kuliah-3 beban harmonis
DESCRIPTION
DINAMIKA STRUKTURTRANSCRIPT
-
Mempelajari respon struktur
akibat beban SINUSOIDAL
-
P0
2T
m
K
)1.........(.................... ".
0)(C REDAMANTANPA KASUS TINJAU
'.".
:
0
0
tSinPKXXM
tSinPKXXCXM
dinamisanKeseimbang
bebansudutgetaranfrekuensi
Keterangan
:
HARMONICBEBAN
TERHADAPSTRUKTURRESPON
-
)4..(........................................ .
)3.....(.................... ..
kerja)beban (pengaruh partikular solusidisebut
bebas)getaran (pengaruh er komplement solusidisebut
)2........(.............................. )(
:adalah atas di dinamisgerak persamaan Solusi
tSinGX
tCosBtSinAX
X
X
XXtX
p
c
p
c
pC
)6.........(.............................. :mana di
)5.(........................................ 1
1.
:diperolehakan
(1) kemasukan dan kali dua pers.(4)Turunkan
2
0
K
PG
-
)8.......(..........sin1
1)(
sehingga 0
dan 1
1.
:diperolehakan 0''
dan 0
:diamkeadaan
dalam sistem pada bekerjaHarmonik beban Jika
)7....(1
1.)(
:didapat (2), pers. kemasukan
(3) pers. bersamadan (4) ke pers.(5)Masukan
2
0
2
0
0)0(
0)0(
2
0
ttSinK
PtX
B
K
PA
XX
XX
tSinK
PtBCostASintX
t
t
-
)9(.................... 1
1)(
)(
)()(
)(
:Respon Rasio
2
0
tSintSintR
KP
tX
statisXtX
tR
Pengaruh Getaran Bebas
Steady State Response
Pengaruh Beban
Transient Response
RESPON GABUNGAN
MPF* X(statis)
2T
2T
)(** statisXMPF
-
)10...(........................................ 1
1
1
'X(t)
:menjadi lengkap solusi Sehingga
1
'
:diperoleh
(7) pers. kedimasukan atas di awal kondisi Jika
''
:diamtidak
yang sistem pada bekerjaHarmonik beban Jika
2
0
02
00
2
00
0
0)0(
0)0(
tSinK
P
tCosXtSinK
PX
K
PXA
XB
XX
XX
t
t
-
t (det) X-A X-B X-TOT t(det) X-A X-B X-TOT
0.000 3.774 -3.774 0.000 0.000 0.000 0.000 0.000
0.020 3.698 -3.247 0.451 0.020 0.750 -0.657 0.093
0.040 3.476 -1.815 1.661 0.040 1.470 -1.130 0.339
0.060 3.114 0.124 3.238 0.060 2.131 -1.288 0.842
0.080 2.629 2.028 4.657 0.080 2.707 -1.087 1.620
0.100 2.039 3.366 5.405 0.100 3.175 -0.583 2.593
0.120 1.367 3.765 5.133 0.120 3.517 0.084 3.602
0.140 0.641 3.114 3.756 0.140 3.719 0.728 4.447
0.160 -0.110 1.594 1.484 0.160 3.772 1.168 4.940
0.180 -0.857 -0.370 -1.228 0.180 3.675 1.283 4.958
0.200 -1.570 -2.232 -3.802 0.200 3.431 1.039 4.471
0.220 -2.221 -3.471 -5.691 0.220 3.051 0.506 3.557
0.240 -2.783 -3.741 -6.524 0.240 2.549 -0.168 2.380
0.260 -3.234 -2.968 -6.202 0.260 1.945 -0.796 1.149
0.280 -3.556 -1.367 -4.923 0.280 1.264 -1.201 0.063
0.300 -3.736 0.615 -3.120 0.300 0.533 -1.272 -0.739
