Non-Reciprocal Wave Propagations in a One-Dimensional Periodic Structure Modified with a Linkage Mechanism

Abstract

Reciprocity is a fundamental property of wave propagations, and many researchers devoted their efforts to breaking the reciprocity and implementing unidirectional wave propagations. At present, the main method to realize non-reciprocal waves uses aperiodic structure as the wave propagation medium. The non-reciprocal bandgap achieved by this method is narrow and difficult to adjust actively. To improve the controllability of non-reciprocal bandwidth, a one-dimensional (1D) periodic lattice structure based on linkage element is proposed in the work. The linkage element enables the lattice structure to have nonlinear stiffness with respect to the asymmetry of the equilibrium position. This stiffness asymmetry leads to the non-reciprocity of wave propagation, which provides a new idea for the design of non-reciprocal structures. To deal with the strong nonlinearity and high dimensional characteristics of the structure, the improved incremental harmonic balance (IHB) method is used to analyze the dispersion and bandgap characteristics of the structure. The results show that the structure has two bidirectional bandgaps (high and low frequency) and four unidirectional bandgaps, and the position, width and direction of the bandgap can be adjusted by the equilibrium position and mechanical parameters of the structure. The obtained structural properties are verified by numerical experiments.