Multi-low-frequency flexural wave attenuation in Euler-Bernoulli beams using local resonators containing negative-stiffness mechanisms

Multi-low-frequency band gaps for flexural waves in beams are realized by using multiple resonators containing negative-stiffness (NS) mechanisms in one unit cell. The resonator is constructed by a vertical spring connecting with two oblique springs, which act as an NS mechanism to counteract the stiffness of the vertical spring, and thus substantially lower the stiffness of the resonator. The band structures of flexural waves in a locally resonant beam are revealed by using the plane wave expansion method, which are validated by numerical simulations. A stop band seamlessly blending attenuation band and complex band is observed, which presents a wide band gap. The band gap can be further broadened by adding more resonators into the unit cell with resonant frequencies surrounding the target frequency by a proper off-set ratio. Finally, an application of this proposed method is demonstrated in attenuating vibrations in a raft beam excited by two forces with different low frequencies, by assigning multi-low-frequency band gaps of receptances at the excitation frequencies.