Introduction

The primary objective of an art museum is to conserve and exhibit the art and objects with which it has been entrusted. The physical condition of the art and the artefacts in a museum, hereafter collectively referred to as the art, varies widely. The magnitude, type, and duration of construction activities (e.g., the vibration source or input) are project-specific and usually determined through discussions between contractor, conservation, and curatorial teams. The hazard posed by these activities stems from the vibration energy produced, which typically travels from the point of construction tool application through the structure (i.e., the museum building) to an exhibition case and/or mount, and ultimately into the art itself. Considering the broad spectrum of art that a museum may house, a fitting solution should be tailored for each specific construction project and the art that it potentially impacts. To face these challenges, it is essential to monitor vibrations throughout the construction process to mitigate the risk of damage to the collection that is within the influence zone of the project. To understand vibration levels, acceleration time histories are typically recorded using sensors placed in strategic locations, and corresponding peak particle velocity (PV) is calculated through numerical integration1,2. Several studies have established threshold levels of vibration at which damage is either possible or probable3,4,5,6,7,8. Some thresholds consider, to varying degrees, peak accelerations, integrated PVs, and/or frequency content. Thickett5 observed that, in most cases, damage to art occurs at acceleration levels of 0.15–0.3 g and noted that the majority of such damage manifests in objects with pre-existing weaknesses. Johnson et al.6 suggested using the PV threshold of 2.5–3 mm/s, and that in the case of the frequency of vibration exceeding 10 Hz, the threshold can be increased to 13 mm/s. However, Smyth et al.7 later indicated that it is not uncommon for art objects in museums to exhibit vibration frequencies between 20 and 30 Hz, as also suggested by other studies on objects such as painting canvases9 and stone statues10. Permitting the increase of the threshold with an increase in frequencies will put museum objects at greater risk since many construction tools operate within a similar frequency range. If the input frequency (i.e., the rotational velocity of a reciprocating tool) coincides with the natural frequency of the structure, the structural system, along with its payload, the art, may enter a state of resonance, significantly amplifying vibration and thus the risk of damage.

Wei et al.11 reported two cases of damage that occurred during the monitoring of vibrations in the World Museum Liverpool during active construction work. The recorded peak velocities at the museum were on the order of 2–3 mm/s, with vibrations above 3 mm/s occurring in only a few instances over a number of days. In light of this observation, the damage was attributed not to the particular threshold exceedance but to the consistent cyclic loading close to the threshold limit, which resulted in stress accumulation and led to localized fracture in two art pieces. Further, multiple projects have performed pilot tests to probe various means and methods to determine the susceptibility of the museum structure—including the building, exhibition cases, and art mounts-to construction vibration inputs12,13. These trials are vital for the identification of appropriate procedures and equipment that would be safe to use when the construction activities take place in close proximity to the art. A pilot test performed at the Philadelphia Museum of Art indicated that due to specific structural characteristics of the Chinese Reception Hall, the supporting structure exhibited resonance at a frequency range of 10–20 Hz and would in turn directly transmit the amplified energy to the art if the vibration input coincided with this frequency range. Consequently, the vibration limits were adjusted with respect to frequency, with a greater level of tolerance for frequencies above 40 Hz14. Another probing test series was performed at the Royal Gallery in the Palace of Westminster, where a large wall painting with pre-existing cracks was monitored to prevent damage due to proximate masonry work15. The conservation team analyzed vibration levels caused by different construction methods and identified those that exceeded the alarm threshold of 0.15 g. As a result, the team further suggested a set of preferable tools for the construction work to reduce the risk of damaging the art. Additionally, to mitigate structural response, damping measures were applied by bracing the supporting structure with timber frames. Several studies have explored object-specific vibration mitigation strategies tailored to the natural frequencies of the art in question2,3,10,16,17,18. These investigations involved numerical models developed specifically for the objects of interest, where field measurements were integrated for analysis of the objects’ dynamic behavior. Xu et al.10 applied computational modeling to identify the dynamic modes of stone statues and determine the locations of the highest stress concentrations. Based on their analysis, the authors reduced the alarm threshold for vibration velocity to 0.22–1.0 mm/s. This reduction was guided by simulated stress levels, which indicated the potential for accumulated stresses to cause damage in the statues.

