The standard picture of the musical instrument, in the musical acoustics literature, is that an instrument consists of a linear distributed resonator (such as a string, or acoustic tube, or bar), coupled to a nonlinear excitation element (such as a bow, hammer, or lip/reed). This picture is sufficient for a lot of instruments, but there are some, for which a linear model of the resonator is insufficient to capture the most perceptually salient effects. A plate, used in a percussion setting, is an example of such an object.
Here is a set of sound examples, generated using a linear plate model, and a finite difference scheme:
Notice that the attacks are rather “dead”; this is essentially what you would get out of using an additive synthesis model. (The phasing you hear comes from slow, subaudio-rate variation in the readout locations on the plate)
The nonlinear model leads to a much wider variety of sounds, and to greatly increased liveliness in the attack portion. Here are a few percussive sounds generated from a short piece of Matlab code simulating a von Karman (nonlinear) plate:
Beyond percussive sounds, you can get interesting sustained, and noisy timbres by bowing the plate at an edge:
and also by driving a plate, with an input sound file, at high amplitudes, in which case you get sounds completely unlike typical plate reverb-processed effects: (Composers seem to like these sort of effects sometimes, rather than pure synthesis…)
Here’s a pretty nice gong-like effect, obtained by attaching a linear string to a nonlinear plate model…you get the crash of the gong, which then settles down to a pitched tone corresponding to the string!