清华大学物理实验A1阻尼振动与受迫振动实验报告.docx
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清华大学物理实验A1阻尼振动与受迫振动实验报告
清华大学
阻尼振动与受迫振动实验
物理实验简要报告
班级姓名学号
结稿日期:
阻尼振动与受迫振动实验报告(简要报告)
、阻尼振动实验数据记录及处理
1、测量最小阻尼(阻尼0)时的阻尼比■和固有角频率-.0
序号
yi=inq
序号
日㈠
%=1n®
Di=yi425-yi
1
129
4.859812404
26
110
4.700480366
-0.159332039
2
128
4.852030264
27
109
4.691347882
-0.160682382
3
127
4.844187086
28
108
4.682131227
-0.162055859
4
127
4.844187086
29
108
4.682131227
-0.162055859
5
125
4.828313737
30
107
4.672828834
-0.155484903
6
125
4.828313737
31
106
4.663439094
-0.164874643
7
124
4.820281566
32
106
4.663439094
-0.156842471
8
123
4.812184355
33
104
4.644390899
-0.167793456
9
122
4.804021045
34
103
4.634728988
-0.169292057
10
121
4.795790546
35
103
4.634728988
-0.161061557
11
121
4.795790546
36
102
4.624972813
-0.170817732
12
120
4.787491743
37
102
4.624972813
-0.162518929
13
119
4.779123493
38
101
4.615120517
-0.164002976
14
118
4.770684624
39
100
4.605170186
-0.165514438
15
117
4.762173935
40
100
4.605170186
-0.157003749
16
118
4.770684624
41
99
4.59511985
-0.175564774
17
117
4.762173935
42
98
4.584967479
-0.177206456
18
116
4.753590191
43
98
4.584967479
-0.168622712
19
115
4.744932128
44
97
4.574710979
-0.17022115
20
114
4.736198448
45
96
4.564348191
-0.171850257
21
114
4.736198448
46
96
4.564348191
-0.171850257
22
113
4.727387819
47
95
4.553876892
-0.173510927
23
112
4.718498871
48
94
4.543294782
-0.175204089
24
112
4.718498871
49
94
4.543294782
-0.175204089
25
110
4.700480366
50
93
4.532599493
-0.167880873
I
工Di
iA
-4.166448636
D
-0.166657945
于是得到:
1—1I1
bD厂(yiI一yj(ln弓I—ln弓)
IIiAIi=1
252
丄a(In325一1n弓)二-4"166448636=_6.66631781810°
入+屆(Di—D)2/(I—1)=25返
—2-4
(Dj-D)/(25-1)=2.56547539510
25i总
严二-0.5
由b=—2二-1得至y:
b2
(-6.66631781810冷2
4冗2b2
4n2(-6.66631781810冷2
=1.06097683610°
d,)2
db
(“2心3/2亠
(4'b)
弟2.56547539510*
■232
4-(-6.66631781810)
=4.08307401110^
从而可得'(1.061_0.041)10-3。
序号
1
2
3
4
5
T=10Td/s
14.926
14.935
14.944
14.951
14.958
由上表,可得均值Td=1.49428s。
1.49428X10-5+0.001=1.014942810-3s
•‘0二2心..讥•1…
=2~
.49428,1-1.0610_32
=4.204826965s'
■:
0
'2
+
1.0149428心0_3f
1.49428
佃097683610‘20.0410_3
1-1.06097683610"
_4
=6.79218621710
也31
角频率的不确定度为:
〉..0一二2.85599677510_-0.0029s
0-0
由此,角频率为:
「0二4.2048-0.0029s
2、测量其他2种阻尼的相关振动参数。
(1)阻尼1
I二intint5
(2丿12丿
序号
引=1nq
序号
8Q
W=1nq
Di=-yi
1
105
4.653960350
6
67
4.20469261
9
-0.449267731
2
96
4.564348191
7
61
4.11087386
4
-0.453474327
3
88
4.477336814
8
56
4.02535169
1
-0.451985123
4
80
4.382026635
9
50
3.91202300
5
-0.470003630
5
73
4.290459441
10
46
3.82864139
6
-0.461818045
I
ZDi
i4
-2.286548856
D
-0.457309771
[一[1
bDQ(%I—yjQ(ln如一In可)
IIiz!
