Simscape Model - calculate inharmonicity in piano string.

版本 1.0.1 (470.3 KB) 作者: Stephen Thompson

SImscape models the flexural vibration of a piano string including the wire bending stiffness. Modal frequencies are a good match to theory.

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更新时间 2023/10/18

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The vibrating “string” of a piano is a thin steel wire that is tensioned to tune it to the intended playing frequency. Sufficient tension in the wire gives it the properties approximately of a flexible string, with its multiple resonance frequencies approximately at harmonic intervals. However the wire bending stiffness modifies the resonance frequencies by a small amount. It is well known that the additional stiffness modifies the resonance frequencies

such that

where

and

is the fundamental frequency of a similar ideal flexible string. A Simscape model of the vibrating string demonstrates this behavior, and its solver has sufficient resolution to match this theoretical prediction.

引用格式

Stephen Thompson (2024). Simscape Model - calculate inharmonicity in piano string. (https://www.mathworks.com/matlabcentral/fileexchange/136764-simscape-model-calculate-inharmonicity-in-piano-string), MATLAB Central File Exchange. 检索来源 2024/7/26.