2023 Volume 44 Issue 3 Pages 269-280
Interactions between the airflow, elastic body of the lips, and acoustic resonator of the instrument cause self-sustained oscillation of the lips when generating sound using brass instruments, and the steady-state oscillation of the instrument can be expected to be periodic. However, quasi-periodic oscillation or period doubling can also occur, and a cascade of period doublings may further introduce chaos. Therefore, given a set of dynamic equations representing the acoustic behaviors of the airflow, lips, and instrument, a method for detecting and obtaining the periodic solution by adopting a shooting method that relies on the match between the initial and terminal states after the time corresponding to the oscillation period has passed is presented in this paper. Experiments were performed for a trumpet model, where the resonance frequency of the lips and the blowing pressure were used as the main control parameters. The minimum blowing pressure was estimated using a linear stability analysis. The method could capture the corresponding changes in the periodic solution very finely when a small perturbation was successively applied to the control parameters; however, it was less effective when the acoustic load of the instrument was capacitive at the oscillation frequency.
