Longitudinal vibration wave in the composite elastic metamaterials containing Bragg structure and local resonator

In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.