In this letter, we discuss a versatile, fully reconfigurable experimental platform for the investigation of phononic phenomena in metamaterial architectures. The approach revolves around the use of 3D laser vibrometry to reconstruct global and local wavefield features in specimens obtained through simple arrangements of LEGO® bricks on a thin baseplate. The agility by which it is possible to reconfigure the brick patterns into a nearly endless spectrum of topologies makes this an effective approach for rapid experimental proof of concept, as well as a powerful didactic tool, in the arena of phononic crystals and metamaterials engineering. We use our platform to provide a compelling visual illustration of important spatial wave manipulation effects (waveguiding and seismic isolation), and to elucidate fundamental dichotomies between Bragg-based and locally resonant bandgap mechanisms.

Over the past two decades, acousto-elastic phononic crystals and metamaterials have received increasing attention due to their unique wave manipulation capabilities. Perhaps, the most well-known property is the ability to open phononic bandgaps,1–5 i.e., frequency intervals of forbidden wave propagation. Another distinctive feature is the frequency-dependent anisotropy (or directivity) observed in their spatial wave patterns6–8 and the ability to feature a negative refractive index.9–11 A number of metamaterial architectures have also been proposed to design acoustic lenses12–14 and attain subwavelength imaging.15–17 

In recent years, the field of phononics has seen a significant increase in the amount of experimental work.18 In the realm of metamaterials design, the need for experiments is pressing on two levels. At the conceptual development stage, it is beneficial to rely on a set of fast and economical, yet accurate experiments to obtain quick proof of concept, or to compare and rank multiple candidate configurations. At the later stages of the process, more precise, ad hoc experiments are required to fully characterize the selected configuration and to verify its actual implementability as a device. For proof of concept, it is often too costly and time consuming to work with specimens fabricated with advanced manufacturing methods, especially when a large number of configurations must be tested; it may be convenient to work with laboratory materials characterized by low cost, fast manufacturing time and high reconfigurability. These attributes are also crucial in the development of prototypes for didactic demonstrations. 3D-printed materials, for example, display many of these characteristics; however, they are typically affected by unreliable mechanical properties and high geometric variability; moreover, their response is often tainted by high levels of damping that are detrimental to the establishment of noise-free wavefields.

Inspired by these considerations, we here explore a versatile platform for rapid verification of phononic phenomena in metamaterial architectures, based on the reversible assembly of patterns of LEGO® bricks on a thin baseplate. LEGO® components have been widely used, especially for didactic purposes, in a variety of scientific environments, including robotics,19 biological sciences,20,21 and physics.22,23 In our approach, bricks of different size and shape can be placed at designated locations on a baseplate as to produce a variety of periodic or disordered stub patterns with different length scales. Thanks to the non-permanent brick-plate contacts it is possible to seamlessly transition between different topologies, effectively switching between radically different tests, in a matter of minutes. Note that the acrylonitrile butadiene styrene (ABS) baseplate, which serves as the wave propagation support, displays relatively low viscosity, which results in low damping and moderate wave attenuation.

For our measurements, we rely on the sensing flexibility of a 3D Scanning Laser Doppler Vibrometer (SLDV), which allows simultaneous in-plane and out-of-plane wavefield reconstruction. Thanks to their sensitivity and frequency bandwidth, and in light of the benefits of non-contact sensing, laser vibrometers have gained increasing popularity for the experimental analysis of phononic structures.24–29 Here, the scanning vibrometer contributes to the sensing side of the problem a dimension of reconfigurability that complements the flexibility that is achieved, at the specimen fabrication level, by using bricks as building blocks.

