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PHNG PHP PHN T HU HN - FEM
Trng i hc Cng nghip TP.HCM
ng Cng Truyn
Chng 4:
PHN T L XO
Phn t mt l xo
Hai nt : i, j
Chuyn v nt : ui, uj (in, m, mm)
Lc nt : fi, fj (lb, N)
cng : k (lb/in, N/m, N/mm)
Phn t mt l xo
Lin h gia lc bin dng l xo:
Phn t mt l xo
Phng trnh cn bng nt i:
Phng trnh cn bng nt j:
Vit di dng ma trn:
Phn t mt l xo
Hay:
k : ma trn cng phn t
u : vc t chuyn v nt phn t
f : vc t lc nt phn t
H l xo
Ba nt : 1, 2, 3
Chuyn v nt : u1, u2, u3 (in, m, mm)
Lc nt : F1, F2 , F3 (lb, N)
cng : k1, k2 (lb/in, N/m, N/mm)
H l xo
Phn t 1:
Phn t 2:
fim l ni lc tc ng
ln nt a phng ica phn t m (i=1,2)
H l xo
Lp rp ma trn cng tng th:
Phng trnh cn bng nt 1:
Phng trnh cn bng nt 2:
Phng trnh cn bng nt 3:
H l xo
Do :
Vit di dng ma trn:
Hay: , K l ma trn cng tng th
H l xo Cch khc lp ghp ma trn cng tng th
Tng kch thc cc ma trn phn t 1 v 2 t 22 thnh 33
Cng 2 ma trn bng nguyn l cng tc dng
H l xo iu kin bin v iu kin ti trng:
Gi s
Ta c:
Rt gn:
H l xo Gii h phng trnh
Ta c chuyn v
V phn lc
V d 1
H l xo chu lc nh hnh v, cho:
Tnh: Ma trn cng tng th Chuyn v nt 2 v 3 Phn lc nt 1 v 4
Lc l xo 2
V d 1
Cc ma trn cng phn t
V d 1 Ma trn cng tng th
V d 1 H phng trnh PTHH
(4)
V d 1 iu kin bin: u1 =u4 =0
Chuyn v nt 2 v 3
Phn lc nt 1 v 4
V d 1 Lc l xo 2
Phng trnh cn bng l xo 2
Lc l xo 2
BI TP V NH(Vit tay trn giy A4, tun sau np)