FIG 1 - uploaded by Chenchen Liu
Content may be subject to copyright.
(a) Elastic metamaterial with PDMS frame and both L1 and L2 insets. (b) Side profile of the elastic metamaterial (c) L1 inset. (d) L2 inset.
Source publication
Though additive manufacturing and novel optimization techniques have led to many recent advances in elastic metamaterials, difficult fundamental challenges (e.g., narrow bandgaps) and practical challenges (e.g., dissipation and friction) remain. This work introduces simple and hierarchical resonant metamaterials made of soft polydimethylsiloxane ru...
Contexts in source publication
Context 1
... elastic metamaterials include a "frame" with a rectangular grid of square unit pockets and steel insets connected to the former with slender PDMS beams. The resulting structures are depicted in Figs. 1(a) and 1(b) for the case of a PDMS frame and Fig. 14 for an epoxy frame. We remark that more unit cells usually means better wave attenuation performance but achieving this effect using the least number of unit cells possible (i.e., with a compact structure) is attractive for real world ...
Context 2
... details of the computational domain used to model the metamaterial are depicted in Fig. 15 for Configuration 2. Its dimensions are directly obtained from the experimental sample, with the exception of the beams. These are idealized as two sets of identical rectangles for the L1 and L2 units, with thicknesses chosen to match their measured average effective stiffness in the longitudinal direction (3250 N/m and 2840 N/m, ...
Context 3
... signs seen in the TL curves from the purely elastic model in Fig. 5 (deeper and narrower bandgaps, enhanced transmission peaks, and low estimates for bandgap frequencies) indicate that viscoelastic effects play a large role in the experimental results. Using Models 1 and 2 as described in Sec. III for the constitutive relation of the PDMS phase, Fig. 10 shows the TL results after adding viscoelasticity to the numerical model in Configurations 1, 2, and 3. Compared to the completely elastic model, the addition of viscoelasticity causes bandgaps to shift to higher frequency, reduce their depth, and increase their widths, in greater agreement with the experimental results. The observed ...
Context 4
... studies 9 and can be intuitively understood from the massspring model in Fig. 4. Indeed, for the limiting cases of zero and infinite damping coefficient, the effective stiffness of the SLS element of the resonator ranges between k r 0 and k r 0 þ k r 1 , respectively, and is thus always increased by the addition of Maxwell arms. The results of Fig. 10 also depict locations and widths of the first bandgap in all configurations that are very close to each other for Models 1 and 2. This, therefore, indicates that the experimentally available DMA data are sufficient for such purposes. We recall that both Model 1 and 2 match the experimental storage and loss modulus data in the lower ...
Context 5
... detailed comparison between the TL curves in Fig. 5 with the purely elastic model and those of Fig. 10 with viscoelastic constitutive relation further shows that the bandgap widening effect of viscoelasticity is useful for combining bandgaps in multiresonant structures. More specifically, Configuration 3, where L2 insets are added to every odd column (i.e., it is a combination of Configurations 1 and 2), clearly depicts three bandgaps ...
Context 6
... is a combination of Configurations 1 and 2), clearly depicts three bandgaps in Fig. 5(c), at frequencies that are consistent with the bandgap of the single resonator in Configuration 1 and the two bandgaps of the hierarchical design in Configuration 2. With the addition of viscoelasticity, the first two bandgaps of Configuration 3 merge, as shown Fig. 10(c). This results in an ultrabroad low-frequency bandgap, in strong agreement with the experimental TL ...
Context 7
... we seek to understand the role of external dissipation (friction) on the TL curves, for which time-dependent simulations are performed with Coulomb friction applied to the resonators. The results are shown in Fig. 11, where it is observed that friction further reduces the depth of some of the bandgaps, though this behavior does not appear to be monotonic throughout the whole frequency range examined. Yet, contrary to what occurs with viscoelasticity, frictional effects do not seem to increase or shift the range of bandgap frequencies (to this we ...
Context 8
... the range of bandgap frequencies (to this we remark that care needs to be taken when choosing the time step in the numerical simulations with friction and that a too large time step may artificially induce a shift in the bandgap frequency). A fully analogous effect is observed when including friction in the one dimensional mass-spring-model of Fig. 4. In Fig. 12, the elastic case with no dissipation is shown for reference along with the results for three friction coefficients. As seen, the attenuation effect within the bandgap is greatly reduced with friction and this effect monotonically increases with the friction coefficient. Again, no shift of the bandgap frequency is observed with the ...
