Physical modeling of Tibetan singing bowls using dynamic forcing
David Etlinger · The Journal of the Acoustical Society of America · 2006
The geometric simplicity of Tibetan singing bowls produces surprisingly complex vibrational behavior. The curvature of the bowls causes strong coupling between modes, and the physical parameters of actual bowls (namely their thickness and deep curvature, as well as their asymmetrical excitation) produce higher-order effects that cannot be neglected. In this paper we present a physical model for the bowl’s acoustical output. The model is based on analytical solutions for the natural modes, and predicts both transient and steady-state behavior. Using the method of dynamic forcing, we investigate bowl response for linear (striking) and nonlinear (rubbing) excitation methods, producing audio as well as numerical data. Finally, we use the model to gain insight into aesthetics and design: by comparing our simulations to actual antique or high-quality bowls, we can begin to determine what parameters contribute most to creating the desired sound.