Nonlinear Energy Transmission in a Finite Dissipative Periodic Structure

We study nonlinear transmission of energy in a finite dissipative periodic structure, which is externally driven at one end with a harmonic force. We show that when the driving frequency is within the stop band of the periodic structure, there is a threshold for the driving amplitude, above which there is a sudden increase in the energy transmitted through the finite structure. This is a generic phenomenon for discrete nonlinear periodic systems. The onset of transmission is due to loss of stability of the harmonic solutions localized at the driven end of the structure. The transmission threshold is predicted analytically based on the underlying bifurcation. The influence of both hardening and softening types of nonlinearity on the transmission phenomenon is discussed.