Centrifuge-based experimental validation of seismic resonant metamaterials for structural protection

The pursuit of efficient seismic protection has advanced considerably over recent decades, expanding beyond traditional methods, such as base isolation and energy dissipation devices. Metamaterial-based approaches introduce novel seismic protection mechanisms, which are not achievable through conventional methods. For example, classical passive control systems – including seismic isolation (e.g. Buckle and Mayes, 1990), tuned mass dampers (e.g. Ikago et al., 2012), and energy dissipation devices (e.g. Arvind and Santhi, 2022) – have been proven to be effective in mitigating earthquake-induced structural responses by decoupling structures from the ground motion, modifying their dynamic characteristics to facilitate energy transfer, and enhancing energy dissipation mechanisms, respectively. However, all these approaches are predominantly applicable to newly constructed buildings. Their application for the retrofitting of existing structures can be challenging, as they typically require substantial structural modifications. Consequently, there is still a need for development of alternative, non-invasive seismic protection techniques for new and – especially – for existing structures.

In this context, the field of seismic resonant metamaterials has emerged in recent years, drawing inspiration from developments in electromagnetic (Pendry et al., 2006) and acoustic (Craster and Guenneau, 2012) metamaterials. Metamaterials are artificially engineered composites, typically arranged in periodic architectures composed of multiple unit cells, capable of controlling wave propagation by filtering, wave guiding, and lensing (Aguzzi et al., 2022a). These effects are achieved through mechanisms such as Bragg scattering (e.g. Krushynska et al., 2017) and local resonance (e.g. Ma and Sheng, 2016), while non-linear inclusions attempt to enhance their performance (e.g. Chondrogiannis et al., 2022). In particular, seismic resonant metamaterials are composed of multiple unit cells embedded within the soil, each featuring an internal mass connected to an external host medium by elastic links (e.g. Kanellopoulos, 2025; Miniaci et al., 2016). When properly tuned, these locally resonant systems generate subwavelength band gaps – frequency ranges within which waves cannot propagate – thereby providing a novel means of seismic wave attenuation.

The concept of seismic resonant metamaterials has been investigated in two principal configurations: (a) directly beneath structures in the form of metafoundations (Basone et al., 2019), which is practically applicable only to new structures (not further discussed herein); and (b) within the soil surrounding the structures in the form of metabarriers (Colombi et al., 2020), which does not require any structural intervention and are therefore relevant for all structures – especially existing ones. This is a key advantage of metabarriers compared to the aforementioned passive seismic response control systems and the traditional structural retrofitting methods, such as jacketing techniques for reinforcing structural elements (e.g. Júlio et al., 2003; Raza et al., 2019), steel bracing (e.g. Badoux and Jirsa, 1990), or adding a shear wall (e.g. Blagojević et al., 2026). Despite undeniable challenges for scaling metabarriers to real-world applications (e.g. space requirements, construction, and maintenance), discussed later, avoidance of structural modifications makes this concept particularly attractive in cases where structural intervention cannot be done, such as heritage buildings, or scenarios where occupant relocation or business disruption is not feasible. These advantages make seismic metabarriers worth exploring further.

Early studies primarily targeted the attenuation of surface waves (Krödel et al., 2015), including Rayleigh (Palermo et al., 2016) and Love waves (Palermo and Marzani, 2018), demonstrating the formation of frequency band gaps through periodic resonant inclusions at the ground surface. Notably, Palermo et al. (2016) proposed single-mass resonators for Rayleigh wave mitigation; multi-mass resonators were introduced later (Palermo et al., 2018) to achieve broadband attenuation. More recently, Russillo et al. (2024) proposed hydrodynamic metabarriers, consisting of periodic arrays of resonant water-tank units, achieving tunable attenuation of Rayleigh waves through easily adaptable surface-embedded systems. These studies revealed that vertically polarised surface resonators can induce a mode conversion mechanism, transforming Rayleigh waves into shear body waves that propagate deeper into the soil, away from the surface.

However, potential drawbacks of the metabarrier approach for Rayleigh wave mitigation have been identified. Zaccherini et al. (2020a) demonstrated that in more realistic soil profiles, characterised by inhomogeneous layers with depth-increasing stiffness, surface waves initially redirected downwards tend to bend upwards as they encounter stiffer layers, eventually returning to the ground surface. This phenomenon suggests that surface-wave diversion, intended to protect one structure, could inadvertently amplify the ground motion at neighbouring buildings.

While most of the literature on metabarriers has concentrated on the mitigation of surface waves, only a limited number of studies have addressed body shear (S) waves, which are more critical for structural safety. Cacciola and Tombari (2015) introduced a predecessor to metabarriers, the so-called Vibrating Barrier (ViBa), which consists of a large horizontally oscillating mass enclosed in a buried box, designed to shield structures from horizontal seismic excitation. Subsequently, Colombi et al. (2020) demonstrated the potential efficiency of resonant metamaterials in mitigating both surface and body waves for a simplified linear elastic structure resting on linear elastic soil, subjected to Ricker pulse excitations. More recently, Kanellopoulos (2025) examined the behaviour of seismic resonant metamaterials under vertically propagating horizontal shear waves, employing high-fidelity numerical modelling to investigate dynamic metamaterial–soil–structure interaction (meta–SSI). Extensive numerical parametric analyses were first conducted for idealised single-degree-of-freedom (SDOF) systems to investigate the efficiency of metamaterials for structural protection (Kanellopoulos et al., 2022a). Building on these results, their effectiveness was subsequently demonstrated for a typical multi-degree-of-freedom (MDOF) reinforced concrete (RC) moment-frame structure subjected to real seismic records, including non-linear SSI effects (Kanellopoulos et al., 2022b). In addition, their ability to mitigate high-frequency vibration modes of critical equipment/components housed in structures of high importance was recently demonstrated for the reactor vessel inside a nuclear power plant reactor building (Kanellopoulos et al., 2024), achieving 20% response reduction at 20 Hz with a total vibrating unit-cell mass of only 4% of the reactor building mass. Across these studies, numerical results consistently indicate that tuning the resonant frequency of metamaterials to match – or be slightly lower than – the fundamental frequency of the structure yields the most effective seismic protection. Attention is required though for highly non-linear soil profiles, as soil non-linearity may alter the dominant frequencies of the soil–foundation–structure system, posing challenges to the tuning of the unit cells.

