Physics-based sound synthesis of the vibrations of a cantilever steel beam using the finite element method
Rivadeneira Bolaños, David Andrés · USFQ Digital Repository (Universidad San Francisco de Quito) · 2017
Through history, the design of musical instruments has been a slow process of trial and error, and to improve and optimize their design more quickly, it would be very useful to know how their sound would change when changing specific characteristics of the instrument. This would normally require the building of a prototype of the instrument, which would require time and money. This step, however, could be avoided if a computational model of the instrument that could reproduce its sound was build. In the present work, a 2-dimensional computational model of a simple musical instrument: a cantilever beam surrounded by air, was built, and using finite elements, the sound produced by the beam when giving it an initial excitation was calculated. The synthesized sound was compared to a microphone recording of the sound produced by a real cantilever beam to verify that the synthesized soundwave had been calculated correctly. The frequencies in the synthesized and recorded soundwaves were compared in the frequency range from 100 to 2000 hz since the recorded soundwave had most of its frequencies in this range, and it was found that the frequencies in both soundwaves differed by a maximum of 8.08 %, which was attributed in part to variations of the elastic properties of the beam. It was also found that the damping of the frequencies in both soundwaves was larger for larger frequencies than for lower frequencies. It was concluded that the synthesized soundwave represented satisfactorily the frequencies contained in the real sound, despite having used a 2-dimensional beam model to accomplish this, which had implicitly the assumption that the beam had an infinite width. Besides improving already existing musical instruments, the methodology presented in this work could be used to create instruments never imagined before.