Part of my PhD was devoted to simulating the physics of nonlinear plates. Plates are very interesting systems, as they display a chaotic (better, turbulent) behaviour when struck at high amplitudes - see also the video below. From a sound synthesis perspective, this leads to the typical shimmering and bright sound of gongs and cymbals. The sound examples below are created entirely from numerical simulations of linear and nonlinear plate dynamics. See also this paper. In this video, the linear and nonlinear dynamics are displayed side by side. The nonlinear plate has a much more interesting dynamics, including modal coupling, energy cascade, and turbulence. These effects are all important for realistic sound synthesis!
One of the most attractive features of linear plate dynamics is perhaps the possibility of simulating plate reverberation. Despite not being sound synthesis per se, this effect can be entirely modelled using physical principles. A major advantage of physical modelling over convolution or sample-based reverb, is the possibility of extracting the output dynamically on the plate, by moving the output locations; this results in a very enjoyable phase movement. The following examples compare dry and wet sounds, using different plate settings. The sounds were obtained using Physical Audio PA1 plate reverb plugin, available here.
|Vocals (Wet, Static)|
|Vocals (Wet, Dynamic)|
For sufficiently small plates, a modal algorithm can run fast enough to allow real-time simulations even on consumer hardware. The plates can be designed at will, and played at multiple locations with different amplitudes, resulting in very organic sound textures.
HIGHLY NONLINEAR PLATES
Larger plates at high amplitudes give extremely rich simulations, from gong-like to cymbal sounds. In this example, different plates are driven with control signals (pure tones), and the output displays an extremely rich spectral content. This is a trace of Wave Turbulence!
One of the advantages of physical modelling is the possibility of designing instruments with unrealistic dimensions. Here's an example of an extremely big plate, with no loss. Here you can hear the turbulent cascade developing from low to high frequencies.