![Page 1: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/1.jpg)
ANALISIS DINAMIK STRUKTUR
Pertemuan ke-5
MODEL MDOF FREE VIBRATION
![Page 2: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/2.jpg)
Lanjutan : SDOF
EI 2EI EI
F(t)
5 m
E = 2 x 106 kg/cm2
I = 500 cm4
W = 2500 kgg = 980 cm/det2
W
• Berapa frekuensi natural dan periode dari struktur berikut ?
Kol A Kol B Kol C
![Page 3: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/3.jpg)
Lanjutan : SDOF
EI 2EI EI
F(t)
5 m
E = 2 x 106 kg/cm2
I = 500 cm4
W = 2500 kgg = 980 cm/det2
W
• Berapa frekuensi natural dan periode dari struktur berikut ?
Ksdof
Kol A Kol B Kol C
Ksdof = K kol A + K kol B+ K kol C
![Page 4: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/4.jpg)
SDOF (?)
EI EI
F(t)
5 m
E = 2 x 106 kg/cm2
I = 500 cm4
W1 = W2 = 2500 kgg = 980 cm/det2
W1
• Berapa frekuensi natural dan periode dari struktur berikut ?
Kol A Kol B
EI EI
W2
5 m
SDOF ?
![Page 5: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/5.jpg)
MDOF (multi degree of freedom)
EI EI
F(t)
5 m
W1
• Berapa frekuensi natural dan periode dari struktur berikut ?
K1
Kol A Kol B
EI EI
W2
5 m
MDOF
F(t)
m1
m2
K2
F2
F1
![Page 6: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/6.jpg)
MDOF (multi degree of freedom)
Persamaan tersebut dapat diperluas untuk mengakomodasi pemodelan MDOF
K1
m1
m2
K2
F2
F1
F1 (t)
F2 (t)
u u
Matrix massa
Matrix percepatan
Matrix kekakuan
Matrix displacement
Matrix beban
![Page 7: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/7.jpg)
kekakuan struktur MDOF
K1
m1
m2
K1+K2
F2
F1
F1 (t)
F2 (t)
Mode shape 1
1
K2
K2
K1
m1
m2 1 K2
K2
Mode shape 2
0
u u
![Page 8: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/8.jpg)
MDOF (multi degree of freedom)
EI EI
F(t)
5 m
W1
• Matrix kekakuan struktur untuk model MDOF berikut?
K1
Kol A Kol B
EI EI
W2
5 m
MDOF
F(t)
m1
m2
K2
F2
F1
![Page 9: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/9.jpg)
MDOF (multi degree of freedom)
• Persamaan gerak untuk model MDOF
![Page 10: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/10.jpg)
MDOF (multi degree of freedom)
![Page 11: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/11.jpg)
MDOF (multi degree of freedom)
![Page 12: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/12.jpg)
MDOF (multi degree of freedom)
EI EI
F(t)
5 m
W1
Kol A Kol B
EI EI
W2
5 m
F(t)
E = 2 x 106 kg/cm2
I = 500 cm4
W1 = W2 = 2500 kgg = 980 cm/det2
Penyelesaian merupakan permasalahan “ Eigenproblem”
Dengan solusi
![Page 13: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/13.jpg)
a
acbbx
2
42
2,1
kekakuan
![Page 14: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/14.jpg)
Contoh soal :
EI EI
F(t)
3 m
W1
Kol A Kol B
EI EI
W2
3 m
F(t)
E = 2 x 106 kg/cm2
I = 100 cm4
W1 = W2 = 1500 kgg = 980 cm/det2
Penyelesaian merupakan permasalahan “ Eigenproblem”
Dengan solusi
![Page 15: ANALISIS DINAMIK STRUKTUR - afifshulhan.files.wordpress.com · kekakuan struktur MDOF K 1 m 1 m 2 K 1 +K 2 F 2 F 1 F 1 (t) F 2 (t) Mode shape 1 1 K 2 K 2 K 1 m 1 m 2 1 K 2 K 2 Mode](https://reader031.vdocuments.net/reader031/viewer/2022013110/5d1f7ae088c993364d8cef38/html5/thumbnails/15.jpg)
Operasi matrix
• Determinan matrix
• Nilai determinan dari suatu matriks merupakan suatu skalar.
• Contoh :
2221
1211
aa
aaA
21122211)det( aaaaA 2221
1211)det(
aa
aaA
31
52A 156)det( A
31
52)det( A