Phononic Crystals and elastic mechanical metamaterials have shown some unusual light and mechanical wave manipulating properties. These novel structure-type materials are also finding extensive use in energy harvesting as well as vibration control and attenuation. Phononic Crystals are mechanical metamaterials which are composites of two or more linear elastic materials of different mechanical properties, having vibration energy propagation inhibition over certain range of frequencies. These are called phonic band gaps, whose presence essentially signifies the reduction of flow of phonons in the form of elastic wave energy. Phononic crystals are generally constructed with some periodicity in geometry or boundary so that they are lightweight with a choice of tailoring their mechanical and dynamic properties. Some three dimensional recently developed phononic crystals with Acoustic Black Holes (ABH) also show flexural wave energy localisation inside a structure.
The present study concerns with the finding of wave energy localisation in an elliptic ABH engraved square periodic plate and the generation of locally resonant dispersion curves. Flexural band gaps are observed from the displacement component plots of the structure after simulation. The square periodic plate was next studied with extended external beam surfaces with added masses on the beams. The dispersion curves were plotted and the displacement component plots show torsional wave propagation modes. Now these two structures were combined to form a novel structure comprising of an elliptic ABH engraved square periodic plate with extended beams with masses on them. Coupled bending and torsional band gaps are seen in the structure. The displacement components show attenuation of vibration in torsion as well as flexure.
The numerical analysis was done using Comsol Multiphysics for all the three cases. The elliptic ABH plate is made of Structural Steel, for the torsion and coupled flexure-torsion cases, the plate and beams are made of Aluminium and the masses on the extended beams are made of structural steel. Floquet Theory was used for the Periodic Boundary Condition 1-D and the natural frequencies are found out for each type of unit cell. The frequencies are next swept along the reduced wave vector space to get the dispersion diagram for each unit cell, which show a complete band gap for the flexure case (around 2.5 kHz to 2.7 kHz) and the coupled flexure-torsion case (around 4 kHz to 4.4 kHz). These band gaps are mainly due to the local resonance feature of the unit cells, and was absent in the torsion unit cell. Next, a cantilver beam is constructed with each unit cell. A frequency domain analysis is performed in Comsol and the displacement, velocity and mean-square velocity transmissibility are next plotted in MATLAB for an input point at the mid-point of loaded edge and output point at the mid-point of periodic edge near the fixed edge. Beams are studied with 3, 5, 7 and 10 unit cells 

Coupled Flexural and Torsional Vibration Attenuation With Acoustic Black Hole Metamaterial

<p>Elastic metamaterials are architected structures that have constitutive properties not commonly found in nature. By tailoring such properties, elastic metamaterials have the ability of mitigating elastic waves generated by, for instance, impact waves. The first models of elastic metamaterials for impact wave attenuation were based on the concept of negative effective mass density. Such unique property was obtained by mass-spring dissipative systems containing one or more internal resonators. The stop band frequency obtained in such systems depends on the number of resonators involved in the design. Several researches have reported high performance of mass-spring dissipative systems for attenuation of impact waves. However, their fabrication is still a complex issue, because of the internal geometry and the use of different materials. Furthermore, the band gap produced by the mass-spring system corresponds to a narrow range of frequencies, which requires adding more internal resonators to increase the bandwidth limitation.</p><p>This work proposes an elastic metamaterial for absorbing energy from impact waves. The mechanism behind such design is equivalent to a mass-spring dissipative system. However, instead of using multiple materials representing each component, we design a structure made of a single material. Such structure is composed by internal structures whose geometric parameters are chosen to perform the same functionality of the mass-spring system. The stop band average frequency is defined by geometric parameters, which allows tailoring the metamaterial for different applications. Finite Element Analysis is performed to obtain the band structure and the transmissibility of the elastic metamaterial as a function of the geometric parameters. A series of numerical simulations is conducted to evaluate the impact wave mitigation behavior. The proposed metamaterial is verified by comparing its outcomes with those obtained by the equivalent mass-spring system. The findings of this work contribute to increasing the performance of protective structures in reducing the effect of impact waves.</p>

Single Phased Elastic Metamaterials for Wave Filtering

Paper Proceedings: https://asmedigitalcollection.asme.org/SMASIS/SMASIS2021/volume/85499

ASME 2021 Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS2021)

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