Lumped mass model of a 1D metastructure for vibration suppression with no additional mass

Abstract

The article examines the effectiveness of metastructures for vibration suppression from a weight standpoint. Metastructures, a metamaterial inspired concept, are structures with distributed vibration absorbers. In automotive and aerospace industries, it is critical to have low levels of vibrations while also using lightweight materials. Previous work has shown that metastructures are effective at mitigating vibrations, but do not consider the effects of mass. This work takes mass into consideration by comparing a structure with vibration absorbers to a structure of equal mass with no absorbers. These structurers are modeled as one-dimensional lumped mass models, chosen for simplicity. Results compare both the steady-state and the transient responses. As a quantitative performance measure, the ! norm, which is related to the area under the frequency response function, is calculated and compared for both the metastructure and the baseline structure. These results show that it is possible to obtain a favorable vibration response without adding additional mass to the structure. Additionally, the performance measure is utilized to optimize the geometry of the structure, determine the optimal ratio of mass in the absorber to mass of the host structure, and determine the frequencies of the absorbers. The trends from this model are replicated using previous experimental results.

Expanding the teaching of single frequency vibration absorption to broadband attenuation using subordinate oscillator arrays via fettuccine pasta

“…In such a scenario, a new peak is introduced in the frequency response function of the host structure. For instance, an untuned fettuccine strand of 8 in has natural frequency around 8.5Hz, which does not lie in the two frequency bandwidths of interest [ 4-5.5 ] Hz and [12][13][14] Hz. Due to the low mass-ratio as well the fact that the natural frequency of the substructure is significantly different from that of the host, the frequency corresponding to the induced peak can be considered as a good approximation of the substructure's natural frequency.…”

“…It should also be noted that the novel concepts of meta-structures can also be explained via this very simple example. For instance, Inman et al develop a set of meta-structures in [13] that are simply a more sophisticated approach to the same concept. Although meta-structures can be elusive for entry level teaching and classes, an example such as this can relate the simple concepts of DVA and extend As a part of this goal, SOAs are developed using non-conventional, yet mundane materials such as fettuccine and modeling clay.…”

Exploring the dynamics of hourglass shaped lattice metastructures

“…Encouraged by the development of the tunable metamaterials, metastructures have emerged with excellent wave absorption abilities as well as stiffness-to-weight ratio 3 , 11 , 12 . It is well proven that the tailoring of geometric and elastic properties of the building blocks of the metastructures could tune its wave behavior 13 , 14 .…”

Wave propagation in tunable lightweight tensegrity metastructure

“…Metastructure, as a metamaterial inspired concept, has recently emerged to refer to a structure-like periodic material system with excellent wave absorption abilities and stiffness-to-weight ratio (Hussein, et al, 2014;Reichl and Inman, 2017). Hussein, et al, (2014) introduces metastructure as an emerging research field involving vibration/acoustic engineering and condense matter physics.…”

“…Hussein, et al, (2014) introduces metastructure as an emerging research field involving vibration/acoustic engineering and condense matter physics. Reichl and Inman (2017) emphasized on the lightweight and vibration absorption abilities of the metastructure with optimized microstructure geometries. Although tailoring the geometric and elastic properties of the metastructure's building blocks could tune its wave behavior (Liu, et al, 2011;Zhu, et al, 2011), a broadband design still requires additional unit cells (Zhu, et al, 2014) which inevitably increase the overall weight of the engineering structure.…”