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In this paper, flexural vibration in a locally-resonant (LR) beam with periodically attached separated force and moment beam-like resonators is investigated theoretically and experimentally. The relationship between the distance parameter and the band structure of an Euler-Bernoulli beam with proposed locally resonators is provided using the transfer matrix theory. The frequency response functions of finite periodic systems are calculated with the finite element method over a range of different parameters of the resonators. Finally, we use LR beam specimens with separated force and moment resonators mounted on a free-free host beam for experimental measurements of the vibration transmittance. The experimental results show a good agreement with those of the theoretical and numerical except some small discrepancies at high frequencies. Our study confirms that the bandwidth of band-gaps will become wider with the increasing of the distance parameter until it reaches its peak, which provides an effective way for LR periodic structures with resonators to obtain broad band-gaps in low-frequency range, and makes the structure had potential applications in the control of vibration and wave propagation in flexural beams.

A vibration energy harvesting generator was studied in the present research using point-defect phononic crystal with piezoelectric material. By removing a rod from a perfect phononic crystal, a resonant cavity was formed. The elastic waves in the range of gap frequencies were all forbidden in any direction, while the waves with resonant frequency were localized and enhanced in the resonant cavity. The collected vibration energy was converted into electric energy by putting a polyvinylidene fluoride film in the middle of the defect. This structure can be used to simultaneously realize both vibration damping and broad-distributed vibration energy harvesting.