Context 9
... better understand the effects of beam stochasticity on the TL diagram for Configuration 1, we examine two cases, both using the viscoelastic Model 1. The first, shown in Fig. 13, considers that each of the four beams have random beam widths drawn from a Gaussian distribution, with 10% and 20% of the beam width as the standard deviation for subfigures (a) and (b), respectively. In either case, the variability on the TL curve is not found to be significant as compared to the deterministic case, and only a mild ...
Context 10
... (mixture of Hexion Epon TM 828 and its cross-linker Epikure TM 3223 in weight ratio of 3:1) was injected into the PDMS outline and subsequently cross-linked at 60 C for 2 h. The steel parts, with masses of 8.5 g and 9.8 g for the L1 and L2 insets, respectively, were then inserted manually at the desired locations. The completed sample is shown in Fig. 1 for the PDMS frame and Fig. 14 for the epoxy ...
Context 11
... and its cross-linker Epikure TM 3223 in weight ratio of 3:1) was injected into the PDMS outline and subsequently cross-linked at 60 C for 2 h. The steel parts, with masses of 8.5 g and 9.8 g for the L1 and L2 insets, respectively, were then inserted manually at the desired locations. The completed sample is shown in Fig. 1 for the PDMS frame and Fig. 14 for the epoxy ...
Similar publications
In order to study the waterproof performance of elastic rubber gasket in shield tunnel lining joints, an innovative sensitivity analysis method is proposed by combining the Monte Carlo method with the stochastic finite element method (FEM) in this paper. The sensitivity values of the waterproof performance respecting to elastic rubber gaskets are o...
Citations
... The inertial amplification mechanism often needs external moving components to amplify the effective inertia of the small mass [17], which limits the application range of the principle. While using a locally resonant structure, we just need to lower the stiffness of the resonator to obtain a low-frequency bandgap [14,[18][19][20]. As for broadband tunability of the bandgap, active [15,21], semi-active [22][23][24][25], and passive control [19,26] are some recently developed strategies. ...
Mechanical metamaterials with low-frequency and broadband bandgaps have great potential for elastic wave control. Inspired by the ancient window mullions, a novel plate-type metamaterial with a two-dimensional bandgap is designed. Based on the local resonance mechanism, the broadband low-frequency in-plane and out-of-plane bandgaps on the designed structure are realized. The bandgaps can be adjusted by the mass re-distribution of the main-slave resonators, the stiffness design of the support beam, and the adjustment of the excitation amplitude. A semi-analytical method is proposed to calculate the in-plane and out-of-plane bandgaps and the corresponding wave attenuation characteristics of the infinite periodic metamaterial, and we explored how mass re-distribution, stiffness changes, and geometric nonlinearity influence the bandgap. Then, to verify the conclusions, we fabricated a finite periodic structure and obtained its wave transmission characteristics both numerically and experimentally. Finally, the designed metamaterial is applied to the waveguide control, elastic wave imaging, and vibration isolation. This study may provide new ideas for structural design and engineering applications of mechanical metamaterials.
... Recently, the use of metamaterials in MRI has been shown to improve its measurement sensitivity, RF transmission efficiency, and decoupling between the individual coils in a multicoil array [13][14][15][16][17][18][19]. Metamaterials and artificial materials represent a novel group of structures, which can be deployed to control electromagnetic wave propagation [14]. ...
... Recently, the use of metamaterials in MRI has been shown to improve its measurement sensitivity, RF transmission efficiency, and decoupling between the individual coils in a multicoil array [13][14][15][16][17][18][19]. Metamaterials and artificial materials represent a novel group of structures, which can be deployed to control electromagnetic wave propagation [14]. Metamaterials can efficiently redistribute the magnetic fields generated by the existing RF coils, thus enhancing the signal in the regions with lower signal strength and improving RF field homogeneity [15]. ...
Magnetic resonance imaging (MRI) is a widely used clinical diagnostic tool, which is based on the principle of nuclear magnetic resonance of hydrogen atoms in human body. The Larmor frequency of precession of the hydrogen atoms is determined by the strength of static magnetic field (B 0) of MRI. A higher B 0 can directly improve signal-to-noise ratio (SNR) of MRI. But this method involves expensive hardware installation, which could have adverse effect of tissue-heating and make MRI unsafe for patients with medical implants. Hence, efforts have been made to increase the SNR of MRI without increasing B 0. An effective solution in this direction would be to boost the radiofrequency (RF) magnetic fields emitted by the body part undergoing scan, particularly by using metamaterials. The higher the received RF signal strength, the greater the SNR of MRI. For a metamaterial to be used as an 'add-on' in commercial scanners, its dimensions need to be designed appropriately so that it fits in the available gap between the transceiver coil and the human body. In this article, a 10-mm-thick metallo-dielectric metamaterial is designed by stacking of alternate square-shaped capacitive patches and inductive apertures for enhancing the RF magnetic flux density and hence, the SNR of a 1.5T MRI system. The inter-layer electromagnetic coupling in the stacked structure is deployed for spatial localization of magnetic fields at the resonant frequency (~64 MHz) which is equal to the Larmor frequency of 1.5T MRI. An equivalent circuit model, comprising a lumped-element third order bandpass filter, validated the transmissivity characteristics of the metamaterial obtained using full-wave simulations. Magnetic flux density enhancement by a factor of 55 is obtained when the metamaterial add-on is placed between a surface coil and a bio-model of human head.
