Supratransmission in a β-FPUT square lattice

Abstract

The supratransmission effect allows a nonlinear lattice to be excited by an external driving at frequencies outside the phonon spectrum if the driving amplitude is sufficiently large. Here we numerically study the energy flux into a β-Fermi-Pasta-Ulam-Tsingou square lattice from a pair of harmonically driven particles. Depending on the driving amplitude, a critical frequency ${\Omega }^{⁎}$ is found, above which no energy is transferred to the lattice. When the driving frequency is close to ${\Omega }^{⁎}$, spatially localized large-amplitude vibrational modes called discrete breathers (DBs) are formed that move along a densely packed row of particles. When the excitation frequency is well below ${\Omega }^{⁎}$ but above the phonon band, irregular particle oscillations are excited. This is because the lattice under consideration supports multiple DB solutions. Excitation frequencies close to the supratransmission threshold will excite only one type of DB, while driving at lower frequencies will excite different types of DBs, leading to irregular dynamics.