As promising as it may sound as an alternative non-invasive seismic protection method, metabarriers come with limitations, as well as several practical challenges that must be addressed in real-world applications. An obvious limitation is the space required around buildings to install such metabarriers. The current configuration requires unit cells on both sides of the structure, and for comprehensive protection against bidirectional shaking, arrays would also be needed on all sides – making implementation challenging in dense urban environments due to space constraints. A potential bidirectional unit-cell design could partially alleviate this issue. Designing and constructing full-scale resonant unit cells that behave as expected in real soil for real structures is a major challenge, as optimal tuning remains critical for their effectiveness – a key aspect successfully demonstrated experimentally by this study at small scale. This is compounded by long-term maintenance requirements to ensure performance over each unit cell's lifecycle. A common challenge across all aspects is cost – from excavation and unit-cell construction/installation to ongoing maintenance. Since the total unit-cell oscillatory mass should be of a similar order of magnitude to the participation mass of the structure's protected vibration mode, and considering that the mass of a structure represents ∼20% of the total building construction cost, this provides an indication of the expected metabarrier cost. Compared to traditional retrofitting methods requiring substantial structural interventions – which can exceed original building costs, plus indirect costs from occupant/business disruption – this method appears worth exploring at this preliminary investigation stage.

Addressing these practical challenges lies, however, beyond the scope of this paper. The objective of this proof-of-concept study is not to propose a practical unit-cell design for a specific structure, but rather to build upon previous numerical research and experimentally demonstrate the working principles of seismic resonant metamaterials and their seismic protection potential for structures at their fundamental vibration mode. Despite notable analytical and numerical advances in the field of seismic resonant metamaterials, experimental validation remains limited. A few experimental studies have investigated surface wave attenuation using resonant metamaterial inclusions (e.g. Palermo et al., 2016; Zaccherini et al., 2020a, 2020b). In addition to focusing on surface waves (which are typically less critical than S waves for structures), all of these studies were conducted at 1 g and are therefore prone to scale effects. Centrifuge modelling provides a rigorous means of addressing these issues. By increasing the gravitational acceleration, the geotechnical centrifuge reproduces the soil confining stresses of the prototype, thus maintaining similarity and allowing for realistic modelling of soil response (Madabhushi, 2017).

Aiming to bridge the gap between theory and experiment, this study provides unique experimental evidence demonstrating the potential of seismic resonant metamaterials as an innovative method for seismic protection of structures against vertically propagating horizontal shear waves. Through a series of centrifuge model tests conducted at 50 g, the study investigates meta–SSI effects under realistic conditions, offering the first direct experimental comparison between an unprotected structure on a conventional foundation and one shielded by resonant unit cells. The insights gained from this work validate and extend the findings from previous numerical and analytical studies, advancing the Technology Readiness Level (TRL) of seismic resonant metamaterials to TRL 3 (Experimental proof of concept). The results also demonstrate the method’s robustness under realistic conditions, achieving stable tuning of small-scale unit cells in a real soil environment under 50 g centrifugal acceleration and earthquake loading, enhancing its potential for future practical implementation in earthquake resilience strategies – particularly where traditional seismic protection methods are not feasible. Notably, this represents the first experimental study of resonant metamaterials under vertically propagating horizontal shear waves, providing valuable experimental data for future model validations.

Two prototype problems are considered to investigate meta–SSI effects. In the first, a standalone structure is placed atop a 20-m-thick soil layer and subjected to a series of one-component horizontal seismic excitations to capture its unprotected response. In the second, unit-cell resonant metamaterials are incorporated at the two sides of the same prototype structure, with an identical seismic excitation sequence applied to quantify the effect of resonant metamaterials on structural response.

To illustrate the effectiveness of resonant metamaterials in structural protection, the prototype structure is simplistically assumed as an SDOF system, representing a three-story building on a shallow foundation with a 4.7 × 8.1 m footprint. This SDOF system representation is intentionally adopted as a proof-of-concept configuration to experimentally validate the meta–SSI protection mechanism at the structure’s fundamental vibration mode. Previous numerical work by the first author (Kanellopoulos et al., 2022b) has already examined the performance of resonant metamaterials for realistic MDOF RC moment-frame buildings, demonstrating that, when tuned to the fundamental period of the structure, metamaterials can substantially reduce demands (e.g. drift ratios) associated with the first mode. Each floor mass is set to 20 Mgr (equivalent to a 0.21 m RC slab), yielding a total oscillatory mass of 60 Mgr. The prototype structure’s fixed-base fundamental vibration frequency/period is set to 3.2 Hz/0.31 s, anticipating a small frequency drop/period increase due to SSI effects. The prototype structure is protected by two rows of three SDOF unit cells on each side, fully embedded within dense sand soil, with external unit-cell dimensions of 2.7 × 2.7 × 2.35 m. As demonstrated by previous studies (Colombi et al., 2020; Kanellopoulos et al., 2022a), the beneficial effects of resonant metamaterials arise when their resonant frequency/period matches or is slightly lower/larger than that of the structure. Accordingly, the fundamental vibration frequency/period of the unit cells is set to 3 Hz/0.33 s in this study. In addition, the structure–metamaterials mass ratio is required to be at least 1 to enable meaningful meta–SSI. Consequently, each unit cell features an internal oscillatory mass of 10 Mgr, resulting in a total mass of 60 Mg and a ratio of 1.

