阻尼振动和受迫振动实验报告

1、阻尼振动和受迫振动实验报告工程物理系 郑吉家 2014011785一、实验目的  1.观测阻尼振动，学习测量振动系统基本参数的方法； 2.研究受迫振动的幅频特性和相频特性，观察共振现象；  3.观测不同阻尼对受迫振动的影响。二、实验原理1.有粘滞阻尼的阻尼振动弹簧和摆轮组成一振动系统，设摆轮转动惯量为J，粘滞阻尼的阻尼力矩大小定义为角速度d/dt与阻尼力矩系数的乘积，弹簧劲度系数为k，弹簧的反抗力矩为-k。忽略弹簧的等效转动惯量，可得转角的运动方程为记0为无阻尼时自由振动的固有角频率，其值为0=，定义阻尼系数=/（2J），则上式可以化为：小阻尼即时，阻尼振动运动方程的解为

2、（*）由上式可知，阻尼振动角频率为，阻尼振动周期为2.周期外力矩作用下受迫振动的解在周期外力矩Mcost激励下的运动方程和方程的通解分别为这可以看作是状态（*）式的阻尼振动和频率同激励源频率的简谐振动的叠加。一般t>>后，就有稳态解稳态解的振幅和相位差分别为其中，的取值范围为（0，），反映摆轮振动总是滞后于激励源支座的振动。3.电机运动时的受迫振动运动方程和解弹簧支座的偏转角的一阶近似式可以写成式中m是摇杆摆幅。由于弹簧的支座在运动，运动支座是激励源。弹簧总转角为。于是在固定坐标系中摆轮转角的运动方程为也可以写成于是得到由m的极大值条件可知，当外激励角频率时，系统发生共振，m有极大

3、值。引入参数，称为阻尼比。于是，我们得到3、 实验仪器 波尔共振仪四、实验步骤1.打开电源开关，关断电机和闪光灯开关，阻尼开关置于“0”档，光电门H、I可以手动微调，避免和摆轮或者相位差盘接触。手动调整电机偏心轮使有机玻璃转盘F上的0位标志线指示0度，亦即通过连杆E和摇杆M使摆轮处于平衡位置。染货拨动摆轮使偏离平衡位置150至200度，松开手后，检查摆轮的自由摆动情况。正常情况下，震动衰减应该很慢。2.开关置于“摆轮”，拨动摆轮使偏离平衡位置150至200度后摆动，由大到小依次读取显示窗中的振幅值j；周期选择置于“10”位置，按复位钮启动周期测量，体制时读取数据。并立即再次启动周期测量，记录每

4、次过程中的的值。（1）逐差法计算阻尼比；（2）用阻尼比和振动周期Td计算固有角频率0。3.依照上法测量阻尼（2、3、4）三种阻尼状态的振幅。求出、Q。4.开启电机开关，置于“强迫力”，周期选择置于“1”，调节强迫激励周期旋钮以改变电机运动角频率，选择2个或3个不同阻尼比（和任务3中一致），测定幅频和相频特性曲线，注意阻尼比较小（“0”和“1”档）时，共振点附近不要测量，以免振幅过大损伤弹簧；每次调节电机状态后，摆轮要经过多次摆动后振幅和周期才能稳定，这时再记录数据。要求每条曲线至少有12个数据点，其中要包括共振点，即=/2的点。五、实验结果1. 测量最小阻尼时的阻尼比和固有角频率0。序号振幅/

5、°振幅对数11294.85981240421294.85981240431274.84418708641264.83628190751254.82831373761244.82028156671234.81218435581224.80402104591214.795790546101204.787491743111194.779123493121184.770684624131174.762173935141154.744932128151154.744932128161134.727387819171134.727387819181114.709530201191114.7095

6、30201201094.691347882211074.672828834221074.672828834231054.65396035241054.65396035251044.644390899序号 振幅/°振幅对数261034.634728988271024.624972813281014.615120517291004.60517018630994.5951198531994.5951198532984.58496747933984.58496747934984.58496747935964.56434819136964.56434819137954.553876892389

7、44.54329478239934.53259949340924.52178857741924.52178857742904.4998096743904.4998096744894.4886363745884.47733681446874.46590811947864.45434729648864.45434729649844.43081679950844.430816799b-0.008791567Sb6.49507E-05由得到：=序号12345/s15.37815.39115.40415.41515.423 2、测量其他2种或3种阻尼状态的振幅，求出、Q。阻尼2 序号振幅/°振