0.320 -3.767 2.426 -1.341 0.320 -0.220 -0.987 -1.207
0.340 -3.648 3.560 -0.088 0.340 -0.964 -0.427 -1.392
Beban Fungsi SINUS Beban Fungsi COSINUS
-
0.360 -3.384 3.701 0.317 0.360 -1.670 0.252 -1.418
0.380 -2.985 2.809 -0.176 0.380 -2.309 0.861 -1.448
0.400 -2.467 1.134 -1.333 0.400 -2.856 1.229 -1.626
0.420 -1.850 -0.858 -2.708 0.420 -3.289 1.255 -2.034
0.440 -1.160 -2.610 -3.770 0.440 -3.591 0.931 -2.660
0.460 -0.423 -3.634 -4.058 0.460 -3.750 0.347 -3.403
0.480 0.330 -3.645 -3.315 0.480 -3.759 -0.334 -4.093
0.500 1.070 -2.638 -1.568 0.500 -3.619 -0.922 -4.540
0.520 1.768 -0.896 0.872 0.520 -3.334 -1.252 -4.586
0.540 2.395 1.097 3.492 0.540 -2.916 -1.233 -4.149
0.560 2.927 2.783 5.710 0.560 -2.382 -0.870 -3.253
0.580 3.342 3.693 7.035 0.580 -1.753 -0.265 -2.018
0.600 3.623 3.573 7.196 0.600 -1.054 0.415 -0.640
0.620 3.761 2.456 6.216 0.620 -0.314 0.979 0.665
0.640 3.748 0.654 4.402 0.640 0.440 1.269 1.709
0.660 3.586 -1.331 2.255 0.660 1.176 1.206 2.382
0.680 3.281 -2.944 0.337 0.680 1.865 0.806 2.671
0.700 2.845 -3.736 -0.891 0.700 2.479 0.182 2.661
0.720 2.296 -3.486 -1.190 0.720 2.995 -0.494 2.501
0.740 1.655 -2.263 -0.608 0.740 3.391 -1.031 2.360
0.760 0.948 -0.409 0.539 0.760 3.653 -1.281 2.371
0.780 0.204 1.559 1.763 0.780 3.768 -1.174 2.594
0.800 -0.549 3.092 2.543 0.800 3.733 -0.739 2.995
0.820 -1.280 3.763 2.483 0.820 3.550 -0.098 3.452
-
-8.000
-6.000
-4.000
-2.000
0.000
2.000
4.000
6.000
8.000
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000
Res
po
n P
erp
ind
ah
an
(c
m)
Waktu (detik)
Respon Beban Harmonis (Beban Fungsi COSINUS, C=0)
pengaruh beban
pengaruh getaran bebas
Respon Total
-
-6.000
-4.000
-2.000
0.000
2.000
4.000
6.000
0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600
Pe
rpin
da
ha
n (
cm
)
Waktu(detik)
Respon Beban Harmonis (Beban Fungsi SINUS, C=0)
pengaruh beban
pengaruh getaran bebas
RESPON SISTEM
-
t(det)
0.1 0.3 0.5 0.7 0.9 0.99
A 3.367003 3.663004 4.444444 6.535948 17.54386 167.5042
` 2.9277 8.783101 14.6385 20.4939 26.3493 28.98423
-
0.1 0.3 0.5 0.7 0.9 0.99
A 3.367003 3.663004 4.444444 6.535948 17.54386 167.5042
` 2.9277 8.783101 14.6385 20.4939 26.3493 28.98423
0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.020 0.011 0.033 0.055 0.076 0.097 0.107
0.040 0.083 0.248 0.409 0.563 0.708 0.769
0.060 0.258 0.762 1.237 1.663 2.025 2.164
0.080 0.540 1.579 2.501 3.240 3.753 3.903
0.100 0.900 2.586 3.947 4.830 5.162 5.132
0.120 1.281 3.584 5.175 5.783 5.377 4.911
0.140 1.617 4.350 5.762 5.499 3.779 2.698
