Controllable flexural wave bandgap in extensible metamaterial beams with embedded multiple resonators

The interest in phononic crystals and acoustic metamaterials has been an intensive subject of research in recent years. Finding a robust way to significantly expand or actively control the bandgap has received extensive attention. In this study, we propose a prestressed metamaterial beam attached with multiply local resonators connected by actively tunable piezoelectric springs. The Euler-Bernoulli beam theory and Timoshenko beam theory are applied in the theoretical analysis of the system. Further, the spectral element method is utilized to analytically compute the dispersion relation and transmission ratio and excellent agreement with reference to the benchmark is reported. The influences of an external axial force on the bandgap range and attenuation behavior are further studied. Subsequently, the effect of resonator number and mass on the local resonance bandgap structure is investigated in two parametric studies. The active control of bandgap range and frequency is then verified. By analyzing frequency response function, the tunable transmission ratio of a supercell can be observed. To conclude, this paper not only provides a guideline for designs of wave attenuation with multiple frequency regimes in a one-dimensional system, but it can also be extended to sub-wavelength wave manipulation designs.