The aforementioned projects underline the necessity of vibration monitoring in museums and highlight the importance of a priori knowledge of the dynamics of art objects and the structural characteristics of the systems that support them. Nevertheless, the number of studies on the impact of construction activities on museum objects remains limited, with the majority focusing on vibration threshold limits19,20. In fact, a recent study8 attempted to summarize thresholds for vibration levels associated with damage of various art objects. However, the study suggests an analytical approach by predicting the stress levels in the objects using standalone numerical models, and did not account for the effects of support structures and mounting details on vibration transmission and amplification, nor did it consider the specific dynamic characteristics of the galleries that house the art. The objective of this article is to present an investigative case study examining the impact of various construction methods and tools on vibration of wall-mounted reliefs, based on accelerations and integrated velocities recorded during a series of pilot tests. These tests were performed before the start of construction activities in the galleries at the Metropolitan Museum of Art (MMA). We present a detailed analysis of the vibration levels to support the development of guidelines and safety procedures for the construction team and museum staff to ensure the preservation of the art at the museum. This work specifically focuses on the role of the museum building, art support structure, and mounting details in the transmittal, damping, and potential amplification of vibration to the art. The specifics of the case study and the risks posed to the Assyrian art are described in the “Methods” section, along with the details of the art mounting, supporting structural system, and the setup of the vibration monitoring system. The “Results” section presents findings from ambient condition measurements, construction method probing tests, and in-service load tests, followed by a numerical simulation of one of the reliefs. The “Discussion” section of the manuscript presents a detailed analysis of the results and the conclusion of the study.

Methods

The MMA is currently renovating its Galleries for the Art of Ancient West Asia (Department of Ancient West Asian Art, formerly Department of Ancient Near Eastern Art) and Art of Ancient Cyprus (Department of Greek and Roman Art) to improve the visitor experience and update gallery designs, while also providing disability access and improving visitor flow throughout the southeastern quadrant of the second floor of the museum. The work proposes the removal of various structural masonry wall sections and, most notably for this project, the installation of a wheelchair ramp to connect two internal museum structures per ADA (Americans with Disabilities Act) requirements. The structural system supporting the construction area primarily consists of a set of long-span steel beams measuring 12.2 m in length that frame, on each side, into structural masonry walls. The masonry walls have a substantial thickness of approximately 1 m. One such wall will be cut back to improve visitor flow and provide access to the ADA ramp. The broadening of walkways and portals will require the use of heavy machinery for the demolition of portions of these structural brick walls. Additionally, the gallery renovation will include the rebuilding of existing flooring and stairs. The art located in the future construction zone consists of twenty partial and complete relief panels and two gateway guardian figures in the form of a human-headed winged lion and bull, known as lamassu, all from the site of Nimrud, ancient Kalhu, in northern Iraq. Almost all of the sculptures come from the Northwest Palace of the Assyrian king Ashurnasirpal II (r. ca. 883–859 BCE); the two exceptions come from the same king’s contemporary building work on the nearby Temple of Ninurta. The surfaces are carved in low relief, often with very fine detail, and were originally painted, although few traces of pigment survive today. They were carved on the faces of large blocks of gypsum stone that were set into thick mudbrick walls that continued above up to the ceiling in the palace. As with most other Mesopotamian architecture, the walls of the Assyrian palaces were not built of stone but of mud brick, and the stone reliefs served as the facing for the rooms in the 9th-century BCE palace. The transportation of monumental lamassu figures from quarry to palace was depicted in later reliefs from Nineveh that included scores of workers hauling ropes under the supervision of Sennacherib.

