Ultra-low-frequency broadband of a new-type acoustic metamaterial beams with stiffness array

Periodic structures are effective in attenuating waves in a low frequency range at local resonance (LR) conditions, but it is still a challenge to achieve this in a very low frequency range, because the system stability can be damaged due to the excessive quality or the deduction of stiffness. However, the structural stability theory shows that the structural stability is closely related to the support surface; the larger the support surface, the more stable the structure, and thereby the array structure has the feature of maintaining the stability of the system through expanding the support surface. Based on the theoretical principle, a new type of local resonator with stiffness arrays is presented to further lower the band gaps of flexural wave propagation in LR beams, in which the traditional stiffness is equally divided into an array form. Due to the stiffness array connections, the system stiffness is not only reduced to a very low value, but also the stability is still better maintained through expanding the support surface. Meanwhile, the band structures of the LR beams with stiffness array connections, obtained by the finite element method, demonstrate that the lower bound of the band-gap can be successfully decreased more times than that of conventional LR beams under the premise of maintaining the stability of the system, and an ultra-low-frequency broadband of 25-395 Hz is realized. Clearly, the strategy of dividing the traditional stiffness into the stiffness array can successfully realize the low frequency band gap and overcome the shortcomings of the system instability in the traditional method. Therefore, two puzzles of realizing the ultra-low-frequency broadband and simultaneously maintaining the system stability may be successfully resolved through introducing the stiffness arrays into the local resonance system, and the new structures with stiffness arrays could have potential applications for ultra-low-frequency vibration and noise attenuation.