Sound model of an orchestral kettledrum considering viscoelastic effects

The modeling of the mechanical systems that describe musical instruments has long been a topic of interest for acoustic physicists. The orchestral kettledrum, distinguished by a broad spectrum of sounds, has been the subject of multiple investigations related to the goal of generating a realistic digital sound synthesis. In the present work, we apply the Green function method to estimate modal frequencies considering an air-loaded viscoelastic membrane. We propose a method that includes viscoelasticity to accurately predict the sound spectrum of the modeled kettledrum. Results are compared to real sound recordings of an orchestral kettledrum obtained in controlled conditions. The calculated modal frequencies are found to coincide well with the real values with an absolute mean error of 1.25±0.76 Hz and 1.87±1.83 Hz for the A2 and B₂ ^♭ tuned drumheads respectively. The spectral envelope of the synthesized sound spectrum coincides well with the Fourier transform of the real sound. The viscoelastic term was found to generally reduce the amplitude of the sound spectrum and in certain cases, better approximate the modal frequencies and decay times. The modal synthesis method used here is numerically lightweight and can be adapted to be used in real-time applications with low computational resources. To reproduce our experiment, the recorded kettledrum sounds and Python source code of the model are freely available.