中文摘要：

分析了琴弦的亥姆霍兹运动,设计了一个基于高速摄影的非接触式光学测量系统,用于测量真实小提琴上琴弦的振动.通过特殊的光路设计和在琴弦上设置标定点,以7 000 frame/s的速度和336×480的图像分辨率拍摄了拉弦和拨弦时琴弦上标定点的三维振动形态.采用圆形霍夫变换图像处理算法、奇异值分解算法和自动批处理,对记录的大量序列图像进行处理,提取了弦振动的位移和轨迹等数据.实验结果表明,该测量系统能够精确跟踪小提琴琴弦的振动状态和包络轨迹,振动位移曲线的图像处理精确度达到0.03 mm.该系统为进一步研究提琴琴弦的振动机理和建立精确的琴弦振动理论模型提供了一种有效的实验方法.

英文摘要：

The ＇Helmholtz movement~ of a bowed string was analyzed, and a non-contact optical measurement system based on high-speed photography was designed to measure the vibration of string of a violin. By designing a special path and setting a marked point on the string, the three dimensional vibration state of the marked point on string was measured on plucking and bowing the violin string with a high speed shooting rate of 7 000 frame/s and image resolution of 336 X 480. On the imaging processing algorithm based on the circular Hough transform, singular value decomposition algorithm and an automatic batch program, a large number of sequential images recorded were processed and the displacement and trajectory were extracted. The experimental results show that the proposed measurement system accurately tracks the motion and trajectory of the violin string, and the data processing accuracy of vibration displacement is 0. 03 mm. The designed measurement system and image processing algorithm provide a valid experimental method for studying the mechanism of violin string vibration and developing an accurate theoretical model for string motion.