论文和技术资料

This paper describes a simulation study performed with the goal of quantifying the correlation between violin design and sound quality. The investigation first explored the resonant modes of the front plate of a violin by examining its eigenfrequencies. Chladni patterns of increasingly complex plate shapes were modeled using COMSOL Multiphysics^® simulation software, specifically the 2D Plate interface of the Structural Mechanics Module. The plate had a thickness of 10 mm without prior velocity or displacement, and with all edges unconstrained with no loads. The material was a generic soft wood, chosen due to its similarity to materials used in violin-making. The study examined eigenfrequencies between 175 Hz and 2700 Hz, a range chosen based on the pitch range of the violin, i.e. G₃ = 196 Hz through ~E₇ = 2637 Hz.

The initial geometry for this simulation was a triangle with a fine triangular mesh. After running the simulation with this mesh, the results were mirrored three times: the first to create a smaller square, then a rectangle, and lastly to create a larger composite square of length 0.24 m. The results from this manipulation did not match published experimental results of Chladni patterns of squares [1]. In order to validate the simulation, the geometry was refined to be a square of length 0.24 m. The simulation results from this new geometry matched over half of the experimentally-found modes [1], validating the model. This allowed for the final stage to be implemented, the violin geometry. With the simulation running the violin geometry, the results showed the first breathing mode and other higher modes corresponding to published results [2-3].

Changes in geometry show visible differences in the Chladni patterns, and by matching specific modes to experimental results, a refinement of the geometry is possible. The second phase of the project will focus on incorporating the curvature of the front plate in the z-direction as well as modeling of different part interactions. This will include the back plate of the violin and the interaction of front and back plates with air cavity modes in order to better identify the paired component modes. Coupled front and back plates will be modeled using the 3D Shell interface of the Structural Mechanics Module. If differences in resonant modes between diverse violin geometries can be properly modeled, they can create another metric to be utilized in improving violin sound quality. For mass-produced violins, this could allow for a reduction in manufacturing costs while increasing sound quality.

[1] M. D. Waller, “Vibrations of free square plates: part I. Normal vibrating modes,” Proceedings of the Physical Society, vol. 51, no. 5, pp. 831–844, 1939.

[2] C. Gough, “The violin: Chladni patterns, plates, shells and sounds,” The European Physical Journal Special Topics, vol. 145, no. 1, pp. 77–101, 2007.

[3] E. Ravina, “Analysis of the Mechanical Behavior of Violins Based on a Multi-physics Approach,” COMSOL Conference 2008 Hanover, 2008.