The experimental campaign comprises two centrifuge model tests, with and without unit cells, conducted at a centrifugal acceleration of (⁠$N$ = 50) g at the newly constructed beam centrifuge facility of the ETH Zurich Goetechnical Centrifuge Center (GCC). With an effective diameter of 8.25 m, the beam centrifuge has a maximum capacity of 500 gtonne. To transition from prototype to model scale, specific scaling laws are derived for each parameter, as described in Madabhushi (2017). In particular, the scaling factors for length, mass, stress, time, frequency, displacement, and acceleration are 1/$N$⁠, 1/$N3$⁠, 1, 1/$N$⁠, $N$⁠, 1/$N$⁠, and $N$⁠, respectively. For example, a length of 1 m at prototype scale corresponds to 1/$N$ = 1/50 = 0.02 m at model scale. An overview of the two centrifuge models within the employed laminar container that allows the contained soil to deform naturally in the horizontal direction is provided in Figure 1.

Since the primary focus is on the comparison of these two configurations, ensuring consistent preparation of the centrifuge models is crucial. Provided this consistency, the deviations between the centrifuge models and prototype response – such as scale effects related to shear band volumetric response or discrepancies arising from the spin-up process (Sakellariadis and Anastasopoulos, 2024) – are not considered critical. A detailed description of all model components is provided in subsequent sections.

As shown in Figure 2, the SDOF structure is materialised with a model consisting of two horizontal aluminium plates (162 × 80 mm × 10 mm) representing the foundation and the top slabs of the structure, respectively. Two vertical stainless-steel (⁠$ρstain.steel$ = 7.85 gr/cm³) plates (162 × 85.5 mm × 1.5 mm) connect the horizontal plates, reinforced by additional aluminium (⁠$ρalum.$ = 2.7 gr/cm³) bars along their length, and secured with four screws per connection. This design ensures that the vertical plates are rigidly connected to the horizontal ones, minimising the undesired flexibility of the connections.

Each unit-cell model (54 × 54 mm × 47 mm) – excluding the inner mass – is 3D-printed from durable Nylon 12 plastic (PA12) using selective laser sintering technology by Shapeways. Inspired by the work of Zaccherini et al. (2020a), its intricate internal structure has been further modified to meet the requirements of the current study, ensuring that each unit cell effectively behaves as a SDOF system, allowing vibration of the internal mass solely in one horizontal direction. To this end, as illustrated in Figure 3, each unit cell incorporates the following design elements:

• two truss-like springs, enabling horizontal oscillation of the internal mass container;

• eight horizontal ligaments, restricting rotational vibration of the internal mass about the vertical axis;

• four vertical ligaments, providing vertical support while restricting rotational motion about the horizontal axes;

• four horizontal and two diagonal stiffeners, ensuring the rigidity of the external unit-cell casing; and

• an internal mass (20 × 20 × 20 mm), made of brass (⁠$ρbrass$ = 8.4 gr/cm³), separately inserted into the unit-cell mass container.

To verify and accurately tune the structure model to the target fixed-base frequency of 160 Hz (3.2 Hz at prototype scale), vertical plates of varying heights were experimentally tested prior to the centrifuge experiments, as illustrated in Figure 4. A portable shaker was positioned adjacent to the structure (securely fixed to an optical table with screws), producing a chirp excitation signal with a constant, sufficiently broad frequency spectrum covering the range of interest (100–200 Hz). Using a PSV-500 Scanning Vibrometer by Polytec (e.g. Aguzzi et al., 2022b; Zaccherini et al., 2022), the horizontal vibration response was recorded at the base (point B) and top (point A) of the structure. By varying the height of the vertical plates, the optimum height was selected (85.5 mm), achieving the target frequency of 160 Hz. The corresponding horizontal velocity frequency response function (FRF) magnitude from point B to point A, calculated as $FFTA/FFTB$ (Chondrogiannis et al., 2023), is plotted on the right side of Figure 4 and confirms that the fixed-base resonant frequency of the selected configuration matches the target frequency of 160 Hz.

Given the imperfections associated with 3D printing, small deviations of the resonant frequency of the unit cells were initially observed. To accurately tune the unit cells to the target frequency of 150 Hz (3 Hz at prototype scale), these small deviations were compensated by placing additional brass slices (measuring 20 × 20 mm × 1 mm) at the base of the unit-cell mass container when required, prior to installing the larger mass on top. Similar to the tuning of the structure, each unit cell was fixed to the table using removable hot glue. The tuning was performed employing a trial-and-error process, progressively inserting additional brass slices, until the 150 Hz frequency was accurately matched. To scan the vibration of the metamaterial mass with the vibrometer, two tiny holes (for symmetry) were drilled on one side of each unit cell, allowing the laser beam to hit the internal mass at point A, as shown in Figure 5. Using the same chirp signal as before, responses were recorded at points A (internal mass) and B (external case); the calculated horizontal velocity FRF magnitude is plotted on the right side of the figure. Notably, all six unit cells have the same 150 Hz fundamental frequency, confirming the success of the tuning process. The final total internal mass of all unit cells is approximately 423 grams, while the mass of the top plate of the SDOF structure is 430 g, resulting in a mass ratio close to 1. This ratio has been shown to be sufficient to achieve the beneficial effects of resonant metamaterials (Kanellopoulos et al., 2022a).

