Mechanical low-frequency filter via modes separation in 3D periodic structures

Abstract

This work presents a strategy to design three-dimensional elastic periodic structures endowed with complete bandgaps, the first of which is ultra-wide, where the top limits of the first two bandgaps are overstepped in terms of wave transmission in the finite structure. Thus, subsequent bandgaps are merged, approaching the behaviour of a three-dimensional low-pass mechanical filter. This result relies on a proper organization of the modal characteristics, and it is validated by performing numerical and analytical calculations over the unit cell. A prototype of the analysed layout, made of Nylon by means of additive manufacturing, is experimentally tested to assess the transmission spectrum of the finite structure, obtaining good agreement with numerical predictions. The presented strategy paves the way for the development of a class of periodic structures to be used in robust and reliable wave attenuation over a wide frequency band.

3D auxetic single material periodic structure with ultra-wide tunable bandgap

“…The non dimensional frequency f nd is defined as the ratio between the product of the frequency f and the unit cell dimension a and the sound velocity in the material with E and ρ the Young’s modulus and the density of the material, respectively. The low level of the frequency that opens the bandgap is in agreement with the results of a previous study 15 , that is referred to a structure with a similar dyamic behavior, basically governed by modes separation. In the present case, the mode that defines the bottom limit of this bandgap is located in the symmetry point R and is characterised by the rigid rotation of the masses with respect to the principal axis of each ellipsoide and by the consequent flexural-torsional deformation of the elastic connections.…”

“…In this work, a 3D single-phase PnC structure endowed with ultra-wide complete 3D bandgaps is proposed. The tunability of the first bandgap is obtained by exploiting the negative Poisson’s ratio of its unit cells, whose topology is a mix of oustanding PnC properties 15 and 3D-extension of the results of a proper topology optimization on the auxetic behaviour 42 , 43 . In the first part of the paper, numerical simulations are adopted to prove the bangap tuning as a strict consequence of the expansion in all the orthogonal directions of the auxetic unit cell.…”

Bandgap engineering of three-dimensional phononic crystals in a simple cubic lattice

“…With a beam thickness similar to our design, gap widths reach values as high as 132% 32 and 159%. 34 These results confirm the approach of optimized spheres connected by thin beams to converge to the theoretical maximum gap to mid-gap ratio of 200%.…”

“…31 This has allowed ultra-wide phononic bandgap materials, 32,33 with previously unattainable bandwidths. 34 Most experimental works focus on one unit cell design and variations to characteristic dimensions. We present a comprehensive theoretical and experimental comparison of different unit cell geometries arranged in a simple cubic lattice to illustrate this avenue of utilizing complex 3D designs for precise engineering of desired phononic bandgap characteristics over an ultrawide frequency range.…”

Experimental and numerical evidence of comparable levels of attenuation in periodic and a-periodic metastructures

“…The intrinsic nature of the bandgap in elastic metamaterials without a significant impedance mismatch has been demonstrated to rely on modal separation. 18,19 The unit cell is able to exploit frequency gaps between low and high frequency modes. For these structures, bandgap maximization through dispersion analysis led to the definition of structures with a reduced number of modes (like a spring-mass chain) within a certain frequency range.…”