Prediction of the dynamic oscillation threshold of a clarinet model: Comparison between analytical predictions and simulation results

TL;DR

This paper investigates the discrepancy between static and dynamic oscillation thresholds in a clarinet model, focusing on bifurcation delay and its sensitivity to numerical precision through analytical and simulation comparisons.

Contribution

It provides a detailed comparison between analytical predictions and simulation results for the dynamic oscillation threshold in a clarinet model, highlighting bifurcation delay effects.

Findings

Bifurcation delay causes higher oscillation thresholds in dynamic conditions.

Simulation results are highly sensitive to numerical precision.

Analytical models can predict the dynamic threshold with reasonable accuracy.

Abstract

Simple models of clarinet instruments based on iterated maps have been used in the past to successfully estimate the threshold of oscillation of this instrument as a function of a constant blowing pressure. However, when the blowing pressure gradually increases through time, the oscillations appear at a much higher value than what is predicted in the static case. This is known as bifurcation delay, a phenomenon studied in [1] for a clarinet model. In numerical simulations the bifurcation delay showed a strong sensitivity to numerical precision.