0.160 1.857 4.711 5.408 3.678 0.358 -1.271
0.180 1.979 4.595 4.042 0.481 -4.137 -5.892
0.200 2.000 4.056 1.865 -3.446 -8.337 -9.495
0.220 1.969 3.254 -0.699 -7.120 -10.680 -10.439
0.240 1.948 2.404 -3.118 -9.494 -9.972 -7.804
0.260 1.996 1.704 -4.898 -9.776 -5.897 -1.897
0.280 2.144 1.275 -5.726 -7.696 0.726 5.668
0.300 2.390 1.120 -5.548 -3.618 8.071 12.387
0.320 2.694 1.129 -4.567 1.517 13.810 15.698
0.340 2.995 1.122 -3.167 6.444 15.857 13.940
t(det)
-
0.360 3.230 0.912 -1.776 9.917 13.108 7.088
0.380 3.353 0.376 -0.729 11.058 5.926 -3.039
0.400 3.356 -0.501 -0.166 9.608 -3.832 -13.233
0.420 3.263 -1.613 -0.005 5.987 -13.287 -19.910
0.440 3.129 -2.764 0.009 1.170 -19.398 -20.367
0.460 3.019 -3.728 0.193 -3.603 -19.941 -13.838
0.480 2.985 -4.316 0.793 -7.178 -14.309 -1.950
0.500 3.052 -4.440 1.875 -8.801 -3.821 11.640
0.520 3.206 -4.136 3.281 -8.293 8.560 22.364
0.540 3.401 -3.550 4.664 -6.055 19.072 26.277
0.560 3.573 -2.888 5.594 -2.892 24.310 21.497
0.580 3.662 -2.349 5.699 0.264 22.333 9.016
0.600 3.632 -2.055 4.791 2.644 13.362 -7.433
0.620 3.483 -2.016 2.947 3.851 -0.171 -22.478
0.640 3.251 -2.129 0.498 3.927 -14.284 -30.865
0.660 2.996 -2.213 -2.055 3.267 -24.631 -29.287
0.680 2.781 -2.078 -4.182 2.415 -27.850 -17.654
0.700 2.653 -1.589 -5.472 1.832 -22.660 0.680
-
0 HARMONIS BEBAN C
diabaikandapat jadi kecil,
makin struktur respon pengaruh
panjang yang waktu Dalam
..
erComplement Solusi
)11(.......... '2"
.'.".
:ankeseimbangpersamaan
)(
02
0
tCosBtSinAeX
tSinM
PXXX
tSinPXKXCXM
t
tC
bekerja efektip belumbeban saat pada
awaldetik -deti pada maks.respon
kecilmakin lamamakin
-
PARTIKULAR SOLUSIluarbeban dengan sama yang
fasa mempunyaiselalu tidak
maka (damping) ada Karena
)(tPX
2220
222
2
0
)(
21
22
21
11
(11) pers. kean subsitusikdan turunkan
)12....(.................... .2.1
KP
G
KP
G
tCosGtSinGX tp
TOTAL RESPON :sehingga diabaikan, )( tCX
)13.........( 21
21
1)( 2
222
0 tCostSinK
PtX
-
ARGAND DIAGRAM
)15...(.......... 21:factor ion magnificat Dynamic
.)(
:ditulisdapat n PerpindahaRespon
1
2tan
)14.....(.......... 21
222
0
2
1
2220
KP
D
D
tSintX
K
P
tt
222
0
21
2
K
P 222
2
0
21
1
K
P
D
0
%2
1 2
1
-
awal kondisi
kanmemperhatidengan ditentukan dan Sedangkan
21
2
21
1
:dimana
)15.....( )(
:menjadistruktur respon maka
gkandiperhitun bebasgetaran pengaruh Jika
222
222
2
BA
D
C
tDCostCSintBCostASinetX t
-
Po = 500000 N
K = 59709 N/mm
m = 285.88 N-det2/mm
0.1 0.5 0.9 1.3
5%
20%
40%
60%
80%
90%
99%
RESPON
SYSTEM ?
