非连续变截面梁振动研究在八音琴中的应用

APPLICATION OF NONCONTINUOUS CHANGING SECTION GIRDER VIBRATION RESEARCH TO MUSICAL MOVEMENT

为提高八音琴的生产效率 ,从八音琴的结构和原理出发 ,完成从建模、理论推导、编程到加工生产的全过程。在建模阶段 ,考虑到八音琴的音键多数都是非连续变截面梁的特点 ,依据音键头部质量占整个悬臂梁质量的比例 ,应用单自由度、等截面悬臂梁和非连续变截面梁三种模型。当音键头部质量占悬臂梁质量 5 0 %或以上时用单自由度模型 ,2 0 %或以下时用等截面悬臂梁模型 ,2 0 %以上 5 0 %以下时用非连续变截面梁模型 ,经理论推导得到计算这三种音键固有频率的公式。对这三种模型均做了计算机辅助设计的模块 ,实践证明用有限元方法计算的结果精度最高 。

The purpose of this work is to gain social and economy benefits by improving manufacturing efficiency of musical movement. By analyzing the structure and principle of musical movement, we finished the whole process of modeling theoretic deduce programming and manufacturing. In the process of modeling, we found that most of the keys of a musical movement were noncontinuous changing section girder, so we prompted three models according to the ratio of weight of head to the whole weight of a key, When the ratio was more than or equal to 50%, single freedom vibration model was adapted, when the ratio was equal to or less than 20%, changeless section socle girder vibration model was adapted, when the ratio was more than 20% and less than 50%, noncontinuous changing section socle girder vibration model was adapted. The equation of natural frequency was deduced. The computer aided design software model for these three models was finished, the finite element analysis is proved the most exact and effective. The results of natural frequency of a noncontinuous changing section socle girder using our software and America RASNA software are very similar, this also proves the reliability and accuracy of the two methods for each other. In the process of manufacturing, our software is used to control this process. Frequency of the key produced is approximate to that frequency of musical note, the error is less than 5‰, The automatic key producing line was used, its productivity is 10?000 per day, 42 times higher than manual producing.