Throughout this letter, all the considered topologies are obtained as assemblies of cylindrical bricks on a baseplate.30,31 The baseplate features periodically distributed studs—small cylindrical protuberances where the bricks can be anchored. The arrangement of studs allows for several periodic configurations with various lattice constants. Note that the brick-stud contact only relies on friction: no use of glue (which would undermine agile specimen reconfiguration) is required. A detail of bricks and baseplate is shown in Fig. 1(a). In Fig. 1(b), we show the scanned surface (the backside of the plate), coated with a thin layer of reflective paint to increase the quality of the optical signal. The excitation is imparted using a Bruel & Kjaer Type 4809 shaker (also shown in Fig. 1(b)), with a 0–20 kHz bandwidth. Sensing is performed by scanning the baseplate with a Polytec PSV-400-3D Scanning Laser Doppler Vibrometer (Fig. 1(c)). To probe the response over broad frequency ranges, we excite the specimen with a pseudorandom waveform featuring a flat power spectrum over the frequency range of interest. To improve the signal-to-noise ratio, measurements at each scanned location are repeated 20 times and averaged. A low-pass filter is used to cut-off all spurious features in the signal above 20kHz.32 

FIG. 1.

Experimental setup. (a) Detail of the baseplate with cylindrical bricks. (b) Scanned surface (backside of the baseplate) and shaker. (c) Front view of the specimen with the three scanning heads of the 3D-SLDV in the background.

FIG. 1.

Experimental setup. (a) Detail of the baseplate with cylindrical bricks. (b) Scanned surface (backside of the baseplate) and shaker. (c) Front view of the specimen with the three scanning heads of the 3D-SLDV in the background.

Close modal

Our first objective is to use our combined fabrication and sensing platform to visually elucidate the phononic bandgap phenomenon. Phononic bandgaps are frequency intervals in which wave propagation is forbidden. The generation of bandgaps can be traced back to two main mechanisms: Bragg scattering and locally resonant effects. Bragg bandgaps are due to the destructive interference between cascades of waves scattered at the internal interfaces in the material. They require periodicity in the structure and manifest when the wavelength of excitation approaches the characteristic size of the unit cell. Locally resonant bandgaps are a byproduct of energy-localization mechanisms; they take place when the frequency of excitation approaches the resonance frequencies of some “microstructural” elements.5 They are subwavelength in nature, i.e., they arise when the wavelengths are about one order of magnitude larger than the unit cell size. In the following, we leverage the versatility of our experimental setup to illustrate the duality between these mechanisms.

Our first specimen comprises 420 bricks arranged as shown in Figs. 2(a) and 2(b). For convenience, we label this topology “dense.” Fig. 2(c) shows the frequency response function (FRF) calculated from surface measurements using the vibrometer in the 014kHz range; the average out-of-plane velocity vzPC measured at the scan points inside the brick-filled area (the actual phononic crystal zone) is divided by the average velocity vzbase measured along the bottom edge of the scanned surface. We observe two bandgaps (shaded areas): a narrow band approximately in the 1.82.6kHz range, and a wider one approximately in the 5.511kHz range. Snapshots of the steady-state response at selected frequencies are shown in Figs. 2(d)–2(h). In all plots, the velocity ranges from 0.4vz,maxbase to 0.4vz,maxbase, where vz,maxbase is the maximum amplitude recorded along the bottom edge of the scanned region at each frequency. The wavefield response provides visual evidence of both bandgaps: Figs. 2(d), 2(f), and 2(h), corresponding to propagation regions, feature appreciable oscillations over the entire scanned area; Figs. 2(e) and 2(g), corresponding to attenuation zones, feature nearly no motion in the crystal region (bordered by the dashed line). A comparison with the FRF of a pristine baseplate, confirming the fact that the bandgaps are due to the presence of the brick arrangement, is given in the supplementary material (SM).32 

FIG. 2.

Bandgap analysis for a dense periodic brick topology. (a) and (b) Specimen with detail of the brick arrangement. (c) Frequency response function (average out-of-plane velocity normalized by the average value measured along the bottom edge). The shaded areas highlight the bandgap regions. (d)–(h) Laser-acquired wavefields sampled at five reference frequencies; the dashed lines delimit the region occupied by the bricks. (d) 1.5kHz. (e) 2.25kHz. (f) 3kHz. (g) 7.25kHz. (h) 13kHz.

FIG. 2.