8、幅对数11264.83628190721154.74493212831054.653960354964.5643481915894.488636376814.3944491557744.3040650938684.2195077059624.12713438510564.02535169111523.95124371912483.87120101113443.78418963414403.68887945415363.583518938b-0.088408581Sb0.000435295=0.01406927 序号12345/s1.5421.5421.5431.5431.545序号678910

9、/s1.5431.5441.5441.5431.544阻尼5序号振幅/°振幅对数11124.7184988712904.499809673714.2626798774564.0253516915443.7841896346363.5835189387283.332204518223.0910424539172.83321334410132.56494935711102.3025850931282.079441542b-0.241189557Sb0.002101376序号12345/s0.5410.5420.5440.5450.543序号678910/s0.5430.5420.5460

10、.5470.5463、 测定受迫振动的幅频特性和相频特性曲线第一次实验数据阻尼2mT相对误差理论值比值701391.544 4.069 87.410 19.9 87.410447970.997406977751421.542 4.075 88.703 15.4 88.70255040.998700631791441.540 4.080 89.998 12.2 89.997650650.999997645841461.538 4.085 -88.706 8.0 91.29443271.001298032871481.536 4.091 -87.408 6.0 92.591579441.00260

11、1805911491.534 4.096 -86.112 3.1 93.887762381.003908978901501.535 4.093 -86.760 3.5 93.239874091.0032549661001481.530 4.107 -83.528 3.7 96.471972571.0065335771171461.528 4.112 -82.243 19.7 97.75741041.007851029148741.510 4.161 -71.085 35.9 108.91476151.019865147135961.516 4.145 -74.700 28.2 105.3003

12、4011.015828742511211.515 4.147 -74.089 51.8 105.91130971.016499256阻尼5mT相对误差理论值比值91 58 1.544 4.069 89.664 1.5 89.664473540.997406977100 57 1.535 4.093 -89.580 10.6 90.419947671.003254966110 54 1.525 4.120 -88.736 20.5 91.264412571.00983368781 58 1.555 4.041 88.747 8.7 88.747234530.99035136575 57 1.56

13、0 4.028 88.333 15.1 88.332615270.98717716267 56 1.570 4.002 87.508 23.4 87.507855490.98088940987 58 1.550 4.054 89.163 2.4 89.163308010.99354604760 50 1.580 3.977 86.689 30.8 86.689253430.97468124873 54 1.565 4.015 87.919 17.0 87.919479430.984023241105 54 1.530 4.107 -89.158 15.6 90.841531431.006533

14、577104 56 1.540 4.080 90.000 61.5 269.99969710.99999764592 56 1.546 4.064 89.497 2.8 89.497193730.99611667补做实验数据阻尼2阻尼2mT相对误差理论值比值7241.711 3.672 11.780 40.6 11.779932710.90005632517451.621 3.876 23.218 26.8 23.217881150.95002860722581.600 3.927 29.917 26.5 29.917026860.96249773327691.587 3.959 36.190

15、 25.4 36.190262450.97038208732901.571 3.999 47.821 33.1 47.821108770.980265037531191.555 4.041 66.216 20.0 66.216397590.990351365761451.540 4.080 89.994 15.5 89.993867010.999997645901481.536 4.091 -83.264 7.0 96.736019911.0026018051181311.525 4.120 -66.020 3.5 113.97994731.009833687149781.509 4.164

16、-47.253 12.2 132.74675691.020541002157581.495 4.203 -36.567 9.5 143.43253991.030097908165381.467 4.283 -24.364 6.0 155.63591391.049758945170201.400 4.488 -12.979 1.8 167.02101421.099997409阻尼5阻尼5mT相对误差理论值比值21 20 1.708 3.679 29.631 29.1 29.630980730.9016372239 36 1.621 3.876 49.001 20.4 49.001262130.9

17、5002860745 42 1.600 3.927 57.056 21.1 57.056163920.96249773354 46 1.587 3.959 62.994 14.3 62.993904050.97038208766 54 1.571 3.999 71.332 7.5 71.332053390.98026503780 57 1.555 4.041 80.668 0.8 80.667833520.99035136590 58 1.546 4.064 86.227 4.4 86.226954820.9961166796 56 1.540 4.080 89.998 6.7 89.997714080.999997645110 54 1.525 4.120 -80.583 10.6 99.417408891.009833687123 46 1.509 4.164 -70.984 12.8 109.01645181.020541002132 42 1.495 4.203 -63.312 13.1 116.68782281.030097908144 32 1.467 4.283 -50.533 11.2 129.46749031.049758945157 18 1.400 4.488 -31.721 5.9 148.27935051.