Woodwind instrument design optimization based on impedance characteristics with geometric constraints

Area of Science:

• Acoustics
• Computational Physics
• Musical Instrument Design

Background:

• Computational optimization and acoustic models offer new avenues for instrument design.
• Automatic discovery of geometries with specific resonance characteristics is a key goal.
• Woodwind instruments present complex acoustic challenges due to intricate geometries.

Purpose of the Study:

• To investigate the design optimization of woodwind instruments with complex geometrical features.
• To search for optimal geometric designs that achieve target acoustic input impedance peaks.
• To address challenges in gradient-based optimization due to non-smooth impedance evolution.

Main Methods:

• Utilizing computational optimization algorithms coupled with acoustic models.
• Developing new formulations for impedance characteristics using a regularized unwrapped angle of the reflection function.
• Applying the approach to a key-less pentatonic clarinet with two registers.

Main Results:

• Demonstrated a strategy for simultaneously adjusting multiple impedance characteristics across all fingerings.
• Successfully applied novel impedance formulations to overcome optimization challenges.
• Identified optimal geometric designs for a complex woodwind instrument.

Conclusions:

• The proposed method effectively optimizes woodwind instrument geometries for desired acoustic properties.
• This approach facilitates the design of instruments with specific resonance frequencies and amplitudes.
• The findings offer practical solutions for instrument manufacturers facing complex design constraints.