机械振动与噪声学_赵玫_课后答案[1-5章].khda

2
8m
3 11 2
1
2 2 k,
2J
2 2
2 2 k, u
2J
11
2 2,
1
11
1.207 cos 1 t
2
2
2 0.207 cos 2 t
3 12 u
1
1.168m 1.424
1
6.908m 8.424
1.168mL 6.908mL
y u 1 x 0.855 0.101L x 0.146 0.101L
Re Z 1 F0 ei t 0
Z
k1 k2 m1 2 i(c1 c2 ) k2 ic2
k2 ic2 k2 k3 m2 2 i(c2 c3)
5 2 0.1, d 19.9 rad/s , 0.63,
x n 1.88 xn 1
5 4 0.0202 , 0.003215, d 44.72 rad/s
c 1.44 Ns/m
5
25
c
1 0.98
m = 5 kg a
k = 10 kN/m
b
c
c (d)
453.4 kg
5.08 mm
0.2308 kg m
(a) 1200 rpm
(b)
(
)
55
1136 kg
5.08 mm
113 kg 15.24 cm/s2
20 Hz k = 2802 N/cm = 0.10
58 58 rpm
11
(a)
(b)
(c)
12
0.20 cm
0.15 s
13
82 Hz
14
10 Hz
4.57 m/s
15 Acos n t + Bcos ( n t + ) = Ccos ( n t + ' )
16
50 g 0 /2
17
x1 = X1 cos t x2 = X2 cos ( + ) t
<<
18
Ae i
( 5-12)
500 kN
400
k2
58 5 13
rpm 272 rpm
59
232 rpm 232 rpm
5 11
5 12
2kg
198
160 320 rpm
61
L
+ 1/2 )C / 2L,
C Eg /
62
L
63
J
n=0 1 2
f =(n
64 6 5 50 50 300 mm
7 1 20
1530 kg / m 1000 Hz
0.2
F = 20 cos 3t (N)
45
k = k0 e i 2
46
Q
47
Q
48
Q
49
49
v
4 10 4 10
m = 20 kg
c = 0.2 kN s /m
x (t)
4 11
4 11
k = 3.5 kN/m
60 rpm
0.01 m
30
4 12
49
t= 0
4 13
4 14 4 15
t t0 t t0 t0
7 2 20
73
74
120 dB
110 dB
75
2 5 10 100 7
0.224 L
1690 Hz
0 dB 120 dB
74 dB
20 dB
1 3 6 10dB 7 6 20
415 1.48 106
,
77
dB
dB
78
n
,
n
79
40
,
n dB,
70 70
L j dB
n = 0,
n
L 10lg (1 10 10 ) (dB) L
5 5 0.58 mm, F T 506.4 N
5 7 3.166 cm/s2
5 9 (a) < 20.7 rpm (b) = 37.6 rpm
5 10 2 . 68 mm
5 12 k 2 5 10 7 N/m
1 35.79 rad/s; 2 73.51 rad/s
13
27
x
(I m r22 m1 r12 ) x (k1 r22 a2 / b2 k2 r22 ) x 0 2 10 243 E I ( 4 L 3 )
2 11 ke k1cos 2 a2k2 b2
2 12
me
(1
1 3n2
1 n
)m
2 14 m 0 x
0 J0
k1
R k1
x0
R k 1 R 2 ( k 1 k 2)
k cos2 (1 2 )2 2
arctan 1
,
2
4 9 v L kg
2W
4 10
k cos 2 m 00
xa a
1
sin ( i t i )
4 2 i 1 i (1 i ) 2 ( 2 i ) 2
2
i
arctan 1
i
2 i
2i
i
m 2k
4 11
c 2m n
m x k x m g sin 30
x(t )
?
l = 15 cm
85 86 87
l x l y l z 10 7 4m3
d
R
100 dB
T60
200 m 2
2m ,
V pe
W 10 4
p
2 e
V T60
8
0.2 ,
T60
88
89 1 2
T60 T6'0
Lp
10 lg ( T6'0 ) T60
lx ly lz 30 15 7 m3
80d B
3
2 18 m1 m2 m2l x 2k 0 x 0
m2l
m2l 2
0 m2 gl
0
10
31
fn
1 2
4
m( 1
1
1 1)
4k1 4k2 k3 k4
33
wk.baidu.com
3c m
3ka2 ml 2
0, f n
1 2
3k a 2 ml 2
Cc
2a 3l
3mk
35
x (t)
37
m 2 2 g h sin
k
t m 2 g cos
(a) 1 + i 3 (b) 2
(f) ( 3 + i ) (3 + 4 i )
(c) 3 / ( 3 - i )
(d) 5 i
(e) 3 / ( 3 - i ) 2
(g) ( 3 - i ) (3 - 4 i )
(h) ( 2 i ) 2 + 3 i + 8
21
0.4 s
W = 30 N
21
0.1 s
100Hz
TL1 40 dB
TL2
TL
1000 Hz
0.2 7500 kg / m3
1000 Hz 25 dB
9
()
1 4 x max 0.0727 m , xmax 287.14 m s 2 , t = 0.1 s
15
0
0
c AB
arc tan B A
0 (A B)
c A2 B2
c AB
(A B) c B A
400
4
5
3m 10m
8 10
50 m2
102
1m
60 dB
2s S j =0.5 m2 , 51
1 2
3
0.1m
91 20 kg / m3
92 0.3
250 Hz 0.04
0.45 9 1 p. 170
0.5
93
20 cm
94 95
1000Hz
10 0.4 mm
2000 kg / m2
100 Hz
31
a
k3 k4
2 18
k1 k2
