Dynamics of metamaterial beams consisting of periodically-coupled parallel flexural elements: a theoretical study

Abstract

Periodic systems have attracted a lot of attention in science and engineering due to the existence of band gaps in their frequency spectra. Here, we study the exural wave propagation in beams that are periodically connected in parallel and investigate how the contrast in the material and cross-sectional properties may aect the band structure of these systems and their dispersion properties. Results suggest that by changing the mass and stiness ratios of the two beams, or by changing the inter-beam connection compliance, several band gaps may emerge and that the band gap width, the lowest band gap edge frequency, as well as the nature of attenuation within the gap may be tuned. Furthermore, by considering a hierarchical system of periodically-connected beam elements with dierent unit cell sizes, we show how the interplay between scales may aect the overall dispersion properties of the system by opening and closing band gaps at dierent frequencies. These ndings suggest that a modular design approach may lead to novel dispersion properties in beam structures. Finally, using a Frequency Response Function approach, we show that the aforementioned results hold in the limit of nite structures.

Flexural waves in a periodic non-uniform Euler-Bernoulli beam: Analysis for arbitrary contour profiles and applications to wave control

“…The deflection in the unit cell can be expressed in the form of Eq. ( 6), and the Bloch theorem requires [45][46][47][48][49][50]…”

Tuning of topological interface modes in an elastic beam array system with inerters

“…The majority of studies are limited to the wave propagation analysis of simple sandwich beams with softcore [46] or rigidly connected through periodically distributed ribs [47]. When more complex multiple coupled structures systems are considered, the analyses are mostly limited to dynamic studies of systems with multiple coupled beams [48] or plates [49] through discrete elastic or viscoelastic medium.…”

Scattering under Linear Non Self-Adjoint Operators: Case of in-Plane Elastic Waves

“…There has been considerable recent research interest in the field of wave propagation through periodic structures under the fields of photonics, phononics, and metamaterials [1][2][3][4][5][6][7][8][9][10][11] . Irrespective of the different properties which metamaterials research in different fields target, the end goal is the same: to design composite materials for the fine-tuned, predominantly frequency-dependent control of the trajectory and dissipation characteristics of waves [12][13][14] .…”