Bandgap analysis for a dense periodic brick topology. (a) and (b) Specimen with detail of the brick arrangement. (c) Frequency response function (average out-of-plane velocity normalized by the average value measured along the bottom edge). The shaded areas highlight the bandgap regions. (d)–(h) Laser-acquired wavefields sampled at five reference frequencies; the dashed lines delimit the region occupied by the bricks. (d) 1.5kHz. (e) 2.25kHz. (f) 3kHz. (g) 7.25kHz. (h) 13kHz.

Close modal

To investigate the dual nature of the observed bandgaps, we test their robustness against changes in topology. Here, we invoke the notion that Bragg bandgaps are sensitive to changes in lattice spacing and to relaxation of the periodicity, while locally resonant bandgaps only depend upon the availability of resonating elements. In Fig. 3, the reference dense topology (Figs. 3(a) and 3(b)) is compared to two other topologies that are assembled via rapid reconfiguration of the brick pattern. The configuration in Fig. 3(c) is obtained by downsampling (by half) the original topology while retaining a periodic arrangement. The corresponding FRF in Fig. 3(d) still displays two main bandgaps: the gap in the neighborhood of 2.2kHz is preserved, albeit narrower than in the dense topology; the larger gap has shifted towards lower frequencies (3.56kHz range, approximately). Shifting towards lower frequencies (longer wavelengths) in response to increases in lattice constant can be seen as the signature of Bragg scattering, which indeed requires compatibility between unit cell size and wavelength. Fig. 3(e), in contrast, is obtained by rearranging the 210 bricks into a (MATLAB-generated) disordered pattern. The FRF in Fig. 3(f) highlights the survival of the 2.2kHz bandgap while the higher gap has vanished. The persistence of the low frequency gap across all topologies highlights its periodicity-independence and hints at underlying locally resonant mechanisms—an aspect recently investigated by Rupin et al.29 The intensity of the resonant mechanisms depends on the number of resonators that can contribute to energy trapping. This confirms the reduction in the first bandgap width in going from the case of Fig. 3(a) to those of Figs. 3(c) and 3(e). In SM,32 we also discuss the influence of the resonators' height on both locally resonant and Bragg bandgaps.

FIG. 3.

Effects of scale coarsening and periodicity relaxation. (a) Dense periodic topology (420 bricks). (b) FRF for the topology in (a). (c) Coarse periodic topology (210 bricks). (d) FRF for the topology in (c). (e) Random assembly of 210 bricks. (f) FRF for the topology in (e).

FIG. 3.

Effects of scale coarsening and periodicity relaxation. (a) Dense periodic topology (420 bricks). (b) FRF for the topology in (a). (c) Coarse periodic topology (210 bricks). (d) FRF for the topology in (c). (e) Random assembly of 210 bricks. (f) FRF for the topology in (e).

Close modal

To substantiate our hypothesis regarding the locally resonant nature of the 2.2kHz bandgap, we attempt to reconstruct experimentally the vibrational behavior of a single brick (mounted at the center of the baseplate) at different frequencies falling inside and outside the bandgap deemed to be locally resonant; a detail of the brick, coated in a thin layer of reflective paint, is shown in Fig. 4(a). For this task, we define a dense cylindrical scan grid on the surface of the brick, as well as a coarser rectangular grid on the region of the plate immediately surrounding the brick. The color given to the scanned points is proportional to the RMS of the three measured velocity components; at each frequency, the velocity is normalized by the maximum velocity recorded over the entire scanned region at that frequency, to highlight the relative motion between brick and baseplate. The black dots mark the original position of the scan points. Fig. 4(b) shows the brick-and-plate motion at 1000Hz (before the bandgap). We can see that the brick moves in the out-of-plane direction in phase with the plate substrate, which undergoes significant deformation. Fig. 4(c) pinpoints a frequency near the onset of the bandgap, 1950Hz: the brick undergoes large tilting motion, while the points on the plate are approximately still. Fig. 4(d) represents a post-gap frequency (3000Hz) where, once again, we observe significant motion of both the plate and the brick. We conclude that we only observe large relative motion between stub and substrate at the onset of the bandgap. This provides evidence of energy trapping and highlights the locally resonant nature of the bandgap.

