1、华中科技大学物理实验音叉的受迫振动与共振华中科技大学物理实验_音叉的受迫振动与共振华中科技大学 音叉的受迫振动与共振 【实验目的】 1.研究音叉振动系统在驱动力作用下振幅与驱动力频率的关系,测量并绘制它们的关系曲线,求出共振频率和振动系统振动的锐度。 2.通过对音叉双臂振动与对称双臂质量关系的测量,研究音叉共振频率与附在音叉双臂一定位置上相同物块质量的关系。 3.通过测量共振频率的方法,测量附在音叉上的一对物块的未知质量。 4.在音叉增加阻尼力情况下,测量音叉共振频率及锐度,并与阻尼力小情况进行对比。 【实验仪器】 FD-VR-A型受迫振动与共振实验仪(包括主机和音叉振动装置)、加载质量块(成
2、对)、阻尼片、电子天平(共用)、示波器(选做用) 【实验装置及实验原理】 一(实验装置及工作简述 FD-VR-A型受迫振动与共振实验仪主要由电磁激振驱动线圈、音叉、电磁线圈传感器、支座、低频信号发生器、交流数字电压表(0,1.999V)等部件组成(图1所示) 1.低频信号输出接口2.输出幅度调节钮3.频率调节钮4.频率微调钮5.电压输入接口6.电源开关7.信号发生器频率显示窗8.数字电压表显示窗9.电压输出接口10.示波器接口Y11.示波器接口X12.低频信号输入接口13.电磁激振驱动线圈14.电磁探测线圈传感器15.质量块16.音叉17.底座18.支架19. 固定螺丝 图1 FD-VR-A型
3、受迫振动与共振实验仪装置图 在音叉的两双臂外侧两端对称地放置两个激振线圈,其中一端激振线圈在由低频信号发生器供给的正弦交变电流作用下产生交变磁场激振音叉,使之产生正弦振动。当线圈中的电流最大时,吸力最大;电流为零时磁场消失,吸力为零,音叉被释放,因此音叉产生的振动频率与激振线圈中的电流有关。频率越高,磁场交变越快,音叉振动的频率越大;反之则小。另一端线圈因为变化的磁场产生感应电流,输出到交流数字电压表中。因为I=dB/dt,而dB/dt取决于音叉振动v中的速度,速度越快,磁场变化越快,产生电流越大,电压表显示的数值越大,即电压值和速度振幅成正比,因此可用电压表的示数代替速度振幅。由此可知,将探
4、测线圈产生的电信号输入交流数字电压表,可研究音叉受迫振动系统在周期外力作用下振幅与驱动力频率的关系及其锐度,以及在增加音叉阻尼力的情况下,振幅与驱动力频率的关系及其锐度。 seal tape stuffing, white lead, after connecting to remove excess filler; 6, pipe installation to ensure that the reserved tee height 500 mm the construction is completed, and to ensure that water meter straight; r
5、isers vertical deviation, not more than 2 mm per metre, not more than ? 10 mm long; 7, after installation is complete, 1.0MPA water pressure test for strength and 0.6MPA hydraulic tightness Drainage installation drainage system using triage system in the interior design, into the sewage system, wate
6、r system parts, riser by bonding of UPVC drainage pipe construction, transfer floor cast iron drainage pipes by centrifugal casting, clasp connection of buried pipeline using centrifugal casting iron pipe, socket socket connections, sealing of cement mortar. Diameter of DN100DN150. Embedded stage of
7、 construction stage is divided into structural and piping installed. 1, submersible pumps installation: systems use submersible pumps of product certification and quality control technical documents. Submersible pump installation shall meet the following requirements: 1.1 location, elevation, the de
8、sign requirements; 1.2 equipment integrity, damage and corrosion, pipe protection intact; turning flexible and no clean sound; 1.3-drive steering confirmation, direction compatible with the pump. Leveling should be based on the level of the pump cover, shaft protruding parts, base level work surface
9、 as the basis for measurement, longitudinal and transverse level deviation should not exceed 0.1%. 1.4 after the driving shaft and the driven shaft 二(实验原理 1.简谐振动与阻尼振动 许多振动系统如弹簧振子的振动、单摆的振动、扭摆的振动等,在振幅较小而且在空气阻尼可以忽视的情况下,都可作简谐振动处理。即此类振动满足 简谐振动方程 2dx2 (1) ,,x,002dt(1)式的解为 (2) x,Acos(,t,,)0K对弹簧振子振动圆频率,K为弹簧