-
0.05 0.2 0.4 0.6 0.8 0.9 0.99
0.010101 0.040382 0.080633 0.120624 0.160231 0.179853 0.197396
8.458172 8.451707 8.431121 8.397141 8.350253 8.322165 8.294343
0 -0.08543 -0.3412 -0.67909 -1.01044 -1.33225 -1.48871 -1.62665
0.04 0.403363 0.147271 -0.19242 -0.52713 -0.85376 -1.01316 -1.15403
0.08 0.890811 0.635255 0.294886 -0.04205 -0.37242 -0.53423 -0.67755
0.12 1.375283 1.121116 0.78121 0.443165 0.110164 -0.05351 -0.19881
0.16 1.85516 1.603233 1.264924 0.9269 0.59238 0.427391 0.280596
0.2 2.328839 2.079992 1.744412 1.407538 1.072617 0.906862 0.759066
0.24 2.794738 2.549803 2.218073 1.883474 1.549271 1.383304 1.234999
0.28 3.2513 3.011096 2.684323 2.353118 2.020749 1.855124 1.706806
0.32 3.697 3.462329 3.141605 2.8149 2.485476 2.320746 2.172911
0.36 4.13035 3.901995 3.588392 3.267278 2.941899 2.778616 2.631757
0.4 4.5499 4.328625 4.02319 3.708741 3.388495 3.227202 3.08181
0.44 4.95425 4.740794 4.444548 4.137814 3.823769 3.665007 3.521568
0.48 5.342048 5.137125 4.851057 4.553062 4.246269 4.090567 3.949561
0.52 5.712 5.516293 5.24136 4.9531 4.654583 4.502462 4.364359
0.56 6.062869 5.877032 5.614152 5.33659 5.047347 4.899315 4.764576
0.6 6.393483 6.218138 5.968188 5.702252 5.423249 5.2798 5.148876
0.64 6.702737 6.538469 6.302286 6.048863 5.781032 5.642646 5.515974
0.68 6.989599 6.836957 6.615328 6.375266 6.119502 5.986641 5.864644
0.72 7.253109 7.112603 6.90627 6.680371 6.437528 6.310636 6.193722
0.76 7.492388 7.364488 7.17414 6.963157 6.734047 6.613547 6.502107
0.8 7.706637 7.591769 7.418041 7.222681 7.008069 6.894364 6.78877
t (detik)
Respon Perpindahan, X(t)
-
0.84 7.895138 7.793687 7.637161 7.458075 7.258678 7.152149 7.052753
0.88 8.057264 7.969567 7.830765 7.668553 7.485037 7.386039 7.293173
0.92 8.192471 8.118823 7.998209 7.853411 7.686389 7.595253 7.509229
0.96 8.300309 8.240955 8.138932 8.012033 7.862063 7.779093 7.700197
1 8.380417 8.335556 8.252464 8.143887 8.011471 7.936945 7.86544
1.04 8.432527 8.402309 8.338426 8.248535 8.134114 8.06828 8.004407
1.08 8.456466 8.440991 8.396531 8.325625 8.229582 8.172661 8.116631
1.12 8.452153 8.451473 8.426584 8.374901 8.297557 8.249738 8.20174
1.16 8.419603 8.43372 8.428486 8.396198 8.337811 8.299255 8.259448
1.2 8.358925 8.387792 8.402229 8.389444 8.35021 8.321044 8.289562
1.24 8.27032 8.313841 8.347902 8.354663 8.334712 8.315035 8.291983
1.28 8.154086 8.212116 8.265686 8.29197 8.291369 8.281247 8.266701
1.32 8.010611 8.082955 8.155856 8.201576 8.220326 8.219792 8.213802
1.36 7.840373 7.92679 8.018778 8.083781 8.12182 8.130876 8.133462
1.4 7.643942 7.744143 7.854911 7.938979 7.996181 8.014797 8.025949
1.44 7.421974 7.535625 7.664803 7.767655 7.843828 7.871941 7.891623
1.48 7.17521 7.301931 7.449087 7.57038 7.66527 7.702787 7.730932
1.52 6.904475 7.043842 7.208485 7.347814 7.461104 7.507899 7.544414
1.56 6.610674 6.762222 6.943801 7.100701 7.232011 7.287928 7.332691
1.6 6.294787 6.458009 6.655919 6.829865 6.978758 7.04361 7.096471
1.64 5.957871 6.132222 6.3458 6.536211 6.702189 6.77576 6.836542
1.68 5.60105 5.785948 6.014482 6.220721 6.40323 6.485273 6.553774
1.72 5.225517 5.420344 5.66307 5.884449 6.082879 6.17312 6.249111
1.76 4.832527 5.036632 5.292738 5.528518 5.742205 5.840344 5.923571
-
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 1 2 3 4 5 6 7
Res
po
n P
erp
ind
ah
an
(m
m)
waktu (detik)
BEBAN HARMONIS C0; =0.1 (Pengaruh Redaman terhadap Respon Struktur)
damping= 5%
damping= 20%
damping = 40%
damping = 60%
damping = 80%
damping = 90%
damping = 99%
=0.1 artinya frekuensi getaran
beban sangat kecil
dibandingkan dengan frekuensi
getaran struktur. Pada kasus ini
amplitudo getaran struktur lebih
dipengaruhi oleh nilai Po/K.
