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Eigenfrequency optimisation of free violin plates.

Sebastian Gonzalez1, Davide Salvi1, Fabio Antonacci1

  • 1Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy.

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Summary
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This study explores how violin top plate shape influences its modal response. Findings show geometric modifications can balance eigenfrequencies, aiding violin makers in achieving desired tonal qualities.

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Area of Science:

  • Acoustics
  • Musical Instrument Design
  • Computational Mechanics

Background:

  • The modal response of violin plates is crucial for tonal quality.
  • Understanding the relationship between plate geometry and vibrational modes is key for luthiery.
  • Historic violins offer insights into optimal design principles.

Purpose of the Study:

  • To develop a parametric model for violin top plate shaping.
  • To investigate the effect of geometric variations on modal response.
  • To provide violin makers with tools to control eigenfrequencies.

Main Methods:

  • Utilizing 3D scans of historic violin plates.
  • Creating a parametric model for smooth interior shaping while preserving boundary.
  • Analyzing the nonlinear effects of shape parameters on plate eigenmodes.

Main Results:

  • A family of violin tops with controllable shapes was generated.
  • The interplay of parameters nonlinearly affects plate eigenfrequencies.
  • Specific parameter settings can match the fifth-to-second eigenfrequency ratio of Cremonese violins.

Conclusions:

  • The developed parametric model is accessible to violin makers.
  • Geometric modifications can be steered to balance free plate eigenfrequencies.
  • Findings offer practical guidance for improving violin acoustics through design.