清华大学物理实验A1阻尼振动与受迫振动实验报告

1、 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）一、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J和固有角频率0I二int-=int(50=2512丿I2丿序号（。）y=In0ii序号0（。）y=In0iiD=y-yii+25i11294.859812404261104.700480366-0.15933203921284.852030264271094.691347882-0.16068238231274.844187086281084.682131227-0.16205585941274.844187086291

2、084.682131227-0.16205585951254.828313737301074.672828834-0.15548490361254.828313737311064.663439094-0.16487464371244.820281566321064.663439094-0.15684247181234.812184355331044.644390899-0.16779345691224.804021045341034.634728988-0.169292057101214.795790546351034.634728988-0.161061557111214.795790546

3、361024.624972813-0.170817732121204.787491743371024.624972813-0.162518929131194.779123493381014.615120517-0.164002976141184.770684624391004.605170186-0.165514438151174.762173935401004.605170186-0.157003749161184.77068462441994.59511985-0.175564774171174.76217393542984.584967479-0.177206456181164.7535

4、9019143984.584967479-0.168622712191154.74493212844974.574710979-0.17022115201144.73619844845964.564348191-0.171850257211144.73619844846964.564348191-0.171850257221134.72738781947954.553876892-0.173510927231124.71849887148944.543294782-0.175204089241124.71849887149944.543294782-0.175204089251104.7004

5、8036650934.532599493-0.167880873Dii=1-4.166448636D-0.166657945于是得到：b=D=工(y-y)=工(In0-In0)TOC o 1-5 h zI12i+1i12i+1ii=1i=11吝-4.166448636=x乙(In0-In0)=-6.666317818x10-3252i+25/252i=1A=1.E(D-D)2/(I-1)=丄E(D-D)2/(25-1)=2.565475395x10-4bIi25i由b=-2兀t-210.5得到：=1.060976836x10-3(-6.666317818x10-3)24xn2+(-6.6663

6、17818x10-3)2A=(dba)2db4兀2,A(4兀2+b2)3/2bx2.565475395x10-44兀2+(-6.666317818x10-3)23/2=4.083074011x10-5从而可得:=(1.061土0.041)x10-3。序号12345T=10F/sid14.92614.93514.94414.95114.958由上表可得均值Td=1.4942&。=1.49428x10-5+0.001=1.0149428x10-3sTd1.49428x0J1-G.06x10-3=4.204826965s-1P-a1.0149428x10-3)1.49428丿U-匚1.0609768

7、36x10-3八“x0.04x10-3.060976836x10-3丿=6.792186217x10-4匚丿A角频率的不确定度为：A二气二2.855996775x10-3=0.0029s-1%00由此，角频率为：=（4.2048土0.0029）s-102、测量其他2种阻尼的相关振动参数。1）阻尼1.(n)I=mt12丿(10)=intI2丿序号9（。）y=ln9ii序号9（。）y=ln9iiD=yyii+5i11054.6539603506674.204692619-0.4492677312964.5643481917614.110873864-0.4534743273884.47733681

8、48564.025351691-0.4519851234804.3820266359503.912023005-0.4700036305734.29045944110463.828641396-0.461818045Dii=1-2.286548856D-0.457309771b=D=工(y-y)=丄工(ln9-ln9)TOC o 1-5 h zI12i+1i12i+1ii=1i=11丫-2.286548856=x乙(ln9ln9)=-0.0914619542452i+5i52i=1A=1J工(DD)2/(I1)=5J工(DD)2/(51)=0.001700575沁0.0017由b=-2兀得到：

9、4xn2lZ49195424424)2=O014555080130=4兀2(4k2+b2b4k24k2+(-0.09146195424匕32x0.001700575=2.705689144x10-4可得阻尼比：0=(1.456土0.027)x10-2序号12345T/sd1.4981.4991.4981.4981.497序号678910T/sd1.4971.4961.4951.4931.493由上表可得均值Td=l4964sA=1.4964x10-5+0.001=1.0149640.5得到：4财和囂囂二=-19872100494兀2A(4兀2+b2)3/2bX0.0019389444兀2+(-