Except for tuning the specimens to their target frequencies, it is also necessary to visualise the mode of vibration at these frequencies to ensure that the structure and especially the unit cells vibrate as intended: purely horizontally as SDOF systems without any spurious rotations. To allow for the representation of motion in all three directions, a PSV-500-3D Scanning Vibrometer attached to a RoboVib (Hejazi Nooghabi et al., 2024; Zhao et al., 2022) is employed to automatically perform experimental modal analysis. Using the same shaker, the resonant vibration modes of the structure and of a unit cell are extracted. For brevity, only the vibration mode of the unit cell is presented in Figure 6 (similar results are obtained for the structure). The superimposed undeformed shape (black lines) helps to verify the desired translational vibration mode of the metamaterials’ internal mass.

Hostun sand is widely used in centrifuge modelling campaigns (e.g. Adamidis and Madabhushi, 2017; Okyay et al., 2014), with the ETH Zurich GCC having significant experience as well. Table 1 summarises the key properties of Hostun sand, including the limiting void ratios $emin$ (determined according to ASTM D4253-16e1 using oven-dried samples) and $emax$ (determined according to ASTM D4254-16 with method C), the soil particle density $Gs$⁠, and the critical state friction angle $φcv$ (as measured by Kassas et al., 2021). Azeiteiro et al. (2017) conducted Bender Element tests to measure the small-strain shear modulus $Gmax$ of air-pluviated Hostun sand in function of void ratio $e$ and mean effective stress $p′$⁠, showing that the effect of previous stress history is insignificant and calibrating Hardin’s (1978) expression to approximate the experimental measurements. A dimensionless expression was proposed for $Gmax$⁠, capturing the experimental data reasonably well, with some discrepancies at smaller void ratios (denser specimens):

where $pref′$ is the reference atmospheric pressure (100 kPa); and $f(e)$ is a function of the void ratio, given by the expression proposed by Hardin and Richart (1963) for angular-grained sands:

A deformable soil container is essential for achieving realistic boundary conditions during seismic excitation. With internal dimensions of 1.0 × 0.4 × 0.4 m (length × width × height), the employed custom-built laminar container can accommodate large-scale models operating at centrifugal accelerations of up to 100 g (accommodating a soil depth of 40 m in prototype scale). It consists of 20 laminate frames, each being 20 mm thick and weighing 7 kg, connected by low-friction industrial sliders. The frames are free to move relative to each other, with a measured friction coefficient below 0.01, enabling the soil to deform as naturally as possible during seismic excitation. To prevent lateral deformation of the aluminium frames due to the developing soil pressures, two lateral supports are incorporated along the longitudinal direction and connected by transverse stiffeners. Stoppers are installed in the longitudinal direction to restrict potential excessive displacement of the frames.

Based on previous numerical work (Kanellopoulos et al., 2022a), five real earthquake ground motion records from the PEER Ground Motion Database were selected as seismic excitations. In addition, an artificial Ormsby wavelet (Jeremić et al., 2025) with 5 g acceleration amplitude (0.1 g in prototype scale) and a frequency spectrum of constant amplitude between 25 and 500 Hz (0.5 and 10 Hz in prototype scale) was employed for system identification purposes. This wavelet was not used for comparison between experiments because the precise reproduction of such pulses by the shaker is practically impossible. The results are presented for three of the five, real records, as summarized in Table 2, which were reproduced with consistent accuracy during both centrifuge tests. All results are presented and discussed at the model scale, with prototype scale values provided occasionally in parentheses to enhance interpretability for the readers.

Targeting the response at the ground level, the selected ground motions were deconvoluted in order to be used as input for the shaker. This is achieved through 1D equivalent linear ground response analysis using ProShake 2.0. Figure 7 illustrates this process, using the Ormsby wavelet as an example. The selected soil profile of 40 cm depth (20 m at prototype scale) is divided in 20 layers, each of 2 cm thickness. Assuming $e=0.63$ (corresponding to $Dr=96%$⁠), the input parameters for each soil layer are determined using the expressions of Table 3.

As shown in Figure 7, the corresponding shear wave velocity $VS, max$ increases non-linearly with depth. The degradation of shear modulus and damping with respect to shear strain $(G/Gmax-γ$ and $ξ-γ)$ is modelled employing the curves of Ishibashi and Zhang (1993), with strength correction enabled. The deconvolution produces the acceleration time history at the base (assumed as bedrock in ProShake), which will serve as input for the centrifuge shaker. The horizontal acceleration FRF magnitude from point B (base of soil column) to point A (top of soil column) indicates that the effective fundamental vibration frequency of the assumed soil profile is 150 Hz (3 Hz at prototype scale). For the stronger motions of Table 2, the fundamental frequency was found to be a bit lower (125 Hz) due to the larger imposed shear strains.

The bespoke Actidyn BC-5810 seismic shaker is employed to apply the deconvoluted motions at the base of the laminar container. The shaker can deliver horizontal motions with peak accelerations up to 25 g at 100 g centrifugal acceleration with a 750 kg payload across a wide frequency range. Before conducting the experiments, the shaker needs to undergo a training process to accurately reproduce the target deconvoluted motions. The training must be performed in flight with a dummy model, having the same mass with the final model and being subjected to the same centrifugal acceleration (50 g). The result of the training process is a transfer function, optimised to replicate the target deconvoluted motions in the best possible manner.

