Design guidelines for flexural wave attenuation of slender beams with local resonators

The complex band structures and attenuation spectra of flexural waves in slender beams with periodically mounted local resonators are investigated with transfer matrix method. It is noteworthy that the frequency range and attenuation coefficient of the locally resonant gap become larger in complex band structures if larger resonators were used. But given the total add-on mass of resonators, the attenuation spectra of finite beams with large but few resonators do not demonstrate such phenomena because the attenuation needs several periods to establish. So with the view of application, a large number of small local resonators widely spread along the beam are preferred given the total add-on mass to the beam.