Defect mode-induced unidirectional flexural wave transmission using prismatic beams with concentrated gradient masses

Abstract

We study and realize unidirectional flexural wave transmission in finite phononic crystal beams based on the boundary defect modes. First, we show that by carrying a periodic array of concentrated masses, conventional prismatic beams become phononic crystal beams having multiple transmittance peaks in odd-order bandgaps. We point out that these bandgap transmittance peaks are induced by pass-band splitting and are essentially defect modes due to the existence of the imperfect boundary in finite beam structures. Significant asymmetric flexural wave propagation can be observed in these defect modes by gradually changing each concentrated mass. Using the spectral element method (SEM), the relationship between the concentrated gradient masses and the directivity at the defect modes is discussed. To realize concentrated gradient masses, we periodically attach near-point-contact steel balls with gradient diameters on a prismatic beam. The formation of the bandgaps and unidirectional displacement transmission are experimentally validated with a high-sensitive point-wise fiber Bragg grating displacement sensing system. Asymmetric one-way flexural wave propagation is further demonstrated in the time domain with a Hanning-windowed tone burst signal excited at the two ends of the phononic crystal beam. Agreements between the SEM and experimental results clearly indicate that the asymmetric one-way flexural wave propagation can be achieved in prismatic beams carrying a periodic array of concentrated gradient masses.