Figure 8 presents a comparison between the target motions and those produced by the shaker after training, showing the acceleration time histories at the bottom and the corresponding Fourier amplitude spectra at the top of the figure. Note that the deconvoluted Ormsby wavelet had to be slightly amplified as its very small amplitude posed additional challenges for the shaker training. The shaker can be seen to reasonably approximate the target ground motions. A more precise reproduction of the target ground motions is not easily attainable but is also unnecessary for the needs of this study. What matters is that the repeatability of the ground motions, so that the two centrifuge models under comparison (with and without protection) are subjected to identical input excitations, allowing for direct evaluation of the effectiveness of resonant metamaterials.

An overview of the instrumentation is provided in Figure 9. Sixteen single-axis accelerometers (Brüel & Kjær, piezoelectric 4518 500 g) are installed withing the soil, distributed across five layers, labelled from A to E, starting from the top; columns are numbered 1–5, starting from the centre of the model. The accelerometers were placed gently on the sand surface with their sensitive axis aligned with the excitation direction, with cables routed and arranged so that no cable tension or bending induces spurious forces, and then covered by sand. The sensors mounted on the SDOF structure and on the laminar container are attached by threaded studs: threads were tapped into the structural and container elements, and the accelerometers were firmly screwed in place, ensuring practically rigid mounting. No intermediate soft pads or adhesive layers were used, so the attachment stiffness is high and the first mounting resonance of the accelerometers lies at 62 kHz – well above the maximum frequency of interest (∼170 Hz).

To capture the metamaterial–soil interaction, the instrumentation density is increased near the ground surface, where such interaction is expected to be strongest. The two vertical arrays of accelerometers offer insights into the vibratory response of the soil both near the free field, and directly underneath the structure. To monitor the response of the SDOF structure, one accelerometer is installed at its base (S3) and another one at its top (S4). In addition, four accelerometers are distributed along the height of the laminar container, and one is installed on the table (seismic shaker) to directly measure the produced input motions. During the 50 g centrifuge spins, the accelerometers remained quiescent and only recorded significant motion during active shaking, further confirming that mounting resonance and cable interaction effects were not influential in the frequency band of interest.

Two high-speed cameras (Photron, Fastcam Mini AX200) are deployed to enable digital image correlation (DIC) measurements of the dynamic deformations of the model. To facilitate the process, the specimens – including the metamaterials, structure, and part of the ground surface – are speckled. DIC is particularly valuable for monitoring the response of the resonant unit-cell masses, where the installation of accelerometers is not possible, as the added accelerometer mass with its cable would significantly alter their vibration response.

To ensure effective DIC, the speckle pattern needs to be random, isotropic (without bias toward any orientation), and of high contrast – targeting approximately 50% coverage of black dots on a white background – with speckles ideally sized between 3 and 5 pixels to optimise spatial resolution. These criteria were carefully considered during specimen speckling. The Speckle Generator tool provided by Correlated Solutions was used to print the speckled paper, which was firmly glued on the top of the structure and the metamaterials (both on the internal masses and external casings). For the ground surface, small metal particles were randomly distributed across the area of interest; the resulting speckle pattern can be seen in Figures 10(a) and 10(b), and later in Figure 15, which also illustrates the field of view of the cameras in flight.

The two high-speed cameras are fixed inside a stiff protective container that is rigidly attached to a robust support frame (Figures 10(a) and 10(b)), which is not connected to the shaking table. A side and top view of the frame, including the cable routing on the frame, are shown in Figures 10(c) and 10(d), respectively. Uniform illumination is provided around the model, as demonstrated in Figures 10(a) and 10(b), to facilitate the image correlation process. Another good practice is to maintain the stereo angle between the two cameras below 60°; as shown schematically in Figure 9, the stereo angle is set at 56°. In addition, it is important to perform the calibration of the DIC system in flight to account for potential geometric distortions of the lenses caused by the increased gravitational acceleration. More information on DIC requirements and procedures can be found in the VIC-3D Testing Guide provided by Correlated Solutions.

The sand is dry pluviated into the laminar container employing an automated sand raining system, which enables control of the relative density by adjusting the drop height, velocity, and aperture of the sand hopper, ensuring repeatability between different experiments. A series of trial pluviations were performed to calibrate the sand raining system, targeting a relative density of 96%, as assumed in the deconvolution analyses. The achieved relative density was measured systematically and found to range between 95% and 100%. The final configuration adopted a drop height of 600 mm, a horizontal velocity of 10 mm/s, and a hopper aperture of 2.15 mm.

Following the calibration of the sand raining system, the model preparation is performed by dry sand pluviation into the laminar container in half cycles (pouring sand in one direction only) or full cycles (pouring sand back and forth). A half cycle deposits a layer of approximately 25 mm thickness, while a full cycle leads to a 50 mm layer thickness. A mesh diffuser (Emil Hitz AG, No. 320.011021; mesh width 1.94 mm; wire 0.6 mm) is placed at the top of the laminar container. Special care is required when a sand layer reaches a sensor installation height: accelerometers must be positioned very carefully at their designated locations within the sand, avoiding disturbance of the soil while ensuring accurate orientation along their longitudinal axis – a process more challenging than it may initially appear.

