图解法用于受迫振动实验的定量研究

doi:10.14139/j.cnki.cn22-1228.2022.02.024

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摘要

用 Origin 科学作图，线性拟合得到自由振动下摆轮振幅 θ 与固有周期Ｔ０的关系 θ＝ 10429－6525Ｔ0 ，为后续实验图像的解析提供明确参考。分别使用逐差法和图解法处理阻尼振动和幅频特性的实验数据，得阻尼系数 β 为0.0594 s-1和 0.0610s-1。受迫振动幅频和相频特性曲线的拟合结果显示，当电机频率 ω 与摆轮固有频率 ω0 相等时发生共振，振幅 θｒ达 144°，摆轮与强迫力的相位差 φｒ为 90°，很好验证了相关物理实验规律。解析共振处的特征参数，算出共振圆频率 ωｒ= 3.9859s-1，与系统固有频率 ω０（3.9868s-1）之间的相对误差仅 0.023％，说明图解法用于《受迫振动》实验数据的定量分析与计算是非常成功的。

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	何学敏
	任银娟
	毛巍威
	李三龙

关键词: 固有频率阻尼系数共振幅频特性相频特性

Abstract:

For the experiment of free vibration ,the relationship between the amplitude θ of balance wheel and the natural period To can be expressed as θ＝ 10429－6525Ｔ0 according to the linear fitting function of Origin software,which can provide a clear reference for the analysis of subsequent experimental images. The experimental data of damping vibration and amplitude-frequency characteristic were processed by using the successive differential method and the graphic method respectively,and the obtained damping coefficients β are 0.0594 s-1 and 0.0610s-1.As for the forced vibration. the fitting results of amplitude-and phase-freouencr characteristic curves show that the resonance occurs when the motor frequency w is equal to the intrinsic frequency wn of balance wheel. the amplitude θr reaches 144°.and the phase difference (φ) between the balance wheel and the external force is just m/2.which well confirms the relevant rules of physical experiments.The resonant circular frequency can be calculated as w = 3.985 9 s by analyzing the characteristic parameters at resonance,and the relative error between w, and w(3.986 8 s)is only 0.023%, indicating that the graphical method is very successful in the quantitative analysis and calculation of the experimental data of forced vibration.

Key words: intrinsic frequency damping coefficient resonance amplitude-frequency characteristic phase- frequency characteristic

出版日期: 2022-04-25 发布日期: 2022-04-25 整期出版日期: 2022-04-25

ZTFLH:

O 4-39

引用本文:

何学敏, 任银娟, 毛巍威, 李三龙. 图解法用于受迫振动实验的定量研究 [J]. 大学物理实验, 2022, 35(2): 112-116.
HE Xuemin , REN Yinjuan , MAO Weiwei , LI Sanlong. Graphic Method for Quantitative Study of Forced Vibration Experiment . Physical Experiment of College, 2022, 35(2): 112-116.

链接本文:

http://dawushiyan.jlict.edu.cn/CN/10.14139/j.cnki.cn22-1228.2022.02.024 或 http://dawushiyan.jlict.edu.cn/CN/Y2022/V35/I2/112

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