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Reed instruments, from small to large amplitude periodic oscillations and the Helmholtz motion analogy

机译：簧片乐器，从小振幅到大振幅的周期性振荡和亥姆霍兹运动类比

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When studying the oscillations of reed instruments different approaches and simplifications can be used to understand the behaviour of such instruments. Two theoretical approaches were successfully used by previous authors. The first one consists in analysing the small oscillations near the threshold. The second one, applied until now only on cylindrical resonators, analyses the squared oscillations with a lossless model of the resonator. The aim of this paper is on one hand to apply the lossless analysis to conical like instruments and on the other hand to try to understand how the small oscillations model matches with the lossless model. In this study the cone is replaced by resonators which are known to be approximately equivalent and for which the input impedances allow analytical developments. Differences in behaviour between cylinders and cones are demonstrated. Contrary to cylindrical instruments, for conical instruments there is a subcritical threshold and no small amplitude oscillations. Moreover, there is more than one regime at the fundamental frequency in conical instruments. Two of these, similar to the Helmholtz motions in bowed string instruments are studied in this paper. Theoretical results are qualitatively compared with experiments using a blowing machine. [References: 44]
机译：在研究簧片乐器的振动时，可以使用不同的方法和简化方法来了解此类乐器的行为。先前的作者成功使用了两种理论方法。第一个是分析阈值附近的小振荡。到目前为止，仅适用于圆柱谐振器的第二个谐振器使用谐振器的无损模型分析平方振荡。本文的目的是一方面将无损分析应用于类似圆锥形的仪器，另一方面试图了解小振荡模型与无损模型的匹配。在这项研究中，锥体被谐振器所替代，该谐振器被认为是大致等效的，并且其输入阻抗允许进行分析开发。演示了圆柱体和圆锥体之间的行为差​​异。与圆柱形仪器相反，对于锥形仪器，存在一个亚临界阈值，并且振幅不小。此外，在圆锥形仪器中，在基频上有一种以上的制度。本文研究了其中两个，类似于弓弦乐器中的亥姆霍兹运动。将理论结果与使用吹塑机进行的实验进行定性比较。 [参考：44]

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