Band-Gap Properties of Finite Locally Resonant Beam Suspended Periodically with Two-Degree-of-Freedom Force Type Resonators - Hangyuan Lv; Shangjie Li; Xianzhen Huang; Zhongliang Yu (Crystals, 2021)
The propagation properties of waves in finite Timoshenko locally resonant (LR) beams resting on forced vibrations and periodically attached two-degree-of-freedom force-type resonators are studied by the wave-based analysis approach. By calculating the motion equations of the beam, the transmission and reflection matrices of waves at the resonator attached point are first derived, and the forced vibration response of the finite periodic beam is deduced by the wave-based approach. Several examples are also analyzed by the finite element method to verify the high accuracy of the developed wave-based analysis approach. Numerical results show that wider low-frequency band-gaps exist in this type of LR beams. It was also found that the resonator masses and spring stiffnesses caused different effects on the band-gap properties of the combined LR beam. The desired band-gap widths of the LR beam can be tuned by adjusting the mass blocks and spring stiffness in the resonators based on the results.