Limits...
Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials

View Article: PubMed Central - PubMed

ABSTRACT

Elastic waves exhibit rich polarization characteristics absent in acoustic and electromagnetic waves. By designing a solid elastic metamaterial based on three-dimensional anisotropic locally resonant units, here we experimentally demonstrate polarization bandgaps together with exotic properties such as ‘fluid-like' elasticity. We construct elastic rods with unusual vibrational properties, which we denote as ‘meta-rods'. By measuring the vibrational responses under flexural, longitudinal and torsional excitations, we find that each vibration mode can be selectively suppressed. In particular, we observe in a finite frequency regime that all flexural vibrations are forbidden, whereas longitudinal vibration is allowed—a unique property of fluids. In another case, the torsional vibration can be suppressed significantly. The experimental results are well interpreted by band structure analysis, as well as effective media with indefinite mass density and negative moment of inertia. Our work opens an approach to efficiently separate and control elastic waves of different polarizations in fully solid structures.

No MeSH data available.


Related in: MedlinePlus

Torsional response and negative effective moment of inertia.The response function is defined as the ratio of the amplitudes of tangential accelerations at two ends of the sample, with rotational actuation situated at the top the sample (Fig. 3c). The measured (orange markers) and simulated response functions (orange solid curves) are plotted in a as functions of frequency (left axis). A bandgap is seen near 1.3–1.6 kHz. The calculated effective moment of inertia Ix is shown in orange dashed curves (right axis). It is seen that Ix turns negative inside the bandgap. Inset shows a drawing of the sample-kx. (b) Shows the simulated displacement profile of the sample-kx at the lower gap edge (1.3 kHz), inside the bandgap (1.5 kHz), and at the higher gap edge (1.7 kHz). Here actuation position is on the top of the meta-rod. Black cones indicate the amplitude and direction of the displacement (in logarithmic scales). Colour fields represent the displacement component that is perpendicular to the slicing plane, with red/blue colours representing positive/negative displacement, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5121349&req=5

f5: Torsional response and negative effective moment of inertia.The response function is defined as the ratio of the amplitudes of tangential accelerations at two ends of the sample, with rotational actuation situated at the top the sample (Fig. 3c). The measured (orange markers) and simulated response functions (orange solid curves) are plotted in a as functions of frequency (left axis). A bandgap is seen near 1.3–1.6 kHz. The calculated effective moment of inertia Ix is shown in orange dashed curves (right axis). It is seen that Ix turns negative inside the bandgap. Inset shows a drawing of the sample-kx. (b) Shows the simulated displacement profile of the sample-kx at the lower gap edge (1.3 kHz), inside the bandgap (1.5 kHz), and at the higher gap edge (1.7 kHz). Here actuation position is on the top of the meta-rod. Black cones indicate the amplitude and direction of the displacement (in logarithmic scales). Colour fields represent the displacement component that is perpendicular to the slicing plane, with red/blue colours representing positive/negative displacement, respectively.

Mentions: We choose sample-kx to investigate the effect of RM on torsional vibration. First, the meta-rod's torsional branch can be excited by a dynamic torque about the x axis. The same torque can also trigger RM(x), in which the steel cylinder and epoxy rotate about the x axis in an anti-phase manner. RM(x) is found at 1,646 Hz (Fig. 1c). Similarly, the anti-crossing due to counter-rotating modes (RM(x) and the torsional branch) yields a polaritonic dispersion. Through the torsional branch's linear dispersion signature and the system's rotational displacement profile, this can be identified in the band structure (orange markers, right panel of Fig. 2c). A bandgap for torsional vibration is also highlighted in orange in Fig. 2c. Experimentally, we verify this torsional bandgap by rotational actuation with a set-up shown in Fig. 3c, in which an electric motor is used to apply a torque pulse to the meta-rod. The measured response function indeed confirms the existence of such a bandgap, as shown in Fig. 5a. The measured results show good agreement with numerical simulation.


Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials
Torsional response and negative effective moment of inertia.The response function is defined as the ratio of the amplitudes of tangential accelerations at two ends of the sample, with rotational actuation situated at the top the sample (Fig. 3c). The measured (orange markers) and simulated response functions (orange solid curves) are plotted in a as functions of frequency (left axis). A bandgap is seen near 1.3–1.6 kHz. The calculated effective moment of inertia Ix is shown in orange dashed curves (right axis). It is seen that Ix turns negative inside the bandgap. Inset shows a drawing of the sample-kx. (b) Shows the simulated displacement profile of the sample-kx at the lower gap edge (1.3 kHz), inside the bandgap (1.5 kHz), and at the higher gap edge (1.7 kHz). Here actuation position is on the top of the meta-rod. Black cones indicate the amplitude and direction of the displacement (in logarithmic scales). Colour fields represent the displacement component that is perpendicular to the slicing plane, with red/blue colours representing positive/negative displacement, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121349&req=5

f5: Torsional response and negative effective moment of inertia.The response function is defined as the ratio of the amplitudes of tangential accelerations at two ends of the sample, with rotational actuation situated at the top the sample (Fig. 3c). The measured (orange markers) and simulated response functions (orange solid curves) are plotted in a as functions of frequency (left axis). A bandgap is seen near 1.3–1.6 kHz. The calculated effective moment of inertia Ix is shown in orange dashed curves (right axis). It is seen that Ix turns negative inside the bandgap. Inset shows a drawing of the sample-kx. (b) Shows the simulated displacement profile of the sample-kx at the lower gap edge (1.3 kHz), inside the bandgap (1.5 kHz), and at the higher gap edge (1.7 kHz). Here actuation position is on the top of the meta-rod. Black cones indicate the amplitude and direction of the displacement (in logarithmic scales). Colour fields represent the displacement component that is perpendicular to the slicing plane, with red/blue colours representing positive/negative displacement, respectively.
Mentions: We choose sample-kx to investigate the effect of RM on torsional vibration. First, the meta-rod's torsional branch can be excited by a dynamic torque about the x axis. The same torque can also trigger RM(x), in which the steel cylinder and epoxy rotate about the x axis in an anti-phase manner. RM(x) is found at 1,646 Hz (Fig. 1c). Similarly, the anti-crossing due to counter-rotating modes (RM(x) and the torsional branch) yields a polaritonic dispersion. Through the torsional branch's linear dispersion signature and the system's rotational displacement profile, this can be identified in the band structure (orange markers, right panel of Fig. 2c). A bandgap for torsional vibration is also highlighted in orange in Fig. 2c. Experimentally, we verify this torsional bandgap by rotational actuation with a set-up shown in Fig. 3c, in which an electric motor is used to apply a torque pulse to the meta-rod. The measured response function indeed confirms the existence of such a bandgap, as shown in Fig. 5a. The measured results show good agreement with numerical simulation.

View Article: PubMed Central - PubMed

ABSTRACT

Elastic waves exhibit rich polarization characteristics absent in acoustic and electromagnetic waves. By designing a solid elastic metamaterial based on three-dimensional anisotropic locally resonant units, here we experimentally demonstrate polarization bandgaps together with exotic properties such as ‘fluid-like' elasticity. We construct elastic rods with unusual vibrational properties, which we denote as ‘meta-rods'. By measuring the vibrational responses under flexural, longitudinal and torsional excitations, we find that each vibration mode can be selectively suppressed. In particular, we observe in a finite frequency regime that all flexural vibrations are forbidden, whereas longitudinal vibration is allowed—a unique property of fluids. In another case, the torsional vibration can be suppressed significantly. The experimental results are well interpreted by band structure analysis, as well as effective media with indefinite mass density and negative moment of inertia. Our work opens an approach to efficiently separate and control elastic waves of different polarizations in fully solid structures.

No MeSH data available.


Related in: MedlinePlus