Ultra-wide low-frequency band gap in a tapered phononic beam

Abstract We propose a tapered phononic beam with a broad low-frequency band gap for flexural waves. A unit cell of the phononic beam consists of two identical uniform parts and a thickness- and width-varying part sandwiched between them. Thickness and width profiles and uniform beam length are controlled to change the shear and rotational stiffnesses of the phononic beam, changing the starting and ending frequencies of the first band gap. By identifying the effects of those geometrical parameters on band structures, we determine the parameter values that enable the phononic beam to yield an ultra-broad and ultra-low band gap from 3.6 Hz to 237.9 Hz with a small lattice constant of λ /25. For experimental realization, a finite phononic beam with three unit cells is fabricated by wire electric discharge machining and its displacement transmission is measured through impact hammer tests. Particularly low transmission of -35 dB to -10 dB is observed at the band-gap frequency range. We briefly present ongoing works to enhance the structural robustness of the phononic beam by changing geometrical parameters or material of a thin and narrow part.