10、劲度系数,为振子的质量,为弹簧,mm00m,m0的等效质量。弹簧振子的周期T满足 24,2T,(m,m) (3) 0K但实际的振动系统存在各种阻尼因素,因此(1)式左边须增加阻尼项。在小阻尼情况下,dx2,阻尼与速度成正比,表示为,则相应的阻尼振动方程为 dt2dxdx2,2,,,x,0 (4) 02dtdt式中为阻尼系数。 ,2.受迫振动与共振 阻尼振动的振幅随时间会衰减,最后会停止振动。为了使振动持续下去,外界必须给系统一个周期变化的驱动力。一般采用的是随时间作正弦函数或余弦函数变化的驱动力,在驱动力作用下,振动系统的运动满足下列方程 2dxdxF2,2,,,x,cos,t (5) 02d
11、tmdt(5)式中,m=m+m为振动系统的质量,F为驱动力的振幅,,为驱动力的圆频率。 0公式(5)为振动系统作受迫振动的方程,它的解包括两项,第一项为瞬态振动,由于阻尼存在,振动开始后振幅不断衰减,最后较快地为零;而后一项为稳态振动的解,其为 x,Acos(,t,,) FmA,式中 。 22222,,,4,022,2,00当驱动力的圆频率 时,振幅A出现极大值,此时称为共振。显然,越小,x,关系曲线的极值越大。描述这种曲线陡峭程度的物理量称为锐度,其值等于品质因素 2urement, longitudinal and transverse level deviation should not
12、 exceed 0.1%. 1.4 after the driving shaft and the driven shaftft protruding parts, base level work surface as the basis for measdrive steering confirmation, direction compatible with the pump. Leveling should be based on the level of the pump cover, sha-pipe protection intact; turning flexible and n
13、o clean sound; 1.3ion, meet the following requirements: 1.1 location, elevation, the design requirements; 1.2 equipment integrity, damage and corros s use submersible pumps of product certification and quality control technical documents. Submersible pump installation shallsystem50. Embedded stage o
14、f construction stage is divided into structural and piping installed. 1, submersible pumps installation: ried pipeline using centrifugal casting iron pipe, socket socket connections, sealing of cement mortar. Diameter of DN100DN1of bubonding of UPVC drainage pipe construction, transfer floor cast ir
15、on drainage pipes by centrifugal casting, clasp connection installation drainage system using triage system in the interior design, into the sewage system, water system parts, riser byage ? 10 mm long; 7, after installation is complete, 1.0MPA water pressure test for strength and 0.6MPA hydraulic ti
16、ghtness Drain is completed, and to ensure that water meter straight; risers vertical deviation, not more than 2 mm per metre, not more than e height 500 mm the constructionseal tape stuffing, white lead, after connecting to remove excess filler; 6, pipe installation to ensure that the reserved te ,f
17、00 Q,f,f,21211其中,表示共振频率,、表示半功率点的频率,也就是对应振幅为振幅最大值的倍fff0122的频率。 3.可调频率音叉的振动周期 一个可调频率音叉一旦起振,它将某一基频振动而无谐频振动。音叉的二臂是对称的以至二臂的振动是完全反向的,从而在任一瞬间对中心杆都有等值反向的作用力。中心杆的净受力为零而不振动,从而紧紧握住它是不会引起振动衰减的。同样的道理音叉的两臂不能同向运动,因为同向运动将对中心杆产生震荡力,这个力将使振动很快衰减掉。 可以通过将相同质量的物块对称地加在两臂上来减小音叉的基频(音叉两臂所载的物块必须对称)。对于这种加载的音叉的振动周期T由下式给出,与(3)式相
18、似 2T=B(m+m) (6) 0其中B为常数,它依赖于音叉材料的力学性质、大小及形状,m为每个振动臂的有效质量有关0的常数。利用(6)式可以制成各种音叉传感器,如液体密度传感器、液位传感器等,通过测量音叉的共振频率可求得音叉管内液体密度或液位高度。这类音叉传感器在石油、化工工业等领域进行实时测量和监控中发挥着重要作用。 【实验内容】 一(必做实验 1. 仪器接线用屏蔽导线把低频信号发生器输出端与激振线圈的信号(电压)输入端相接;用另一根屏蔽线将电磁激振线圈的信号(电压)输出端与交流数字电压表的输入端连接。 2. 接通电子仪器的电源,将输出幅度调节钮2逆时针调到最小,使仪器预热15分钟。 3.