The reliefs were excavated in the middle of the 19th century, most in the years 1845–5121. The reliefs were removed without modern excavation or recording techniques, although the many drawings made by the excavators and artists assisting them, their own publications describing the work, and surviving correspondence archives have all helped to reconstruct their activities, including the original specific locations of the reliefs within the palace. For the site of Nimrud, the main excavator was the English traveler Austen Henry Layard22, and the largest group of sculptures went to the British Museum. The reliefs on display in the MMA were acquired at different times, beginning in 1884 (for the specific provenance of each relief, see individual object records online (The Met Collection23)), but the majority of sculptures in the gallery, including the colossal winged bull and lion, were a gift of John D. Rockefeller, Jr. Following their excavation in northern Iraq, these sculptures had been floated on rafts down the River Tigris to Baghdad and then Basra, shipped first to Bombay (present-day Mumbai) and from there to England, where they were incorporated into a purpose-built “Nineveh Porch” at a country house, completed around 1851. In 1919, the sculptures were purchased by the antiquities dealer Dikran Kelekian. Kelekian shipped them to New York, hoping to sell them to a US museum or a wealthy individual who would gift them to one. The sculptures at one point traveled to Philadelphia and were displayed there in the University Museum before finally being purchased by Rockefeller in 1927 and given to the MMA in 1930 (though they were not accessioned until 1931 and 1932). Their modern history has been researched in detail24,25. The Assyrian sculpture court as seen today is a composite, with reliefs originating in multiple rooms and a layout generally representative of several reception rooms in the palace, while other elements evoke an open courtyard or the façade of the Ninurta Temple, so that the court does not act as a specific reconstruction of any one space26.

The initial excavation and transport of the reliefs resulted in significant damage to them. In order to facilitate shipping, relief blocks were cut down at the back until in many cases, they were only 5–10 cm thick, and some reliefs were further cut into horizontal strips. When acquired by the museum, the relief sections had already been assembled using a range of binders, including plaster and mortar. Before they were moved to a gallery in the museum in the late 1950s, it was decided to assemble the majority of the reliefs into steel frames. Ottavina Corporation, a stonemasonry company founded in 1913 and still in operation, was hired to do this work (Fig. 1a, b). Although little written documentation of their restorations exists, photographs taken at that time indicate that new joins were made using metal pins and Akemi (a bilked polyester-based masonry adhesive). On the reverse, joins were reinforced by applying pieces of flagstone held in place with plaster. Losses on the front were filled with plaster and painted to match the surrounding stone.

Fig. 1: Gypsum alabaster relief panels from the Northwest Palace of Ashurnasirpal II at Nimrud (ancient Kalhu), Iraq, ca. 883-859 BCE.
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a Repair (MMA 32.143.6, final setting of dowelled and glued pieces before placement in steel frame). b assembly of the reliefs by Ottavina Corporation stonemasons (both photographs taken on 8/19/1957), and c example highlighting areas of repair on an assembled relief 31.72.1. with dimensions 235 × 156.2 × 5.4 cm, gift of John D. Rockefeller Jr., 1931. The red-marked lines indicate breaks between repaired sections, while the holes were likely drilled for modern metal staples that have since been removed. Photographs courtesy of the Metropolitan Museum of Art.

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The assembled reliefs have remained intact since this restoration and were safely moved to their current gallery in the early 1980s when they were hung from a steel superstructure and framed by wire lath plaster walls. However, they are inherently brittle and have been mounted in a way that precludes the placement of vibration mitigation materials. Initially, it was thought that the reliefs and the lamassu should be moved before construction began. After evaluating the risks involved in deinstalling and storing the sculptures, it was decided to leave the pieces in place and instead provide robust physical protection along with a vibration monitoring system. Before construction began, condition maps of the reliefs were drawn, and a suite of both natural light and multiband images was created to document their condition, identifying any traces of extant pigment and serving as a baseline for monitoring any changes that might occur during the reconstruction project.

By the time the lamassu figures in the MMA’s collection arrived in New York, they had been hollowed out at the back and cut into four sections. The sections were further assembled at the museum by the stonemasons (Fig. 2a). Upon completion, the lamassu statues were presented to the museum visitors (Fig. 2b). The gypsum in the art material, being a relatively soft stone with a Mohs hardness value of 2, led to breakage during the processes of the cutting the lamassu for transportation, which resulted in internal veins and inclusions in the art.

Fig. 2: Lamassu (Human-headed winged lion) from the Northwest Palace of Ashurnasirpal II at Nimrud (ancient Kalhu), Iraq, ca. 883–859 BCE.
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a Assembly of a statue (photograph taken 9/10/1957). b Completed statue as displayed in the galleries prior to the renovation project: 311.2 × 62.2 × 276.9 cm. Gift of John D. Rockefeller Jr., 1932, 32.143.2. Photographs courtesy of the Metropolitan Museum of Art.