Figure 11 provides an overview of the key steps involved in preparing the centrifuge model with the unit cells, including: (a) the installation of two accelerometers in row C; (b) the installation of five accelerometers in row B, after vacuuming the sand (notice the characteristic stripes resulting from this process) to reach the desired soil depth and level the ground surface, as more sand tends to accumulate at the four corners of the container during the sand raining process (visible in Figure 11(a)); (c) the installation of unit cells following sand vacuuming; (d) the outcome of a half-cycle of sand raining immediately after the previous step, with sand collectors placed on top of the unit cells to prevent the sand from entering their interior; (e) installation of the final five accelerometers in row A; (f) the last half-cycle of sand raining, followed by final sand vacuuming to level the ground surface; (g) placement of the structure in the centre and meticulous sprinkling of small metal particles on the ground surface, serving as an ad hoc speckle pattern for subsequent DIC analysis; and (h) secure mounting of the laminar container on the seismic shaker, which is installed on the beam centrifuge. It is important to note that exactly the same procedure is followed for both models to ensure fair comparison.

The first model tested in the centrifuge is the one with the standalone SDOF structure, used to obtain its unprotected seismic response. After completing all final checks, the model is spun up to 50 g centrifugal acceleration, and the shaker applies the previously discussed deconvoluted ground motions in the same sequence as the records listed in Table 2. The deconvoluted Ormsby wavelet is applied last, as it is used exclusively for system identification. The accelerometers and cameras record each seismic excitation independently, at sampling rates of 1/2500 and 1/2000 s, respectively, providing sufficient resolution to capture soil and structural responses within the frequency range of interest (∼150 Hz). After testing, the centrifuge is gradually decelerated, stopped, and the laminar container is removed and emptied to prepare the second experiment, which includes the metamaterials. Following careful preparation to ensure identical conditions with the first model, the second test is performed following the exact same procedure and shaking sequence. The raw accelerometer recordings from both experiments are publicly available as a supplementary dataset (Kanellopoulos et al., 2026).

Before directly comparing the two experiments to investigate the impact of metamaterials on structural response, it is essential to verify that the dynamic response of all model components (i.e. unit cells, soil, and structure) during the centrifuge experiments aligns with the expected performance. Given the intricate and delicate internal geometry of the unit cells, which could potentially be influenced by the centrifugal acceleration, verifying their dynamic response is crucial. DIC frequency-domain analysis of the vibrating unit-cell masses using the VIC-3D software allows extraction of the metamaterials’ resonant frequency. Figure 12 presents the Fourier amplitude spectra of the six unit-cell masses for all seismic excitations. Their resonant frequencies cluster around 145 Hz, being remarkably close to the 150 Hz measured before the centrifuge tests with the vibrometer. The small reduction in frequency is most likely due to SSI effects. The fundamental vibration frequency of the structure (measured using accelerometers S3 and S4 as shown later in Figure 14) is also shifted to 145 Hz, being lower than its fixed-base value of 160 Hz – an SSI effect slightly more pronounced than for the unit cells. The convergence of the fundamental frequencies of the metamaterials and the structure around 145 Hz is an effective (if not optimal) tuning condition that enables their beneficial interaction, as discussed earlier on.

This remarkable tuning stability – maintained under 50 g acceleration, realistic soil conditions, and real earthquake loading using intricate small-scale 3D-printed unit cells – demonstrates the robustness and stability of the system under realistic conditions. A full-scale unit cell, properly engineered at later TRL stages, will likely be easier to tune precisely than these small-scale models, with lifecycle adjustments possible through regular maintenance to address aging and other long-term issues, aiming to preserve performance.

To evaluate the effective fundamental frequency of the soil deposit subjected to the deconvoluted Ormsby excitation, the Fourier amplitude spectra of the recorded acceleration time histories at the base (⁠$FFTTABLE$⁠) and near the free field (⁠$FFTA4$⁠) are calculated and divided, yielding the corresponding horizontal acceleration FRF magnitude from TABLE to A4 (Figure 13). The results indicate that the effective fundamental frequency of the soil deposit is approximately 95 Hz, substantially lower than the value predicted by the equivalent-linear analysis: 150 Hz for the Ormsby ground motion, decreasing to 125 Hz for the stronger excitations. This discrepancy was found to arise from two main factors. First, the mass of the laminate frames, which cannot be incorporated in ProShake without affecting $p′$⁠, increases the oscillating mass by around 40% and thus lowers the soil’s fundamental frequency. Second, discretising an exponential soil profile into layers for equivalent-linear analysis becomes problematic near the ground surface, where the shear wave velocity approaches zero and results become sensitive to the chosen layer thickness. A non-linear analysis that includes the additional frame mass aligns closely with the experimental observations and is therefore recommended for exponential soil profiles over an equivalent-linear analysis.

To assess possible accumulation of soil non-linearity during the shaking sequence, the El Centro motion (Table 2), which was applied first, was also re-applied at the end of each test series. Comparison of the FRFs from the shaking table to the near-surface sensor A4 (not shown for brevity) showed that the fundamental frequency of the soil remained practically unchanged at ∼95 Hz between the first and last El Centro excitations, indicating negligible stiffness degradation and thus relatively inappreciable non-linear effects under the applied loading levels.