19、 测定共振频率f和振幅。 A0r在音叉臂空载,空气阻尼很小的情况下,将低频信号发生器的输出信号频率调节钮3由低到高缓慢调节(参考值约为250Hz左右),仔细观察交流数字电压表的读数,当交流电压表读数f达最大值时,记录音叉共振时的频率和共振时交流电压表的读数。 A0rf4. 测量共振频率两边的数据。 0在信号发生器输出幅度保持不变的情况下,频率由低到高,测量数字电压表示值A与驱动f力的频率之间的关系。注意:应在共振频率附近,通过调节频率微调钮4多测几个点。总共须i测20,26个数据,记录在表1中。 5. 在音叉一臂上(近激振线圈)用小磁钢将一块阻尼片吸在臂上,用电磁力驱动音叉。在增加f空气阻尼的
20、情况下,按照步骤3、4测量音叉的共振频率,记录音叉振动频率与交流电压表的iA读数,填在表2中。 6. 在电子天平上称出(5对)不同质量块的质量值,记录在表3中。 3the driving shaft and the driven shaftvel work surface as the basis for measurement, longitudinal and transverse level deviation should not exceed 0.1%. 1.4 after ft protruding parts, base ledrive steering confirmation
21、, direction compatible with the pump. Leveling should be based on the level of the pump cover, sha-ment integrity, damage and corrosion, pipe protection intact; turning flexible and no clean sound; 1.3equip s. Submersible pump installation shall meet the following requirements: 1.1 location, elevati
22、on, the design requirements; 1.2submersible pumps installation: systems use submersible pumps of product certification and quality control technical documentd. 1, f cement mortar. Diameter of DN100DN150. Embedded stage of construction stage is divided into structural and piping installeifugal castin
23、g, clasp connection of buried pipeline using centrifugal casting iron pipe, socket socket connections, sealing ocentr e system, water system parts, riser by bonding of UPVC drainage pipe construction, transfer floor cast iron drainage pipes byd 0.6MPA hydraulic tightness Drainage installation draina
24、ge system using triage system in the interior design, into the sewaggth anmore than 2 mm per metre, not more than ? 10 mm long; 7, after installation is complete, 1.0MPA water pressure test for strenved tee height 500 mm the construction is completed, and to ensure that water meter straight; risers
25、vertical deviation, not seal tape stuffing, white lead, after connecting to remove excess filler; 6, pipe installation to ensure that the reser 7. 将不同质量块分别加到音叉双臂指定的位置上,并用螺丝旋紧。测出音叉双臂对称加相同质量物块时,相对应的共振频率。记录,m关系数据于表3中。 f08. 用一对未知质量的物块替代已知质量物块,测出音叉的共振频率,求出未知质量的物mfxx块。 mx*二(选做实验: 用示波器观测激振线圈的输入信号和电磁线圈传感器的输
26、出信号,测量它们的相位关系。 【数据记录及处理】 A1.共振频率和振幅的关系 fr0f(1). 在音叉臂空载,空气阻尼很小的情况下,记录音叉振动的频率与交流电压表的读数iA,数据记录在表1中 fA表1 空气阻尼很小时频率和振幅的关系 if /H iZA/V f /H iZA/V fA(2).根据表1的数据绘制,关系曲线,测出共振频率,求出两个半功率点和,ffi12计算音叉的锐度(Q值) f(3). 在音叉臂上加薄片,增加空气阻尼时,记录音叉振动的频率与交流电压表的读数ifAA,数据记录在表2中绘制,关系曲线,测出共振频率,计算音叉的锐度(Q值),并i,与阻尼小的情况(表1)进行比较说明。 fA
27、表2 阻尼较大时频率和振幅的关系 if /Hi ZA/V f /Hi ZA/V 2.音叉的共振频率与双臂质量的关系 f(1).将逐次加载的质量块m与音叉的共振频率记录在表3. imeet the following requirements: 1.1 location, elevation, the design requirements; 1.2 equipment integrity, damage and corros s use submersible pumps of product certification and quality control technical docume
28、nts. Submersible pump installation shallsystem50. Embedded stage of construction stage is divided into structural and piping installed. 1, submersible pumps installation: ried pipeline using centrifugal casting iron pipe, socket socket connections, sealing of cement mortar. Diameter of DN100DN1of bu
29、bonding of UPVC drainage pipe construction, transfer floor cast iron drainage pipes by centrifugal casting, clasp connection installation drainage system using triage system in the interior design, into the sewage system, water system parts, riser byage ? 10 mm long; 7, after installation is complet
30、e, 1.0MPA water pressure test for strength and 0.6MPA hydraulic tightness Drain is completed, and to ensure that water meter straight; risers vertical deviation, not more than 2 mm per metre, not more than e height 500 mm the constructionseal tape stuffing, white lead, after connecting to remove exc
31、ess filler; 6, pipe installation to ensure that the reserved te4urement, longitudinal and transverse level deviation should not exceed 0.1%. 1.4 after the driving shaft and the driven shaftft protruding parts, base level work surface as the basis for measdrive steering confirmation, direction compat
32、ible with the pump. Leveling should be based on the level of the pump cover, sha-pipe protection intact; turning flexible and no clean sound; 1.3ion, f与双臂质量m的关系 表3 共振频率im /g /Hz f 02,52 T,10/s2(2).根据表3的数据绘制T,m关系曲线图,求出直线斜率B和在m轴上的截距。 m0(3).用音叉共振法测物块质量 2测得共振频率= H,利用T,m关系曲线测得未知物块质量= g。 fmZ0x【注意事项】 1.本实验所绘制的曲线是在驱动力力幅恒定的条件下进行的。所以当低频信号发生器的输出电压一经确定之后。在整个实验过程中都要保持这个电压不变,而且要及时核对调节。 2.注意信号源的输出不要短路,以防止烧坏仪器。 3.请勿随意用工具将固定螺丝拧松,以避免电磁线圈引线断裂。 4.传感器部位是敏感部位,外面有保护罩防护,使用者不可以将保护罩拆去,或用工具伸入保护罩,以免损坏电磁线圈传感器及引线。
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