Abstract
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.
Highlights
Meta-materials are extensively studied for the last decades in many fields of wave physics for their attractive ability to control unusual wave propagation properties [1, 2, 3]
This article reports a detailed analysis of the Bragg band gap exhibited in a continuously periodic corrugated beam in order to provide better physical understanding of such vibration filters.The analysis consists firstly in establishing an analytical model of the band gap, secondly in studying beam demonstrators using 3 complementary numerical approaches and an experimental characterization
The main outcome is the establishment of analytical formulas of the band gap width and central frequency obtained for a so-called two-skins geometry chosen in order to simplify Plane Wave Expansion (PWE) derivations
Summary
Meta-materials are extensively studied for the last decades in many fields of wave physics for their attractive ability to control unusual wave propagation properties [1, 2, 3] In most cases they are designed as periodic and/or locally resonant propagation media from which typical applications concern wave filtering, guiding, lensing and cloaking. A main challenge is to reach attractive mitigation performances even in the low frequency range for which the wavelength and the finite size of the structure of interest are in the same range. Another challenge is to achieve to tune band gaps location and bandwidth to match an expected mitigation template corresponding to a given application. A particular attention is paid to flexural waves because of their major contribution to the structure born sound
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