10、0.1248847508)23/2=3.084097451X10-4沁3.1x10-4这样，阻尼比为：:=(1.987土0.031)x10-2序号12345T/sd1.5001.4991.4871.4901.498序号678910T/sd1.4971.4971.4951.4941.492由上表可得：Td=1.4949sA=1.4949x10-5+0.001=1.014949x10-3s0Td=2兀/1.4949x：1-(0.01987210049匕=4.203910824s-1Am0m0Td丿P-au-匚2匚丿1.014949X10-3)(0.019872100491.4949丿、7X3.08

11、4097451x10-4(1-(0.01987210049=6.789687495X10-4角频率不确定度为：AA=mf=4.203910824x6.789687495x10-4=2.854324075x10-30.0029s-1m00m0角频率为：m=(4.2039+0.0029)s-100.12488475081.4949=0.08354053836dAP卩=0.08354053836x1.014949x10-31.4949(0.001938944)2+(0.1248847508丿=1.298278828x10-3.卩=(83.54土1.3)x103t=1=Td=11.97023648卩b

12、=0.186025909111Q=:2=25.16090336沁25.162x0.01987210049T=11.97土0.19AQ1x3.084097451x10-4十2x0.019872100492丿Q=25.16土0.39=0.3904905672沁0.39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(1.456土0.027)x10-2(1.987土0.031)x10-2o/s104.1993土0.00294.2039土0.00290/s-1(61.12土1.2)xl03(83.54土1.3)xl03T/s16.36土0.3111.97土0.19Q34.35土0.6

13、425.16土0.39二、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o二4.288863691sj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/s0/。申/。19/29/2兀,=/sT011.5145829.429.429.44.1500563460.96763540321.4997339.939.939.94.1915845950.97731821231.4888650.050.050.04.2225707710.98454301141.4829759.559.459.454.2396661990.98852901551.47

14、410670.170.070.054.2626765990.99389416561.46911080.480.480.44.2771853690.99727705971.46511290.190.190.14.2888636911.00000000081.46010999.899.999.854.303551581.00342465791.455102110.3110.3110.34.3183404171.006872852101.44994120.2120.0120.14.3362217441.011042098111.44383129.3129.4129.354.3542517721.01

15、5246015121.44368140.2140.4140.34.3542517721.015246015131.41952150.0149.9149.954.4278966221.032417195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/s0/9/19/29/2兀,=/sT011.5294630.430.230.34.1093429090.95814257721.5095740.040.240.14.1638073610.97084161731.4956750.450.450.44.2027995370.97993311041.4877459.659.559.554.225410

16、4290.98520511151.4787970.370.470.354.2511402620.99120433061.4728279.880.079.94.2684682790.99524456571.4668390.590.590.54.2859381360.99931787281.4598199.9100.11004.3065012391.00411240691.45376110.2110.1110.154.3242844511.008258775101.44671119.2119.1119.154.3452180551.013139696111.43662129.4129.4129.4

17、4.3754772331.020194986121.42452139.4139.4139.44.4123492331.028792135131.40540149.2149.1149.154.4720180121.042704626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。w/w0图1受迫振动幅频特性曲线度/位相0.950.960.970.980.9911.011.021.031.041.05w/w00800图2受迫振动相频特性曲线由图像得O0二4.288863691s-1-4.30s-1，与前面相符。2阳下面

18、逐点求实测相位差与由9二arctan算值的相对偏差。02一20阻尼10二0.06112132735=4.288863691s-1,0表3阻尼1误差与参数关系表序号9/2兀/3=/sT2039二arctan032-320厂9-990129.4441692-0.255502432239.94.19158459531.84448-0.252964407350.04.22257077142.45252-0.177786383459.454.23966619951.00687-0.165529271570.054.26267659966.74388-0.049534429680.44.27718536979.16857-0.015554531790.14.28886369190.00000-0.001111111899.854.303551580103.49020.0351743459110.34.318340417115.66990.04642435110120.14.336221744127.61750.05890649811129.354.354251772136.71620.05387949612140.34.3542517721