 | 61887.3992 | 0.37178292 | 22.5617293 | -1609.49903 |
0.015 | 0.69767967 | 85.637449 | 3707.59634 | 77001.3036 | 0.46257833 | 13.756433 | -1912.61948 |
0.02 | 1.160258 | 99.393882 |1794.97686 | 84354.0794 | 0.50674946 | 3.91201985 | -2025.14579 |
0.025 | 1.66700746 | 103.305902 | -230.168924 | 83482.5636 | 0.50151391 | -6.00624064 | -1942.15841 |
0.03 | 2.16852137 | 97.2996612 | -2172.32733 | 74717.7777 | 0.44886025 | -15.0552211 | -1677.43379 |
0.035 | 2.61738162 | 82.2444401 | -3849.76112 | 59129.5437 | 0.35521536 | -22.4027379 | -1261.57291 |
0.04 | 2.97259698 |59.8417022 | -5111.33403 | 38402.6865 | 0.23070065 | -27.4031458 | -738.59026 |
0.045 | 3.20329763 | 32.4385564 | -5849.92429 | 14658.6314 | 0.08806039 | -29.6529549 | -161.333387 |
0.05 | 3.29135802 | 2.78560146 | -6011.25768 | -9759.02929 | -0.05862648 | -29.0217953 | 413.797253 |
0.055 | 3.23273154 | -26.2361938 | -5597.46043 | -32513.5696 | -0.19532231 | -25.6565371 | 932.306002 |
0.06 |3.03740923 | -51.8927309 | -4665.15442 | -51496.5967 | -0.30936112 | -19.9589865 | 1346.71423 |
0.065 | 2.72804811 | -71.8517175 | -3318.44019 | -65021.1695 | -0.39060876 | -12.5400697 | 1620.8525 |
0.07 | 2.33743934 | -84.3917872 | -1697.58769 | -71969.1034 | -0.43234784 | -4.15556264 | 1732.95032 |
0.075 | 1.9050915 | -88.5473498 | 35.3626323 | -71879.8732 | -0.4318118 | 4.36997957 |...