清华大学物理试验A1阻尼振动与受迫振动试验报告

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；和固有角频率4intf-intf=252)(2)序号6K0)Y=1"序号6K0)¥=lnqD=yl+25-Y11294.859812404261104.700480366-0.15933203921284.852030264271094.691347882-0.16068238231274.844187086281084.682131227-0.16205585941274.84418708629108

2、4.682131227-0.16205585951254.828313737301074.672828834-0.15548490361254.828313737311064.663439094-0.16487464371244.820281566321064.663439094-0.15684247181234.812184355331044.644390899-0.16779345691224.804021045311034.634728988-0.169292057101214.795790546351034.634728988-0.161061557111214.79579054636

3、1024.624972813-0.170817732121204.787491743371024.624972813-0.162518929131194.779123493381014.615120517-0.164002976141184.770684624391004.605170186-0.165514438151174.762173935101004.605170186-0.157003749161184.77068462441994.59511985-0.175564774171174.76217393542984.584967479-0.177206456181164.753590

4、19143984.584967479-0.168622712191154.74493212844974.574710979-0.17022115201144.73619844815964.564348191-0.171850257211144.73619844846964.564348191-0.171850257221134.72738781947954.553876892-0.173510927231124.71849887148914.543294782-0.175204089241124.71849887119944.543294782-0.175204089251104.700480

5、36650934.532599493-0.167880873%1=1-4.166448636D-0.166657945于是得到:i_i1i1b=三口=¥£(¥+-丫)=¥£(111电1-111且)111=111=11255-x(ln+25-ln)=i=l-4.166448636252=-6.666317818x102.565475395x1()7由得到：b2(-6.666317818xlO"3)24T2+b2V4XTT2+(-6.666317818xl0-3)2=1.060976836X10-3aa、2471八j=(京)=2,h：x3

6、2ab(4/r+b)4/4乃-+(-6.666317818x10-3)-=4.08307401lxIO-5X2.565475395X10-4序号123451=10讣14,92614.93514,94414,95114,958从而可得4=(L061±0.04Dxl(y3。由上表，可得均值I；=1.49428s。心=1.49428x105+0.001=1.0149428xlOJs=2“1.49428xl-(l.O6xlO'3)：=4.204826965s-1.0149428x103V(1.494281.060976836x10-3八rx0.04x1O,1-(1.060976836

7、x10-3)-=6.792186217x10-角频率的不确定度为：=dJk=2.855996775xIO3«0.0029s-1g由此，角频率为：4=(4.2048±0.0029)sT2、测量其他2种阻尼的相关振动参数。（1）阻尼1I=int-=int=52jI2J序号伏。）y=ln4序号以。）¥=为4Dl=yi+5-yl11054.6539603506674.204692619-0.4492677312964.5643481917614.110873864-0.4534743273884.4773368148564.025351691-0.451985123480

8、4.3820266359503.912023005-0.4700036305734.29045944110463.828641396-0.461818045Ii-1-2.286548856D-0.457309771ii1i1b=-D=-y(yl+I-y1)=-y(hiI-ln)11i=l1i=l=3X£(In&5-Inq)=2286548856=_0091461954245i=i50.001700575«0.00174=¥z(DB)2/(f=1£(Di-5)2/(5-1)=由6=_2万（4-2_05得到：(-0.09146195424)-八，-=

9、0.014555080134XTT-+(-0.09146195424)-/大片224二吸量=7r1nX=xO.001700575Vdb(42+b2)4/十(-0.09146195424=2.705689144x107可得阻尼比：=(1.456±0.027)xlQ-2序号12345Tjs1.4981.4991.4981.4981.497序号678910Tjs1.4971.4961.4951.4931.493由上表，可得均值E=l.4964s=1.4964x1O-5+0.001=1.014964xlO3s=2/1.4964x1-(0.01455508013)_1(1.014964X103

10、YV1.4964)=6.782819534xIO-4=1.136816041xl0-3./7=(61.1±1.2)xlO-30.01455508013-一-x2.705689144xl041-(0.01455508013)角频率的不确定度为:=q=4.204826965x6.782819534xl04=2.848317766xl0'、0.0029sT%角频率为：(4.1993±0.0029)s-11Td=1.4964=1636090123-0.09146195424b2r=T=16.36090123x（1.014964xl03Y+0.0017005751.49640

11、.09146195424J=0.3043018822/.r=16.36±0.31242x0.01455508013=34.3522670834.35，（-2x0.014555080132X2.705689144X10-4=0.6385849839ao.7/.Q=34.4±0.7(2)阻尼2序号/。)序号次。)y=lnQD=x+5-x11635.0937502016884.477336814-0.61641338621444.9698133007784356708827-0.61310447331274.8441870868684.219507705-0.6246793814

