A common technique in modern music (going back to the Beatles) is to sweep a comb filter over the frequencies. One variant of this is for no particularly good reason called “flanging”, but there are others.
Another common technique is to use FM synthesis, in which the time axis is distorted according to a modulator waveform. Typically this differs from the kind of FM used in FM radio in that, in FM radio, the modulator is many octaves lower than the carrier, while in FM synthesis, typically they are the same frequency or an octave or two apart, so the waveform repeats with the same period as the carrier — so the FM distortion merely produces harmonic distortion, rather than inharmonic sidebands. A typical technique is to gradually reduce the “depth of modulation” down to zero, thus causing the harmonics thus produced to die away, just as the overtones of a string or a bell do.
An interesting thing about FM synthesis is that the carrier wave being distorted is almost invariably a simple sinewave. It would be interesting to use some kind of frequency and phase tracking to apply the same kind of “FM” periodic time-domain distortion to a wave from some other source, such as a singer’s voice.
Most children in the rich world have done something similar by talking or singing through the blades of a spinning box fan to make a “robot voice”, which provides a sawtooth “FM” distortion of time at frequencies somewhat lower than voice frequencies, perhaps 50–100 Hz, and without phase tracking of them.