Wave Propagation in a Network of Buckled Beams Directly and Parametrically Excited at One End

Abstract

Abstract Wave propagation in a network of buckled beams, which represents a finite dissipative periodic structure with quadratic and cubic nonlinearities, is studied. The aforementioned structure is harmonically driven externally and parametrically at one end with forcing frequencies lying within its stop band, one above and one below. Numerical calculations show the occurrence of supratransmission, a sudden increase in the energy transmitted across the finite structure, after a certain forcing amplitude of the external excitation. In essence, this nonlinear wave propagation mechanism for the discrete nonlinear periodic structure occurs due to loss of stability of the periodic solutions that are initially localized to the driven end of the structure (nonlinear instability). It is found that small parametric excitation can considerably decrease the required threshold for the onset of energy transmission within the stop band.