FIG. 4.

Experimental reconstruction of the motion of a cylindrical brick at three frequencies in the neighborhood of the locally resonant bandgap. (a) Detail of the brick. (b) Motion at 1000Hz, before the presumed bandgap region. (b) Motion at 1950Hz, near the onset of the bandgap. (d) Motion at 3000Hz, above the bandgap.

FIG. 4.

Experimental reconstruction of the motion of a cylindrical brick at three frequencies in the neighborhood of the locally resonant bandgap. (a) Detail of the brick. (b) Motion at 1000Hz, before the presumed bandgap region. (b) Motion at 1950Hz, near the onset of the bandgap. (d) Motion at 3000Hz, above the bandgap.

Close modal

We can further exploit the reconfigurability of our specimens to illustrate (using the same brick set) a variety of spatial manipulation phenomena, such as waveguiding and seismic isolation, at different wavelengths. The first topology, shown in Fig. 5(a), is obtained by assembling a dense square phononic crystal and by introducing a two-unit-cell wide snake-like defect path. Defect paths are known to act as waveguides when the frequency of excitation falls inside a bandgap for the crystal. Consistent with the bandgap duality discussed above, waveguiding is attainable for wavelengths that are comparable33–36 or larger26,37 than the unit cell. In Fig. 5(b), we obtain long-wavelength waveguiding (at 2512.5Hz), while in Fig. 5(c), we report waveguiding at shorter wavelengths (at 7000Hz, inside the Bragg gap).

FIG. 5.

Experimental evidence of waveguiding and isolation effects. (a) Snake-like waveguide. (b) Waveguide response at 2512.5Hz. (c) Waveguide response at 7000Hz. (d) Metamaterial realization of the Minnesota M logo. (e) Image of the M at 2362.5Hz. (f) Image of the M at 7000Hz.

FIG. 5.

Experimental evidence of waveguiding and isolation effects. (a) Snake-like waveguide. (b) Waveguide response at 2512.5Hz. (c) Waveguide response at 7000Hz. (d) Metamaterial realization of the Minnesota M logo. (e) Image of the M at 2362.5Hz. (f) Image of the M at 7000Hz.

Close modal

We then proceed to rearrange the bricks into the topology shown in Fig. 5(d), which implements a phononic crystal realization of the University of Minnesota M logo. The wavefields obtained at 2362.5Hz and 7000Hz are shown in Figs. 5(e) and 5(f), respectively. We can see how the energy is predominantly confined outside the crystal region; this effect is especially pronounced in the Bragg bandgap, where the response decays inside the M contour within 12 cell layers. This configuration, in conjunction with the ability to scan both interior and exterior of the crystal, provides an eloquent lab demonstration of the potentials of PCs for vibration and seismic isolation.38,39 In SM,32 we discuss two additional crystal topologies to emphasize the breadth of effects that can be verified using the proposed platform.

As a summary, in this letter, we have illustrated how, through a simple assembly of LEGO® bricks, we can generate metamaterial architectures with locally resonant and Bragg-based bandgaps. The reconfigurability of the brick patterns, together with the availability of bricks of virtually any size and shape, can be leveraged to assemble and test a plethora of metamaterial architectures, thus serving as a versatile experimental platform for proof of concept lab tests. We believe that the intuitive and tangible nature of toy-based specimens, along with the visualization capabilities of laser sensing, can provide a dimension of intuitiveness to the field of experimental phononics and act as perfect platform for far-reaching teaching and outreach activities in the realm of wave mechanics and metamaterials engineering.

The inspiration for this work sprouted from ideas originated during the organization of outreach activities within a project sponsored by the National Science Foundation (Grant CMMI-1266089). We are particularly indebted to Nathan Bausman and Davide Cardella for their insight and assistance with the experiment setup. We also wish to thank Jeff Druce and R. Ganesh for their valuable input.

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Supplementary Material