Stop Band Analytical Design for Flexural Waves in Periodic Continuously Corrugated Beam

The use of meta-materials leads to very efficient techniques for mitigating structural vibrations. Stop band can be created by designing the structure as a periodic distribution of a unit cell. Then, the overall mitigation frequency template can be tuned from a careful setting of the geometrical and mechanical properties of the unit cell. This work focuses on the relation between the Bragg stop band bandwidth and central frequency and the parameters settings of a continuously periodic corrugated beam manufactured from a uniform material. The main goal is to provide original, simple and cost effective tools for the design of cut-band structural waveguide filters. In the case of a ideal geometrical case, a Plane Wave Expansion (PWE) model in the framework of Euler-Bernoulli assumptions aims to derive analytical relations for the first Bragg stop band bandwidth and central frequency. Theoretical prediction are well confirmed by experimental dispersion curves obtained on a sample beam representative of the ideal case. FEM numerical simulations (3D elasticity) are also performed to analyse a second stop band due to in- and out-of-plane wave coupling that can be suitable for vibration mitigation in architected structural waveguides.