Brass instruments: Linear stability analysis and experiments with an artificial mouth

摘要

The self-sustained oscillation of a brass wind musical instrument involves a complex aerodynamic coupling between multimode mechanical vibratory system (the Lips of the player) and a multimode acoustical vibratory system (the air column of the instrument). In this paper the behaviour of the coupled system near the threshold of oscillation is investigated using a simplified model in which a single mechanical lip mode is coupled to a single mode of the acoustical resonator. Linear stability analysis is used to study the theoretical variation of threshold blowing pressure and threshold playing frequency as functions of lip and air column parameters. The theoretical results are compared with experimental results obtained from a systematic study of the near threshold behaviour of a trombone sounded by an artificial lip mechanism. Comparability between theory and experiment is ensured by using model parameter values derived from mechanical response measurements on the artificial lips and input impedance measurements on the trombone. The measured mechanical response curve for the artificial lips exhibits several resonance peaks, each of which can be classified unambiguously as either "inward striking" or "outward striking". For each of these resonance peaks, parameters have been extracted and used in numerical simulation of threshold behaviour as a function of trombone slide extension. However, the experimentally observed threshold frequencies of the coupled system suggest a behaviour which passes smoothly from "inward striking" to "outward striking" character as the trombone slide is extended or the embouchure parameters changed. It seems unlikely that this type of behaviour can be explained using a lip model with only a single degree of freedom. [References: 49]