VIBROACOUSTIC ANALYSIS OF TRUMPET WALL VIBRATIONS

摘要

There has been a long debate whether wall vibrations can affect the sound produced by brass wind instruments. During the last decade unambiguous evidence of the effect of wall vibrations has been provided by experimental measurements. However the underlying mechanism was still unclear, although several explanations had been posited. This led towards physical modelling approaches that aimed at simulating the observed effects, while shedding some light on the way the vibrating walls could significantly alter the sound generated by the instrument. It turns out that axial vibrations of the instrument bore are responsible for the observed effects. Namely, the wall vibrations due to the acoustic pressure dynamically alter the internal bore radius and couple to the air column inside the instrument. It has been shown that this is a broadband effect that may significantly affect the acoustic impedance of the instrument over a considerable frequency range. Numerical simulations using the finite element method verified this behaviour. Subsequently, simplified models were constructed in order to yield efficient simulation tools that are able to capture this effect. By representing the instrument using a series of masses and springs, it has been possible to reproduce the results obtained with the finite element method, with the exemption of one mode of vibration that is related to shear stresses and strains. This paper shows how to incorporate this mode to the aforementioned mass-spring model, which may be coupled to a wave-propagation model for vibroacoustic simulations. The resulting numerical scheme remains computationally efficient in comparison to the finite element model (approximately 100 times faster) and may be used in series of simulations, for example for bore optimisation, sound synthesis and sound analysis of brass wind instruments.