Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom

Abstract

Using the transfer matrix theory, we provided the band structure of flexural waves in an Euler-Bernoulli beam with locally resonant structures, with two degrees of freedom, i.e., a resonator with vertical and rotational vibration. The frequency response function of a finite periodic system was calculated by the finite element method. The material damping of rubber makes the gaps wider in the calculation. These theoretical results show a good agreement with those of the experiment. The measured result provides an attenuation of over $20\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ in the frequency range of the band gaps. The existence of low-frequency band gaps in such a beam provides a method of flexural vibration control of beams.