Supratransmission phenomenon in a Fermi-Pasta-Ulam diatomic lattice.

Abstract

The nonlinear supratransmission phenomenon in a Fermi-Pasta-Ulam (FPU) diatomic lattice with two forbidden bands is investigated. Using a decoupling ansatz for the motion of the two different sublattices combined with the continuum (quasidiscrete) approximation, we derived analytically the threshold amplitudes of supratransmission occurrence when a sinusoidal driving with frequency in the upper forbidden band (lower forbidden band gap between acoustic and optical modes) is applied at one end. The resulting estimate of the threshold of a lattice with a first heavy particle is different to the one obtained from a lattice with a first light particle, showing the influence of the driven particle and giving also the possibility to have two thresholds on each forbidden gap of a diatomic lattice by switching the order of light (m) and heavy (M) masses. In the lower forbidden band, the dependence of the supratransmission threshold on the mass ratio (μ=m/M) has been evidenced and it appears that for large (small) values of μ, that is μ>60%, the coupling between the two modes must (must not) be considered. Numerical explorations were subsequently performed with an emphasis on the dependence of the threshold on the driving frequency and also on the mass of the driven particle (light or heavy). A good agreement is found between the numerical and analytical thresholds. For the limit case where all the masses are identical, the results of the monoatomic FPU previously found in the literature are recovered.