bài tập động lực học

Bai 1:
Thông sô ban  âu hay  iêu kiên biên tai Z=0:
(0) 0
(0) 0
y = y 0( )
M = M 0( )
a
b
=
=



Cung co:
(0) 0
(0) 0
y' = y' 0
Q = Q 0
≠
≠



 iêu kiên biên mut phai (Z=l)
(l)
(l)
y 0(c)
M = 0(d)
=




Thê (a) ,(b) vao (2.9.a) ,(2.9.c) co:
() ()
(z)
()
(z) 0 kiz
3
y' Q
y ( )
Q
M =EJ*y' *ki*D + (f)
kiz kiz
kiz
B D e
ki EJki
B
ki


−

=




Thê (c),(d) vao (e),(f) ta co:
() ()
(l)
()

(l) 0 kil
3
y' Q
y 0
Q
M =EJ*y' *ki*D + 0
kil kil
kil
B D
ki EJki
B
ki




= − =
=



hay
(l) () ()
(l) kil 0 ()
3
y y' Q 0(1)
M =EJ*ki*D *y' + Q 0(2)
kil kil
kil
B D

ki EJki
B
ki


= − =

=




Hê (1),(2) co nghiêm : y’
0
≠ 0 , Q
0
≠ 0 → D = 0
Hay : = 0 →
2 2
0
kil kil
B D
ki ki
   
+ =
 ÷  ÷
   
→
2 2
0

kil kil
B D
+ =
(3)
 â y la ph   ng trinh phi tuyên  ê ac  inh Ki:
Giai pt (3) co :
k
i
l =0.0001 k
i
2
l
2
= 0.0001
2
2
1
2
0.0001 EJ
l m
ω
=

k
i
l =0.0002 ⟹ k
i
2
l
2

= 0.0002
2
⟹
2
2
2
0.0002 EJ
l m
ω
=
k
i
l =0.0003

k
i
2
l
2
= 0.0003
2
2
3
2
0.0003 EJ
l m
ω
=
Bai 2:
Thông sô ban  âu hay  iêu kiên biên tai Z=0:

(0) 0
(0) 0
y = y 0( )
M = M 0( )
a
b
=
=



Cung co:
(0) 0
(0) 0
y' = y' 0
Q = Q 0
≠
≠



 i êu kiên biên mut phai (Z=l)
(l)
(l)
y 0(c)
y ' = 0(d)
=




Thê (a) ,(b) vao (2.9.a) ,(2.9.b) co:
() ()
(z)
()
(z) 0 kiz
3
2
y' Q
y ( )
Q
y ' =y' *A - (f)
kiz kiz
kiz
B D e
ki EJki
C
EJki




= −



Thê (c),(d) vao (e),(f) ta co:
() ()
(l)
()
(l) 0 kil

3
2
y' Q
y
Q
y ' =y' *A -
kil kil
kil
B D
ki EJki
C
EJki




= −



hay
(l) 0 ()
(l) kil 0 ()
3
2
y y' Q (1)
y ' =A *y' - Q (2)
kil kil
kil
B D

ki EJki
C
EJki

= −






Hê (1),(2) co nghiêm : y’
0
≠ 0 , Q
0
≠ 0 → D = 0
Hay : = 0 →
3 3
* *C
0
kil kli kil kli
A D B
EJki EJki
− =
→
* *C 0
kil kil kil kil
A D B− =
(3)
 â y la ph   ng trinh phi tuyên  ê ac  inh Ki:

Giai pt (3) co :
k
i
l =0.001 k
i
2
l
2
= 0.001
2
2
1
2
0.001 EJ
l m
ω
=

k
i
l =0.01 ⟹ k
i
2
l
2
= 0.01
2
⟹
2
2

2
0.01 EJ
l m
ω
=
k
i
l =0.015

k
i
2
l
2
= 0.015
2
2
3
2
0.015 EJ
l m
ω
=