Band gap transmission in a periodic network of coupled buckled beams

Abstract

Wave propagation in a periodic network of coupled buckled beams, which represents a finite dissipative periodic structure with quadratic and cubic nonlinearities, is studied. The aforementioned structure is harmonically forced and parametrically excited at one end with forcing frequencies lying within its band gaps, one below and one above the pass band. Numerical simulations, supported by the analytical estimates using the method of multiple scales (MMS), show the occurrence of supratransmission which is a sudden increase in the energy transmitted across the finite structure due to a certain excitation amplitude. In essence, this nonlinear energy transmission across the discrete nonlinear periodic structure occurs due to the loss of stability of the periodic solutions which are initially localized to the driven end of the structure (nonlinear instability). Practical ways including damping ratio and coupling stiffness variations to alter the transmission threshold are assessed. In particular, it is found that the presence of parametric excitation can considerably lower the required threshold for the onset of energy transmission within the stop band. The presented results of this work may offer some insights to enhance the performance of acoustic and mechanical metamaterials.