While the precise prediction of the fundamental frequency of the soil is not essential for this study – since the focus is on comparative analysis between two systematically prepared models – the observed mismatch significantly affects the analysis of the results. Since the actual fundamental frequency of the soil (95 Hz) is significantly lower than the expected value (150 Hz), the input seismic waves were not amplified around 150 Hz, resulting in very small Fourier spectrum amplitudes at this frequency range near the ground surface at A4 (highlighted in Figure 13). As a consequence, the excitation of the structure at its resonant frequency of 145 Hz is minimal, and a direct time-domain comparison between the two experiments would not be effective, as all response time histories are dominated by low-frequency oscillations and appear very similar. To enable, therefore, a meaningful comparison, the effect of the resonant metamaterials on the SDOF structure near their resonant frequency is examined in the frequency domain. Note that all signals under comparison in this study are synchronised and trimmed, having the same sample frequency (1/2500 s) and number of points before transforming them into the frequency domain.

Figure 14 presents a comparison between the two models for the three deconvoluted seismic motions in the frequency domain. To evaluate the repeatability of the experiments, the Fourier amplitude spectra at A4 (located near the free field) are compared in the top left of the figure. The results are remarkably similar, strongly indicating that the models were prepared consistently and that the sand raining system reliably produces repeatable soil profiles. This nearly identical soil response confirms that the region surrounding the structure experiences the same excitation in both models, enabling a meaningful direct comparison. In addition, Table 4 summarises time-domain reproducibility metrics of the input accelerations at point TABLE for each seismic motion, comparing the peak acceleration errors (PAE) and the normalised root-mean-square errors (RMSE) between the two tests, where $a1$ and $a2$ denote the acceleration time histories recorded during the first and second centrifuge experiments, respectively. The very small PAE and normalised RMSE values reported in Table 4 further confirm that the input excitations are practically identical in both tests, strengthening confidence in the subsequent direct comparison of the two models.

To assess the influence of resonant metamaterials on the structure, the horizontal acceleration FRF magnitudes from the base (S3) to the top (S4) of the structure are compared in the top right of the figure. In the presence of the resonant metamaterials (labelled ‘with’), a pronounced amplitude reduction is observed around the resonant frequency of the structure (145 Hz) for all seismic excitations – particularly for the non-pulse-like El Centro motion – coinciding with the metamaterial resonant frequency. This result demonstrates the beneficial inertial meta–SSI effect, which heavily relies on proper tuning of the unit cells and arises from the out-of-phase oscillation of their internal masses at resonance with respect to the surrounding soil (as also visually explained in the next section). Remarkably, while the experimentally observed soil fundamental frequency (∼95 Hz) differs from the ProShake prediction (∼150 Hz), resulting in reduced excitation energy near the metamaterial–structure resonance (∼145 Hz), the observed attenuation remains substantial. Previous numerical work (Kanellopoulos et al., 2022a) demonstrates that maximum structural response reduction occurs under optimal double-resonance conditions, where the soil layer’s natural frequency aligns with the metamaterial resonant frequency, amplifying unit-cell oscillations. Thus, the current results conservatively demonstrate meta–SSI effectiveness even under non-optimal soil conditions, suggesting even greater potential when optimal double-resonance conditions occur.

Numerical studies (Kanellopoulos et al., 2022a) have previously demonstrated that the protective mechanism of seismic resonant metamaterials depends on their out-of-phase oscillation with the surrounding soil at their resonant frequency. This interaction enables the metamaterials to counteract the movement of the adjacent soil, resulting in reduced accelerations that benefit the protected structure. To experimentally validate this mechanism, a frequency-domain DIC analysis was conducted on the vibrating unit-cell masses and the adjacent soil surface at the right side of the structure, which is unobstructed by accelerometers and therefore fully visible to the cameras. As shown in Figure 15 for Ormsby excitation at 146 Hz, the DIC results offer a visual illustration of the protective mechanism in the frequency domain. Figure 15(a) reveals a clear phase difference between the unit-cell masses and the adjacent soil surface: contours over the masses read −2.2 rad, while those on the soil surface are approximately −0.75 rad, indicating a phase difference of 1.45 rad – very close to $π/$2 (≈1.57 rad). This also confirms that the unit-cell masses are operating near resonance.

Figure 15(b) further illustrates this out-of-phase oscillation over a full vibration cycle, mapping the horizontal displacement contours of the masses and the soil across five consecutive moments, spaced approximately $T/$4 apart (where $T$ is the full oscillation period). At $t≈0$⁠, the purple contours over the masses denote negative displacements, while green contours over the soil indicate positive displacements. At $t≈0.5T$⁠, this relationship reverses, with yellow contours over the masses showing positive displacements, and bluish contours over the soil representing negative ones. Finally, at $t≈T$⁠, both the masses and soil have returned to their initial positions. Transitional states at $t≈0.25T$ and $0.75T$ are also depicted for completeness.

The above findings clearly demonstrate the protective mechanism of resonant metamaterials, which are purely attributed to their inertial interaction with the surrounding soil. To rule out the possibility that kinematic interactions have contributed to the protective mechanism, a comparison is made between the wavelength of the vertically propagating horizontal shear waves and the vertical size of the unit cells. Estimation of the wavelength requires knowledge of the shear wave velocity of the soil deposit. The effective shear wave velocity between points TABLE and A4 was roughly approximated at 100 m/s by dividing the distance between these points by the measured time difference between acceleration peaks. For the target frequency of 145 Hz, this corresponds to a wavelength of approximately $λ = VS/f =$ 0.69 m. Dividing this by the vertical dimension of the unit cell (0.047 m) yields a wavelength to unit-cell size ratio of 14.7 – sufficiently large to rule out kinematic interaction. For context, Bragg scattering effects (arising from kinematic interactions through destructive wave interference in metamaterials) typically occur when the wavelength is approximately equal to the size of the unit cell (Aguzzi et al., 2022a).

