Multi-flexural band gaps in an Euler-Bernoulli beam with lateral local resonators

Flexural vibration suppression in an Euler-Bernoulli beam with attached lateral local resonators (LLR) is studied theoretically and numerically. Hamilton's principle and Bloch's theorem are employed to derive the dispersion relation which reveals that two band gaps are generated. Within both band gaps, the flexural waves are partially transformed into longitudinal waves through a four-link-mechanism and totally blocked. The band gaps can be flexibly tuned by changing the geometry parameter of the four-link-mechanism and the spring constants of the resonators. Frequency response function (FRF) from finite element analysis via commercial software of ANSYS shows large flexural wave attenuation within the band gaps and the effect of damping from the LLR substructures which helps smooth and lower the response peaks at the sacrifice of the band gap effect. The existence of the multi-flexural band gaps can be exploited for the design of flexural vibration control of beams.