Gong Wire beads on a stiff, domed wire: stretching + bending + curvature, struck once

The FPUT chain made into a small gong. Beads on a wire move sideways; the wire resists stretching (which couples the modes), resists bending (which spreads the modes from about 100 Hz to 17 kHz, as in a plate), and can be built as a dome (which adds the three-wave coupling of curved gongs and cymbals). A soft strike rings in its low modes. A hard one sends energy climbing into the high frequencies over tens of milliseconds, the bloom of a gong or a crash, until damping, strongest at high frequencies, pulls it back down.

Physical setupBeads on a wire between two pinned ends, built as a shallow dome (dashed). The beads move sideways, drawn magnified; link thickness shows how hard each link is being stretched.

Three things hold each bead. The links pull it back toward its neighbours and, when stretched, pull harder: this stretching is what passes energy between modes, the same mechanism as in the FPUT chain or the midplane of a plate. Bending stiffness resists kinks, so short waves vibrate much faster than long ones, as in a plate or cymbal (frequency grows with the square of the wavenumber). The dome makes even a small sideways motion stretch the links, which stiffens the wire and adds a coupling that lets two modes feed a third at the sum of their frequencies. The strike gives a few beads a sudden velocity; the sound is the velocity of the bead in the listener ring, or the sum over all beads (Listen at).

Where the energy isShare of strike A's energy in each normal mode over time, log scale, labelled by the mode's pitch. A cascade shows as energy climbing toward the top.
How high it reachesShare of each strike's energy in modes above 4 kHz (solid) and above 1 kHz (thin), for all 8 strikes. Shaded: the chaotic phase of strike A.
The spectrum it rings withEach strike's final share of energy per mode, against the mode's pitch.
Strike AStrike B6 more strikes
How fast nearby strikes separateLocal Lyapunov exponent of strike A (per second). The dashed line is the energy in dB.
What you hearSpectrogram of the selected strike at the listener. Click a strike, or use the ← and → keys, to flip between them; the color scale is shared, so differences in level are real. The selected strike is also drawn bold in the two plots above.