Periodic waves in a Hertzian chain

Strongly nonlinear periodic waves are investigated in an initially compressed chain of spheres under Hertz contact. A harmonic excitation force disturbs the first grain with an amplitude comparable to the initial compression and the steady strain-wave profiles at large distances from this disturbance are compared with predictions from the long wave approximation. Two qualitatively different types of quasi-stationary periodic waves are apparent in the system: one with minimum and maximum strain values above the static value and one whose minimum strain is below and maximum value is above the initial strain. From the frequency spectrums of the calculated force between particles, new forcing functions are constructed that allow rapid formation of quasi-stationary strongly nonlinear periodic waves.