Realization of low-frequency stop band in Timoshenko beam with periodic IDVAs

Abstract

The most prominent dynamic characteristic of metamaterials is that they possess the frequency pass bands and band gaps. In the bandgap, the elastic waves will attenuate significantly, and this property is potentially used to control low-frequency vibrations in civil engineering. To open the low-frequency bandgap of the Timoshenko beam, inerter-based dynamic vibration absorbers (IDVAs) are arranged periodically in the beam. An analytical methodology based on transfer matrix method was developed to predict the flexural wave dispersion characteristics, and was validated by test and numerical experiments. The band gaps can be simultaneously tuned by the parameters of the IDVAs, including spring stiffness, inertance and attached mass. Moreover, the band gaps generated by single IDVAs are independent of each other, and a super-wide bandgap can be achieved by splicing the band gaps for metamaterial beams with graded IDVAs. Explicit formulas with respect to the parameters of IDVAs have been developed to determine the condition of bandgap merging, which can broaden the bandwidth effectively. Finally, a computer-based program was presented to determine the reasonable design parameters.