3D printing defects are often used to explain the mismatch between numerical predictions and experimental results of additively manufactured acoustic materials. Although they are often perceived as desirable, as in most cases, they improve the absorptive behaviour of the system, occurring gains are unplanned and uncontrollable. Among different 3D printing inaccuracies, surface roughness provides additional acoustic losses, mostly due to the enlargement of the boundary layer thickness. On the other hand, roughness is responsible for the shift of the operating frequency compared to the numerical predictions. The goal of this research is to provide efficient modelling methods to capture the effects of surface roughness arising from the additive manufacturing process. First, a direct modelling method will be discussed, which can be computationally expensive as it relies on an accurate geometrical representation of surface roughness. Second, an alternative indirect modelling approach will be presented, which mimics the presence of roughness by adjusting specific air parameters in the locations of interest of the smooth geometry to reduce the computational cost. The two strategies will be compared with each other and to the results of an experiment where additional roughness is added to target locations within the design.
The acoustic metamaterial is a class of artificial structures designed to transmit, prohibit, or trap and amplify vibration waves at certain frequencies by periodically manipulating the physical parameters such as modulus, density and chirality. Compared to the traditional phononic crystals with the fixed configuration of periodic multi-materials or geometric structures, a novel design with homogenous temperature-sensitive material will probably embody the advantages in both fabricability and tunability. To concrete and validate this design concept, a thin plate merely adopting homogenous thermo-sensitive epoxy resin is presented as an illustration in this research. By periodically distributing the heating source in a particular shape, a periodic thermal field can be induced and further naturally elicits a periodic distribution of Young's modulus. The thermal diffusion effect and nearly power-law-decreasing modulus-temperature relation give rise to a concentric circular distribution of Young's modulus, which transforms the homogenous plate into a novel gradient metamaterial plate. The transmitting and prohibiting effect in wave propagation is validated for both longitudinal and bending vibration waves by theoretical modeling and finite element analysis (FEA). Further research shows that the vibration band gaps can be significantly tuned in both frequency and bandwidth by the power density and configuration of the heat source. The longitudinal vibration band gaps indicate attenuation with the larger high-temperature region; nevertheless, the widest bending vibration band gaps are not monotonically changing. Additionally, the frequencies in both vibration modes decrease with the increasing thermal field. This research explores a novel construction concept for the periodic metamaterial plate by homogenous smart material, which may present more possibilities with the development of multi stimulus responsive smart materials and the physical field application technologies in the future.
PurposeUnderstanding the mechanical properties of current pessaries is important to improve on existing designs and innovate on novel solutions. Our objective was to mechanically characterize the force required to compress ring pessaries into a folded shape. We hypothesized that the force required to fold ring pessaries would scale inversely with the diameter squared.Methods
We conducted a compression test on ring pessaries to analyze their folding behavior using a mechanical universal testing system. Ring pessaries size #1 through #7 (diameters 50.1–86.7 mm) were placed in the testing platform in a vertical orientation with the bending axis in the horizontal plane. An axial load was applied to induce deformation.ResultsWith application of an axial force, all pessaries first showed in-plane deformation followed by out-of-plane buckling. Increasing force resulted in a transition between in-plane deformation and out-of-plane buckling, during which the pessary began to fold, analogous to classic Euler buckling of columns. This transition was reflected in the loading curve as a sharp change in slope between the initial strain-softening region and a subsequent nearly horizontal plateau region. The force at the transition point ranged from 4.4 N for a size #7 pessary to 23.5 N for a size #1 pessary. The relationship between force and diameter at the transition point appeared to approximate a 1/L2 dependence, where L is the pessary diameter.Conclusions
Pessary mechanics show buckling and folding behavior with a dependence on pessary architecture. The force required to fold ring pessaries scales inversely with the pessary diameter squared.
