Heuristic finite element models of the Japanese Koto

Abstract

Modeling a traditional, hand-carved performance-grade Japanese koto presents many challenges. A COMSOL Multiphysics finite element model of the instrument, based on CAT scan data, is the most rigorously accurate solution to date. However, a substantially less computationally intensive idealized box model, for example, can provide qualitative assessment of its performance. This paper discusses a COMSOL model based on the physical properties of a solid plank of Australian paulownia wood, its validation, and its elaboration into an idealized but unstable hollow box with internal struts and sound holes of varying geometries. It then reports on the development of the next stage model which has 12 cross-sections lofted along a spline to create curvature as the natural progression towards realism. Comparison of these three models and the complex CAT scan model of the koto is presented. It shows that the box and lofted models are useful in qualitatively interpreting the results of the complex model. Isotropic models, as used in the literature, were unsuccessful in predicting responses, but using best available approximations for anisotropic elastic constants was helpful. Finally, each stage was able to provide timely feedback to inform the development of the next stage model and guide experimentation.