郑百哲, 白坚. 用奇异摄动法求解31号和59号钢琴键弦的泛音频率[J]. 工程力学, 1988, 5(3): 121-127.
引用本文: 郑百哲, 白坚. 用奇异摄动法求解31号和59号钢琴键弦的泛音频率[J]. 工程力学, 1988, 5(3): 121-127.
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Zheng Baizhe, Bai Jian. SOLUTON FOR THE TONE PARTIALS OF THE PIANO STRING OF 31ST KEY AND 59TH KEY BY SINGULAR PERTURBATION METHOD[J]. Engineering Mechanics, 1988, 5(3): 121-127.
Citation: Zheng Baizhe, Bai Jian. SOLUTON FOR THE TONE PARTIALS OF THE PIANO STRING OF 31ST KEY AND 59TH KEY BY SINGULAR PERTURBATION METHOD[J]. Engineering Mechanics, 1988, 5(3): 121-127.
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用奇异摄动法求解31号和59号钢琴键弦的泛音频率

SOLUTON FOR THE TONE PARTIALS OF THE PIANO STRING OF 31ST KEY AND 59TH KEY BY SINGULAR PERTURBATION METHOD

    摘要
  • 摘要: 作者在文献1中用奇异摄动法求得了钢琴弦振动方程在两端错定条件下的一级近似数值解,并应用于31号弦,求得了它用泛音频率。本文应用文献1结果进一步求出了59号弦的泛音频率,所得结果与实验观测值对比,其绝对误差的均方根和相对误差的均方根都远较Rayleigh-Seeback用正则摄动法算得的小。本文还探讨了两端桥式支承和一端钳定,一端桥式支承的情况。

     

    Abstract: In this paper,two methods,one singular perturbation and the other directly numerical solution,are used to find the solution of the stiff string of 3lst key and 59th key for a piano tone partials,with the results compared with Ray-leigh and Seeback's by regular persvrcation method and with those from dire-ct obseruation.

     

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