Flexural Wave Band Gaps in Phononic Crystal Euler-Bernoulli Beams Using Wave Finite Element and Plane Wave Expansion Methods

<div><p>We investigate theoretically and experimentally the forced response of flexural waves propagating in a 1D phononic crystal (PC) Euler-Bernoulli beam, composed by steel and polyethylene, and its band structure. The finite element, spectral element, wave finite element, wave spectral element, conventional and improved plane wave expansion methods are applied. We demonstrate that the vibration attenuation of the unit cell can be improved choosing correctly the polyethylene and steel quantities and we suggest the best percentages of these materials, considering different unit cell lengths. An experiment with a 1D PC beam is proposed and the numerical results can localize the band gap position and width close to the experimental results. A small Bragg-type band gap with low attenuation is observed between 405 Hz - 720 Hz. The 1D PC beam with unit cells of steel and polyethylene presents potential application for vibration control.</p>