Flexural Wave Band Gaps in a 1D Phononic Crystal Beam

The forced response of flexural waves propagating in a 1D phononic crystal (PC) beam and its band structure are investigated theoretically and experimentally. PC beam unit cell is composed by steel and polyethylene. The study is performed by using six methods, finite element (FE), spectral element (SE), wave finite element (WFE), wave spectral element (WSE), conventional plane wave expansion (CPWE) and improved plane wave expansion (IPWE). Simulated examples of a 1D PC beam considering unit cells of different sizes are analyzed. Forced response results are presented in the form of displacement, transmittance and receptance, and the elastic band structure is investigated using its real and imaginary (attenuation) parts. Numerical and analytical results of all approaches are in a good agreement, except by WFE and FE numerical results in high frequencies. The effect of the amounts of polyethylene on the attenuation constant is studied. Depending on the application, choosing polyethylene quantity correctly is not simple, because it is related to the unit cell size and in which frequency the band gap is opened up. An experiment with a 1D PC beam is proposed and numerical and analytical 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 and 720 Hz. The 1D PC beam with unit cells of steel and polyethylene presents potential application for vibration control.