On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

This work aims to provide better physical understanding of Bragg band gap effects in continuously periodic corrugated beams for flexural waves. The main outcome is the establishment of original algebraic formulas for the band gap width and central frequency. It is shown that the band gap width and central frequency only depend on a thickness contrast parameter. To do so, a so called two-skins geometry is proposed to approximate the usual solid beam cross section, in order to greatly simplify analytical derivations following the Plane Wave Expansion (PWE) method applied to Euler-Bernoulli theory. Theoretical predictions in the two-skins geometry successfully match the results in the practical case of a solid geometry obtained from both experiments on a beam demonstrator and numerical simulations done by classical PWE (1D Euler and Timoshenko theories) or finite element (3D elasticity theory) methods. The complete set of results is benchmarked in details so that the geometrical approximation is validated and the algebraic formulas are usable as design tools of such notch filters. Moreover, flexural and longitudinal motion coupling due to the non-symmetrical thickness profile of the demonstrators leads to an additional band gap that is experimentally identified. A numerical study illustrates the resulting double filtering effect. Potential applications of the background provided by this work can concern Noise, Vibration and Harshness (NVH) engineering, for which meta-materials can be very relevant especially when structure lightening is required. (C) 2019 Elsevier Ltd. All rights reserved.