Iid
1J“「、-2.286548856cc“一「
2二(In耳5-In^J2.0914*******
5i5
•:
bn1、'(Dj-D)2/(l-1)」「(Dj-D)2/(5-1)=0.001700575:
0.0017
.2-0.5
由b--2二-1得到:
I丫5耳
0.01455508013
.0914*******了
2232
4b2
4■:
4n2(-0.09146195424)2
T422320.001700575
4兀2+(—0.09146195424升
=2.70568914410°
可得阻尼比:
'(1.456-0.027)10-2
序号
1
2
3
4
5
Td/s
1.498
1.499
1.498
1.498
1.497
序号
6
7
8
9
10
Td/s
1.497
1.496
1.495
1.493
1.493
由上表,可得均值Td二1.4964s
-5-3
Td=1.496410+0.001=1.01496410s
d
=4.199312323s
*1.014964"0-3
1.4964
J'0.01455508013
(1-(0.01455508013f
、2
x2.705689144"0-4
■4
=6.78281953410
角频率的不确定度为
=4.2048269656.78281953410-4=2.84831776610-^0.0029sJ
0'0
角频率为:
p二4.1993-0.0029s'
.0914*******
0.06112132735
Td
1.4964
=0.06112132735
『1.014964"0-3辽
1.4964~」
2
+F0.001700575.0914*******
=1.13681604110”
-=61.1—1.210^
1
Td
~b
1.4964
.0914*******
=16.36090123
=16.36090123
'‘1.01496400
-3€
1.4964
2
0.001700575
.0914*******
=0.3043018822
.=16.36_0.31
Q1134.35226708:
34.35
220.01455508013
1
20.014555080132
2.70568914410~
=0.6385849839:
0.7
.Q=34.4_0.7
(2)阻尼2
序号
()
W=Ind
序号
yi=lnd
Di=y^—y
1
163
5.093750201
6
88
4.47733681
4
-0.616413386
2
144
4.969813300
7
78
4.35670882
7
-0.613104473
3
127
4.844187086
8
68
4.21950770
5
-0.624679381
4
113
4.727387819
9
60
4.09434456
2
-0.633043256
5
100
4.605170186
10
53
3.97029191
-0.634878272
1一11
b=「D=^送(y_—yj=市送(lnq卡一InQ)
IIi4Ii4
=\'(In哥§-In弓)=-3.1221218769=_o.i2488475O8
5i45
二1「(Di-D)2/(I-1)=
5,(
—2
Dj-D)/(5-1)=0.001938944:
0.0020
(-0.1248847508『
~22
4n2(-0.1248847508)
2
4二
2_2\3/2
(4b)
4二2(-0.1248847508)2
0.001938944
“2丄5
由b=-2慕汁-1得到:
-0.01987210049
■4・4
=3.084097451103.110
这样,阻尼比为:
'(1.987-0.031)10-2
序号
1
2
3
4
5
T/s
1.500
1.499
1.487
1.490
1.498
序号
6
7
8
9
10
Td/s
1.497
1.497
1.495
1.494
1.492
由上表可得:
T;=1.4949s
_5_3
飞T494910+0.001=1.01494910s
1.4949
1-0.01987210049
=4.203910824s」
■':
-0
彳014949><10
-3%2
1.4949
l,Z0.01987210049
0.019872100492
-4
肚3.08409745仆10
■4
=6.78968749510
角频率不确定度为
也閒=肌经=4.203910824<6.789687495x10-4=2.85432407510-30.0029s,
■-0
-0.1248847508
1.4949
角频率为:
0二4.2039—0.0029s'
.0835*******
二.0835*******
二(0.001938944]2
丿1-0.1248847508丿
3
1.01494910-
1.4949
=1.29827882810”
,•”P=(83.54±1.3門0‘
1
Td
b
=11.97023648
「-3\2严*2
=11.97023648
j1.014949^10丄i0.001938944■
1.4949丿1-0.1248847508.丿
-0.1860259091
=11.97—0.19
Q=—125.16090336:
25.16
220.01987210049
.Q=25.16_0.39
1
20.019872100492
-4
3.084097451104
=0.3904905672:
0.39
F面将两个阻尼的部分振动参数的计算结果整理在表格中
名称
阻尼1
阻尼2
U-
:
(1.456±0.027)10-2
(1.987±0.031)10-2
/-1现/s
4.1993±0.0029
4.2039±0.0029
P/sA
(61.12±1.2产10」
(83.54±1.3尸10」
T/S
16.36±0.31
11.9^0.19
Q
34.35±0.64
25.16±0.39
、受迫振动实验数据记录及处理测定受迫振动的幅频特性和相频特性曲线
由于实验中途更换仪器,现直接给出实验二的"4.288863691s
①阻尼1
表1阻尼1受迫振动振幅和相位关系对应表
序
号
T/s
e/°
%/°
2,国二—/s
T
⑷0
1
1.514
58
29.4
29.4
29.4
4.150056346
0.967635403
2
1.499
73
39.9
39.9
39.9
4.191584595
0.977318212
3
1.488
86
50.0
50.0
50.0
4.222570771