Another important aspect of resonant metamaterials is the size of their influence zone – the adjacent area affected by their presence. This zone is crucial both for the protected structure and nearby ones. For instance, wide structures may not receive adequate protection if the influence zone is relatively small, whereas a large influence zone could lead to unintended interactions with nearby structures, potentially amplifying their response and deteriorating their seismic performance. Previous numerical work of the first author (Kanellopoulos et al., 2022a) has concluded that metamaterials’ effect in realistic soil profiles practically vanishes beyond ∼3.5 times their height (embedment depth), posing no threat to nearby structures outside this zone. Figure 16 provides a rough estimate of the influence zone by comparing the FRFs at the first-row accelerometers of the two models for the Kalamata ground motion. For each accelerometer, the FRF magnitude from A5 (rather than from the model base) is calculated in an attempt to exclude the contribution of 1D soil response and, therefore, focus only on the influence of the unit cells and the structure on the first-row accelerometers. The first clear observation in Figure 16 is the antiresonance peak near 140 Hz, produced mainly by the resonance of the structure and, secondarily, by the resonance of the metamaterials around this frequency. As expected, this antiresonance is more pronounced at points A1 and A2, closest to the specimens, and it diminishes progressively at A3, practically vanishing beyond points A4 and A5. This combined structure–metamaterial influence zone up to point A3, although primarily driven by the structure, is a strong indication that metamaterials’ effect should also practically vanish beyond point A3.

To isolate the contribution of the metamaterials to this antiresonance, a comparison between the two models is required. Inspection of the FRFs within the semi-transparent highlighted regions shows that the responses with (magenta) and without (grey) metamaterials differ noticeably in the range of the metamaterials’ resonant frequency only at A1, A2, and A3. This indicates that their influence zone extends up to point A3, with no detectable effect further away (A4 and A5). The influence zone can therefore be approximated as the lateral distance from the unit cells to point A3, which is 118 mm (5.9 m at prototype scale). Dividing this distance by the vertical dimension of the unit cells (47 mm) yields a ratio of 2.5, implying that the metamaterials’ influence zone extends laterally to about 2.5 times the unit-cell height – compatible with the above-discussed numerical work. To further support the validity of this observation, a rough analogy is drawn with analytical Boussinesq solutions for uniform loading of a rectangular foundation over a homogeneous isotropic elastic half-space. In the case of such a foundation with an aspect ratio of 1:3, the vertical stress practically vanishes (reduces to 10% of the applied load) at a depth 3.5 times the width of the foundation (Yu, 2023). Although the context is different, this similarity provides qualitative support to the observed extent of the unit-cell influence zone. Results for the Parkfield motion showed similar trends, while the data from the El Centro ground motion were too noisy for a reliable interpretation.

This paper offers the first experimental study of dynamic metamaterial–soil–structure interaction (meta–SSI) via two centrifuge experiments at 50 g centrifugal acceleration. In the first experiment, a simplified SDOF structure is subjected to a series of single-component (horizontal) seismic motions to capture its unprotected response. In the second experiment, three properly tuned unit-cell resonant metamaterials or metabarriers are embedded on each side of the structure and exactly the same motions are applied. The main findings are summarised as follows:

• Properly tuned resonant metamaterials can mitigate structural vibration. Tuning the metamaterials to the fundamental vibration frequency of the SDOF model structure (approximately 145 Hz, corresponding to 2.9 Hz vibration frequency of the prototype structure) leads to a significant reduction of the horizontal acceleration FRF magnitude at this frequency for all studied seismic excitations.

• The seismic protection mechanism arises from the out-of-phase oscillation of the unit-cell masses (at resonance) relative to the applied excitation by the adjacent soil (inertial metamaterial–soil interaction). This opposition to the soil motion reduces the soil response near the resonant frequency of the metamaterials, thereby benefiting the structure and highlighting the importance of precise metamaterial–structure tuning.

• The influence zone of the resonant metamaterials – where their effects are experimentally observed – extends laterally about 2.5 times the height of a unit cell. This should be considered both for the target structure and for its neighbouring structures to ensure effective protection and to prevent unintended adverse effects, respectively.

This unique experimental study validates the protection mechanism of resonant metabarriers, highlights their potential for seismic protection of both existing and new structures, and provides valuable experimental data for the validation of numerical models in future studies. Certain simplifications arising from the proof-of-concept nature of this work – such as the use of an idealised SDOF structure, the simplified SDOF unit-cell models coupling only with a single horizontal wave component, the assumption of vertically propagating shear waves, and a limited set of seismic excitations – constitute its key limitations. Nonetheless, costly and complex geotechnical centrifuge tests provide high-fidelity data, precluding broad parametric studies. Accordingly, a complementary ongoing study will use the available experimental data to validate high-fidelity meta–SSI finite element models and perform extensive parametric analyses to rigorously evaluate the protection efficiency of resonant metamaterial across various structural types, soil profiles, and more realistic seismic wavefields.

To enable the application of resonant metamaterials in practice, advancing beyond the current proof-of-concept stage (TRL 3) is required. To reach the next TRL level (TRL 4 – Technology validated in lab), future experimental research should prioritise the development of realistic multi-directional unit-cell designs and rigorously evaluate their protection efficiency for realistic MDOF structural models. These efforts will support technology maturity and facilitate integration into practical seismic protection solutions – particularly for cases where structural intervention is prohibited due to aesthetic or operational constraints, making conventional seismic protection methods entirely unsuitable.

The raw accelerometer recordings from the two centrifuge experiments are publicly available as a supplementary dataset (Kanellopoulos et al., 2026).