sedangkan pangaruh dan juga
sangat kecil
-
-15
-10
-5
0
5
10
15
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Pe
rpin
da
ha
n (
mm
)
Waktu Detik)
BEBAN HARMONIS C0; =0.5 (Pengaruh Redaman terhadap Respon Struktur)
damping= 5%
dampng= 20%
damping= 40%
damping= 60%
damping= 80%
damping= 90%
damping= 99%
Pada kasus ini pengaruh
redaman sudah muai
nampak, dimana Amplitudi
selain dipengaruhi oleh
naiai Po/K, juga oleh nilai
dan
0.05 0.2 0.4 0.6 0.8 0.9 0.99
0.067 0.261 0.490 0.675 0.818 0.876 0.922
11.141 10.788 9.852 8.719 7.636 7.148 6.742
t (detik)
Respon Perpindahan, X(t); =0.5
-
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1 1.2
Pe
rpin
da
ha
n (
mm
)
Waktu (detik)
BEBAN HARMONIS C0; =0.9 (Pengaruh Redaman terhadap Respon Struktur)
damping= 5%
damping= 20%
damping= 40%
damping= 60%
damping= 80%
damping= 90%
damping= 99%
Pada 1, atau
frekuensi getaran
struktur mendekati
frekuensi getaran
beban, pengaruh
sangat berarti
-
-15
-10
-5
0
5
10
15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Pe
rpin
da
ha
n (
mm
)
waktu (detik)
BEBAN HARMONIS C0; =1.3 (Pengaruh Redaman terhadap Respon Struktur)
damping= 5%
damping= 20%
damping= 40%
damping= 60%
damping= 80%
damping= 90%
damping= 99%
-
0.2 0.4 0.6 0.8 0.9 0.99
' 2.890398 5.780797 8.671195 11.56159 13.00679 14.30747
0.02083 0.047583 0.093477 0.218669 0.442374 1.37243
8.721042 9.957784 13.02728 22.70724 39.83114 82.92728
0 -0.18165 -0.47364 -1.21598 -4.92589 -17.0512 -81.3011
0.04 0.825392 1.818473 3.265532 5.481232 3.099609 -59.4959
0.08 1.821412 4.013791 7.358107 14.73681 22.43013 -18.7305
0.12 2.793113 5.995453 10.57432 20.89637 35.82492 28.00413
0.16 3.727519 7.657976 12.5311 22.66585 39.73931 65.81425
0.2 4.612155 8.912861 12.99541 19.67351 33.13741 82.65045
0.24 5.435209 9.693312 11.91193 12.54799 17.7663 73.14731
0.28 6.185691 9.957784 9.409716 2.7863 -2.30633 40.33332
0.32 6.853581 9.6922 5.786785 -7.56076 -21.7686 -5.33424
0.36 7.42996 8.910696 1.474636 -16.3194 -35.4703 -49.3019
0.4 7.907134 7.654873 -3.01315 -21.6495 -39.7853 -77.5578
0.44 8.27873 5.991578 -7.14205 -22.4313 -33.572 -81.0973
0.48 8.539787 4.009349 -10.4203 -18.5006 -18.4744 -58.7925
0.52 8.68682 1.813701 -12.4575 -10.6831 1.512134 -17.7514
0.56 8.717864 -0.47849 -13.011 -0.62123 21.09847 28.94672
0.6 8.632507 -2.74521 -12.0148 9.571167 35.10149 66.42001
0.64 8.431887 -4.86581 -9.58768 17.75278 39.81553 82.72634
0.68 8.118682 -6.72739 -6.01861 22.20475 33.99313 72.66914
0.72 7.697076 -8.23087 -1.73271 21.99176 19.17506 39.45347
0.76 7.172698 -9.29622 2.759558 17.15858 -0.71733 -6.33536
0.8 6.552548 -9.86673 6.923156 8.720576 -20.4199 -50.1052
Respon Perpindahan, X(t)
t (detik)
-
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
pe
rpin
da
ha
n (
mm
)
Waktu (detik)
Respon Beban Harmonis ( dan : tetap, : bervariasi)
beta = 20%
beta = 40%
beta = 60%
beta = 80%
beta = 90%
beta = 99%