0.984543011
4
1.482
97
59.5
59.4
59.45
4.239666199
0.988529015
5
1.474
106
70.1
70.0
70.05
4.262676599
0.993894165
6
1.469
110
80.4
80.4
80.4
4.277185369
0.997277059
7
1.465
112
90.1
90.1
90.1
4.288863691
1.000000000
8
1.460
109
99.8
99.9
99.85
4.30355158
1.003424657
9
1.455
102
110.3
110.3
110.3
4.318340417
1.006872852
10
1.449
94
120.2
120.0
120.1
4.336221744
1.011042098
11
1.443
83
129.3
129.4
129.35
4.354251772
1.015246015
12
1.443
68
140.2
140.4
140.3
4.354251772
1.015246015
13
1.419
52
150.0
149.9
149.95
4.427896622
1.032417195
②阻尼2
表2阻尼2受迫振动振幅和相位关系对应表
序号
T/s
6/°
半2八
2兀/
国二——/s
T
1
1.529
46
30.4
30.2
30.3
4.109342909
0.958142577
2
1.509
57
40.0
40.2
40.1
4.163807361
0.970841617
3
1.495
67
50.4
50.4
50.4
4.202799537
0.979933110
4
1.487
74
59.6
59.5
59.55
4.225410429
0.985205111
5
1.478
79
70.3
70.4
70.35
4.251140262
0.991204330
6
1.472
82
79.8
80.0
79.9
4.268468279
0.995244565
7
1.466
83
90.5
90.5
90.5
4.285938136
0.999317872
8
1.459
81
99.9
100.1
100
4.306501239
1.004112406
9
1.453
76
110.2
110.1
110.15
4.324284451
1.008258775
10
1.446
71
119.2
119.1
119.15
4.345218055
1.013139696
11
1.436
62
129.4
129.4
129.4
4.375477233
1.020194986
12
1.424
52
139.4
139.4
139.4
4.412349233
1.028792135
13
1.405
40
149.2
149.1
149.15
4.472018012
1.042704626
根据表1和表2的数据,借助MATLAB计算机仿真,得到受迫振动的幅频特性曲线如
图1所示。
同时,受迫振动的相频特性曲线如图2所示。
120
(0.9993,83)
1.05
1
w/w0
图1受迫振动幅频特性曲线
5
9002
ooooooO
6420864T—
、芦位相
97
O
6
£
0.980.9911.011.021.031.041.05
w/w0
图2受迫振动相频特性曲线
11
由图像得,o=4.288863691s—4.30s-
下面逐点求实测相位差
-与由「0=arctan2算值的相对偏差。
o0-O
与前面相符。
①阻尼1匕=0.061121327354.288863691sJ
表3阻尼1误差与参数关系表
序号
卩/°
2兀蛍=——/s
T
2?
©
申0=arctan2
q>_币
E=0
1
29.4
4.150056346
23.41692
-0.255502432
2
39.9
4.191584595
31.84448
-0.252964407
3
50.0
4.222570771
42.45252
-0.177786383
4
59.45
4.239666199
51.00687
-0.165529271
5
70.05
4.262676599
66.74388
-0.049534429
6
80.4
4.277185369
79.16857
-0.015554531
7
90.1
4.288863691
90.00000
-0.001111111
8
99.85
4.303551580
103.4902
0.035174345
9
110.3
4.318340417
115.6699
0.046424351
10
120.1
4.336221744
127.6175
0.058906498
11
129.35
4.354251772
136.7162
0.053879496
12
140.3
4.354251772
136.7162
-0.026213426
13
149.95
4.427896622
155.9330
0.038369043
②阻尼2=0.08354053836矶=4.288863691s」
表四阻尼2误差与参数关系表
序号
0/。
2兀
«=/sT
%=arctan严①2
o0一蛍
(p币
E=0%
1
30.3
4.109342909
24.48479
-0.237502956
2
40.1
4.163807361
33.35051
-0.202380413
3
50.4
4.202799537
43.85588
-0.149218759
4
59.55
4.225410429
52.57484
-0.132671065
5
70.35
4.251140262
65.60277
-0.072363255
6
79.9
4.268468279
76.24877
-0.047885756
7
90.5
4.285938136
87.99366
-0.028483188
8
100
4.306501239
101.8978
0.018624543
9
110.15
4.324284451
112.8923
0.024291294
10
119.15
4.345218055
123.83
0.037793749
11
129.4
4.375477233
135.7498
0.04677576
12
139.4
4.412349233
145.5451
0.042221277
13
149.15
4.472018012
155.0306
0.037931866
附:
原始数据记录表格