Mathcad - Dinamica Dan Varianta 3
7
Determinarea valoriilor proprii Rpp 2.631 0.666 0.649 0 0 0.666 2.631 0 0.649 0 0.649 0 6.46 1.333 0 0 0.649 1.333 9.489 1.2 0 0 0 1.2 3.6 Rpp 1 0.41895 0.10961 0.04507 0.01444 4.81219 10 3 0.10961 0.41579 0.01767 0.03228 0.01076 0.04507 0.01767 0.16457 0.0254 8.46584 10 3 0.01444 0.03228 0.0254 0.11605 0.03868 4.81219 10 3 0.01076 8.46584 10 3 0.03868 0.29067 Rnn 0.569 0.569 0.569 2.578 Rpn 0.526 0.526 0.526 0.526 0 0.526 0.526 0.646 0.939 0.586 Rnp 0.526 0.526 0.526 0.526 0.526 0.646 0.526 0.939 0 0.586 Rnn Rnp Rpp 1 Rpn 0.36015 0.47768 0.47768 2.17128 R ufinal 0.36015 0.47768 0.47768 2.17128
-
Upload
nistrean-daniel -
Category
Documents
-
view
2 -
download
0
description
dinamica
Transcript of Mathcad - Dinamica Dan Varianta 3
Determinarea valoriilor proprii
Rpp
2.631
0.666
0.649
0
0
0.666
2.631
0
0.649
0
0.649
0
6.46
1.333
0
0
0.649
1.333
9.489
1.2
0
0
0
1.2
3.6
Rpp1
0.41895
0.10961
0.04507
0.01444
4.81219 103
0.10961
0.41579
0.01767
0.03228
0.01076
0.04507
0.01767
0.16457
0.0254
8.46584 103
0.01444
0.03228
0.0254
0.11605
0.03868
4.81219 103
0.01076
8.46584 103
0.03868
0.29067
Rnn0.569
0.569
0.569
2.578
Rpn
0.526
0.526
0.526
0.526
0
0.526
0.526
0.646
0.939
0.586
Rnp0.526
0.526
0.526
0.526
0.526
0.646
0.526
0.939
0
0.586
Rnn Rnp Rpp1
Rpn0.36015
0.47768
0.47768
2.17128
Rufinal0.36015
0.47768
0.47768
2.17128
F Rufinal1 3.92063
0.86254
0.86254
0.65032
EI0 75000
Rufinal EI02.70113 10
4
3.5826 104
3.5826 104
1.62846 105
M75
0
0
140
Cr Rufinal F1
0
0
1
D F M294.04759
64.69025
120.75514
91.04414
D12294.04759 λ
64.69025
120.75514
91.04414 λ
λ
D12 λ2 385.09173 λ 18959.6297552376
a 1 b 385.09173 c 18959.62975
λ1b b
2 4a c
2 a327.13517
λ2b b
2 4a c
2 a57.95656
ω12
EI0
λ2
35.97322rad
sω11
EI0
λ1
15.14143rad
s
k11 2.70113 104
k12 3.5826 104
m1 75 m2 140 ϕ11 1
ϕ12 1
ϕ21k11 ω11
2m1
ϕ11
k120.27401
ϕ22k11 ω12
2m1
ϕ12
k121.95512
ϕ11
0.27401
(0.274)
ϕ1T 1 0.27401
ϕ21
1.95512
(-2.733)
(-29)ϕ1
T M ϕ2 1.14037 103
Metoda iterarii matriciale pentru det. modurilor normale de vibraratie
Modul 1
ϕ01
1
λ0 414.80273C1 D ϕ0
414.80273
155.73439
ϕ1 Dϕ0
λ0
1
0.37544
C2 D ϕ1339.38415
98.87205
λ1 339.38415
ϕ2 Dϕ1
λ1
1
0.29133
C3 D ϕ2329.22693
91.21395
λ2 329.22693
ϕ3 Dϕ2
λ2
1
0.27705
C4 D ϕ3327.5034
89.91448
λ3 327.5034
ϕ4 Dϕ3
λ3
1
0.27455
C5 D ϕ4327.20033
89.68598
λ4 327.20033
ϕ5 Dϕ4
λ4
1
0.2741
C6 D ϕ5327.14672
89.64556
λ5 327.14672
ϕ6 Dϕ5
λ5
1
0.27402
C7 D ϕ6327.13721
89.63839
ϕ21 0.27402 ϕ11 1
Modul 2
m1 75 m2 140
A2
ϕ21 m2 ϕ11 m1
0.5115
S10
0
0.32344
1
D2 D S10
0
25.64839
70.12072
ϕ01
1
λ0 25.64839C1 D2 ϕ0
25.64839
70.12072
ϕ1 D2
ϕ0
λ0
1
2.73392
C2 D2 ϕ170.12071
191.70465
λ1 70.12071
ϕ2 D2
ϕ1
λ1
1
2.73392
C3 D2 ϕ270.12073
191.70468
λ2 70.12073
ϕ3 D2
ϕ2
λ2
1
2.73392
ϕ11
0.27402
ϕ21
2.73392
ϕ12 1 ϕ22 2.73392
V1 ϕ1T M ϕ2 179.88083
ω1
EI0
327.1351715.14143
rad
s
rad
sω2
EI0
57.9565635.97322
T1 2π
ω10.41497 s
T2 2π
ω20.17466 s
Calculul vibratiilor fortate
Pasul 1: Mase generalizate [kNs^2/m]
M1 ϕ1T M ϕ1 85.51217 M2 ϕ2
T M ϕ2 1.1214 103
Pas 2. Forte generalizate [kN]
P0330
410
P1 ϕ1T P0 442.3482 P2 ϕ2
T P0 1.45091 103
Pasul 3. Factorii de participare modala [m]
ν1
P1
M1 ω12
0.02256 ν2
P2
M2 ω22
9.99813 104
Pasul 4. Forte statice modale echivalente [kN]
F1 ν1 ω12
M ϕ1387.96949
198.44795
F2 ν2 ω22
M ϕ297.03727
495.21198
Ω1 18
Pas 5. Coeficient dinamic modali
ψ11
1Ω1
2
ω12
2.42 ψ21
1Ω1
2
ω22
1.334
Pas 6. Raspunsul Dinamic. maxim in deplasare
u1 ψ1 ν1 ϕ11 2 ψ2 ν2 ϕ21 2 0.0546
u2 ψ1 ν1 ϕ12 2 ψ2 ν2 ϕ22 2 0.05472
Pas 7 Raspunsul Dinamic maxim m mom incovoietor [kN]
F1max F1 ψ1938.88437
480.24311
F2max F2 ψ2129.44729
660.6106
Pasul 8. Moment maxim
Mmax1 391.872
262.53
2
471.6822 kNm
Mmax2 117.792
98.07
2
153.27168 kNm
