An improved method for unidirectional mechanical wave propagation in a metamaterial beam

Recent attention has been drawn to breaking reciprocity due to its astounding applications. Metamaterials can be utilized to break the time-reversal symmetry of a system. This paper investigates the theoretical propagation of waves in a space–time modulating medium and presents a novel Fourier series expansion for avoiding flat wave method barriers. The acquired results are validated by comparing them to those reported in the literature and the simulation results in COMSOL commercial software. Additionally, a theoretical function is created to discuss the effect of various parameters on the position and bandwidth of bandgaps. The plane wave expansion (PWE) approach is incapable of predicting the higher-mode bandgaps. In contrast, the proposed technique accurately detects a bandgap, as demonstrated by FEM results. On the other hand, it is demonstrated that the convergence rate of the presented method is significantly higher than that of the PWE method and decreases the computation time appropriately, indicating that this method is more accurate and reliable than the traditional PWE method, particularly in predicting the higher-mode bandgaps. The findings of this study could be utilized for intelligent periodic structures that use piezoelectricity to regulate wave propagation.