12、1134.7273878199604.094344562-0.63304325651004.60517018610533.970291914-0.634878272IZRi=l-3.122118769D-0.624423754i_i1i1b=7D=7T£（X+i-y1）=7TS（lnI-ln）111=111=1=±X£（lnq.5-1n4）=3122?8769=-0.12488475085-i-i5-b=1=-jZ（DB）2/（5-l）=0.001938944=0.0020I5由b=_2/T（4r_i）«5得到：b2(-0.1248847508)2八八八

13、_-=1=0.01987210049+b2丫4xTT+(-0.1248847508)-"原纵)，=(4±3严冬=豆0.001938944442+(-0.1248847508)2一=3.084097451x1043.1x104这样，阻尼比为：=<1-98710.031)x10-序号12345Td/s1.5001.4991.4871.4901.498序号678910又51.4971.4971.4951.4941.492由上表可得：立=1.4949sX=1.4949X10-5+0.001=1.014949xl03s例=2介7)=21.4949x11(0.0198721004

14、9)2=4.2039108245_1(L014949X103V一W_1.4949-+=6.789687495x10“0.019872100491-(0.01987210049)2X3.084097451X104角频率不确定度为:“=4卞=4.203910824x6.789687495x104=2.854324075x103%0.0029s-1A角频率为：=(4.2039±0.0029)s'1-0.12488475081.4949=0.08354053836=0.08354053836xL014949xl(y31.4949-0.001938944Y-0.1248847508)=

15、1.298278828xlO-3.”=(83.54±L3)x10-3r=-=11.97023648Pb=11.97023648xIf1.014949xlO3M1.4949-(0.001938944)+1-0.1248847508=0.1860259091.r=11.97±0.19=25.16090336=25.162x0.01987210049q.Q=25.16±0.39Jf-rx3.084097451xl0-4l=0.3904905672=0.39琳2x0.019872100492)卜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i阻尼24(1.45

16、6±0.027)xlO2(1.987±0.031)x10-2COq/s-14.1993±0.00294.2039±0.00294/s-i(61.12±1.2)xl0-3(83.54±1.3)xlO-3r/s16.36±0.3111.97±0.19Q34.35±0.6425.16±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4=4288863691s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夕/。收/。6尸0/。2乃

17、，co=/sTCO%11.5145829.429.429.44.1500563460.96763540321.4997339.939.939.94.1915845950.97731821231.4888650050.050.04.2225707710.98454301141.4829759.559.459.454.2396661990.98852901551.47410670.170.070.054.2626765990.99389416561.46911080.480.480.44.2771853690.99727705971.46511290.190.190.14.2888636911.0

18、0000000081.46010999.899.999.854.303551581.00342465791.4551021103110.3110.34.3183404171.006872852101.44994120.21200120.14.3362217441.011042098111.44383129.3129.4129.354.3542517721.015246015121.44368140.2140.4140.343542517721.015246015131.41952150.01499149.954.4278966221.032417195阻尼2表2阻尼2受迫振动振幅和相位关系对应

19、表序号T/sO!Qg/。仍/。©/。/sTCO例11.5294630.430.230.34.1093429090.95814257721.5095740.040.240.14.1638073610.97084161731.4956750450.450.44.2027995370.97993311041.4877459659.559.554.2254104290.98520511151.4787970.370.470354.2511402620.99120433061.4728279.880.079.94.2684682790.99524456571.4668390.590.590.5

20、4.2859381360.99931787281.45981999100.11004.3065012391.00411240691.45376110.2110.1110.154.3242844511.008258775101.44671119.2119.1119.154.3452180551.013139696111.43662129.4129.4129.44.3754772331.020194986121.42452139.4139.4139.44.4123492331.028792135131.40540149.2149.1149.154.4720180121.042704626根据表1和

21、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/wO图1受迫振动幅频特性曲线160140054竺汽I#图2受迫振动相频特性曲线与前面相符。由图像得4=4.288863691s-】4.30sT卜.面逐点求实测相位差夕与由稣=arctan字:算值的相对偏差。州2阻尼1/7=0.06112132735=4.288863691s-1表3阻尼1误差与参数关系表序号©/。2万,CD=/ST1P(D%=arctan-E=%129.4441692-0.255502432239.94.19158459531,84448-0.252964407350.04.22257077142,45252-0.177786383459.454.23966619951,00687-0.165529271570.054.26267659966,74388-0.049534429680.44.27718536979,16857-0.015554531790.14.28886369190,00000-0.001111111899.854.303551580103.49020.035174345911034.3183404171