m
b
k3 a
31
a b
m
32
33 (a)
m
O
(b)
(b) 35
m2
34
(a)
(c)
m1
k
h
m1
b (c)
32
33
34
36 kg/m
x0 = 0.01 m, x0 = 0
m = 10 kg s2/m
37 37 k = 7 kN/m
x0 25mm, x0 0 (b)
m 38
i
1 8 (a) 2 e 3
f) 10 e i 1 456, h) 5 e i 0 64
22
3k 3g 0
2m 2 l
24
3m x 2
2k (R
a)2 x
0
R2
2 5 (m M ) x k x 0, 2
2 6 [m1L12 m2L22 m3(L3 L4)2] L32c
(L3 L4)2k m2gL2 0
0
2 15
m1 0 x1 0 m2 x2
c1 c1 x1 c1 c1 x2
k1 k2 k3
k3 x1 0
k3
k3 k4 x2 0
2 16 2 0 x 1
T 2 1 x1 0
0 1 x2 m2 L 1 2 x2 0
2 17
1
2
J1 0
1
2 k r2 k r2
1
0
0 J2 2
k r2 2 k r2 2
0
L < 0 . 1dB n
7 10 81
L
L2 L L2 ,
L1
L
L2
L1 10lg(1 10 10 ) (dB)
0.01m
1000 Hz
0.05m/s
50m
82
0.01 m
1000 Hz
1m 83
74 dB
pe 0.1
Wm
10-3
84
0.005 m
f = 100 Hz
0.008 m/s
L < 1dB n L2
3 13 u 1 1 , u 11
1 1 1, 2m 1 1
y1
1 2
(
x
1
x2 )
y2
1 2
(
x
1
x2 )
3 15 2 2 T , R 3mL
2 R
9T ),
14 m L
2 1
T 2mL
2 R
2 R
2 1
2 1
(Dunkerley)
11
41
X
cA
,
(k m 2 )2 (c )2
2
tan 1 k
c m
2
42
mL2 a2
c
(k
mgL a2
)
kA cos t , a
k Aa
cos ( t )
(ka2 mgL) (1 2 )2 (2 )2
,
n n
a2c
2L m(ka2
a2k g mL2 L
, mgL)
arctan 2 1
2
4 5 mx kei2 x F0 e i t ,
x(t)
F0 e i ( t )
T
2 15
2 11 L
EI m
m1 m2 ( m1 = 2 m2 )
2 12 O
2 17
2 13 2 17
2 14
2 15
2 16
k1 = k2 = k3 = k m1 = m2 = m r1 = r2 = r J1 = J2 = J
2
2 18 2 18
m1
k
m2
L
31
32 33 34 35
2 17
kt
( m1 m2 ) k
m1 m2
k
m1 m2
4 7.56 mm , x max 644.5 mm / s ,
210.8 mm / s , x 1.46 mm
39
2
1
2
1
0.81 k m
2
2.62 k m
1
1
u
1.086 0.46
3 10
2 23 97 k ,
1
8m
1
1
u
1.42 8.42
L
L
2 23 97 k
m = 9 kg = 0.15 (a)
(c)
(d)
3
35 k = 1000 0 0.2 1.0
37
4F/k ( F
)
39
39
(
)
3 10 3 10
C
39 3 11 3-11
(b)
3 10 k1 = k2 = k J1 = 2 J2 = 2 J (a)
1(0) = 1 rad 2 (0) = 2 rad 1(0) 2 (0) 0
4 20
J
4 21
(c)J d / J 4 21
4 12 4 13
4 20
T sin t
(a)
Jd
(b)
Jd
1.2
4 19
4 20
4 21
51 52
53 54
55
56 57
5
m = 17 5 kg
k = 70.0 N/cm
c = 0.70 N s/cm
(a)
(b)
(c)
(d)
m = 1 kg,
k = 5 kN/m,
t=0
t < t1
t > t1 4 15
4 10
F0 4 12
F0 t t0
? 4 14
4 11 Duhamel
t0 ( 4 13) t0 /
Duhamel
4 12 4 16
4 13 t=0
4 14 5
4 15 f (t) = a t ( a = const )
Duhamel
4 17
4 18
4 19 4 19
3 12
3-10
[u]
u
3 13
3 13
[u]
u
3 14
3-14
J
= mR 2/4 R = L/4
3 15 41
3 11 Rayleigh 41
42 43
42 43
Dunker ley
3 13 2 16
m
k
y = A sin t
3 14 c
F 0 sin t
44
41
k = 3 kN/m
42 4
43 1s
gs
mg
sin
n
nt
( 1 cos 2k
n t)
t1
2
m k
arctan (
4k s ) mg
4 12 x F0 (1 cos nt)/ k 4 17 x F0 (1 cos nt)/ k
4 19
n km n km
1
sin t
kT
2
2(k J 2 ) 2 k 2 2(k J 2 )T
12
4 21 x1 x2
( a)
(b)
22
22
L
m
k
O
23
23
m
r
O
k
24 25
21
24 a
25
22
m
R
k
23 O
26 26
24 L2
1
25
27 28
27
28 )
(
m2 > m1
26
29
29
2 10
L
2 11
2 11
2 12
m
12
L O
27
L3 x
O nL
28 2
29
2 13
2 13
2 14 2 14 J0
2 15 2 16 2 16
(a)
0.01 m (b)
180 N (c)
900
0.01 kg m ( 2 ) 1200 rpm
59 59
2500 kN (a)
6
k = 800 kN/m
= 0.1
(b)
5 10
85
5 11
5 11
20 1600 rpm 2200 rpm
0.5 Hz
0.5 m
5 12 rpm
600 rpm 125 kN