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A potential issue that may arise due to dynamic loading induced by construction vibrations is the stiffness incompatibility between the repair materials and the reliefs’ stone pieces. The reliefs were repaired with polyester resin that has a lower modulus of elasticity than the stone. Because of this mechanical mismatch, the materials will move/vibrate at different amplitudes causing an uneven distribution of stresses, concentrating at the interface. Under vibrational loads, these stress concentrations can lead to the initiation and propagation of cracks, particularly at the edges where stress is highest27. Furthermore, it can result in the separation of the resin and the relief pieces, known as delamination. The reliefs have a relatively slender thickness and considerable width and length, ranging from 1 to 2.3 m. Such dimensions will likely cause them to behave as imperfect diaphragms and exhibit complex dynamic modes. The diaphragms are vulnerable in the direction of their thickness, making them highly sensitive to out-of-plane external vibrations. In contrast, the lamassu, despite being previously sectioned, act as large lumped masses that attenuate the majority of the vibrations they receive in all directions, making them less sensitive to dynamic loads. Moreover, the slab beneath the statues has been reinforced with additional beams due to the heavy weight of the art, which has likely reduced the floor’s dynamic motion under the pieces. The exact details surrounding the original installation of the slab stiffeners do not appear to have been documented; thus, their contribution to the dynamic response of the floor is uncertain without direct measurement. The stone reliefs considered in this study are mounted on a wall on the southern side of the gallery, which is laterally supported by a superstructure consisting of steel beams and columns designed as a simply supported structure (i.e., pinned end connections that do not transfer bending moment loads). The superstructure is an important structural component and is laterally braced to the structural masonry wall at the mezzanine level on the southern side of the gallery. The steel frames with the relief panels rest on horizontal steel beams attached to the superstructure, shimmed by the use of a multitude of steel stock of varying thicknesses. Out-of-plane lateral support is provided at the top of each panel by steel brackets that connect the relief panel backplane with the steel beam of the superstructure.

The museum renovation plan includes the removal of the mezzanine floor and its lateral bracing system. This procedure will significantly impact the reliefs, as they are laterally braced by the superstructure. To assess what level of vibration to expect and what equipment is safe to use during the mezzanine removal and other construction activities, a series of exploratory probes with simultaneous vibration monitoring were performed.

Vibration monitoring

To evaluate the potential impact from the renovation project, a network of sensors was installed to measure the vibration of the art and the supporting structure through a series of pilot tests. The primary objective of these tests is to map the effect of various vibration inputs on the building, the superstructure, and ultimately, the art. The tests were conducted in three phases. Initially, measurements of ambient vibrations within the gallery were collected over a period of ten days while the gallery remained open to visitors. These measurements were subsequently analyzed to establish a statistical baseline for the vibrations in the gallery under normal museum operation. This phase helped to gain more information about the building, the structural elements, and the art dynamics. Subsequently, after the gallery was closed to the public, a series of probes involving various construction methods and tools were executed for a short time in proximity to the art. Lastly, the third phase involved a set of dynamic live load tests conducted within the gallery space, also while the gallery was closed.

The monitored reliefs are located in the southern part of the gallery and are numbered from 1 to 5 in an east-west direction (Figs. 3, 4). The monitored lamassu is sited at the southeastern corner of the gallery.

Fig. 3: Southern part of the gallery with Assyrian reliefs and lamassu, gallery plan view.
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Red arrows show the direction of the measurements.

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Fig. 4: Elevation view of the gallery with Assyrian reliefs and lamassu.
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In a east-facing direction. b south-facing direction. The sensors’ instrumentation of the art is shown in red.

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The vibrations were measured through 24 acceleration sensors (PCB Model 393B04 ICP Accelerometer: sensitivity 102 mV/m/s²; frequency range 0.05–750 Hz; broadband resolution: 0.00003 m/s² RMS). Each sensor was connected to a compact data acquisition device (cDAQ-9191 with NI-9234 4-Channel Sound and Vibration Input Module) using a shielded coaxial cable, with a maximum of four sensors per device. All data was acquired at a frequency of 1706 Hz and anti-aliased using an onboard hardware low-pass filter. To measure the acceleration levels, the sensors were placed on the exposed concrete slab, five Assyrian stone reliefs, lamassu statue, and the superstructure elements. Figure 5 illustrates the support system of the reliefs and the setup for vibration monitoring in the gallery where the tests were performed. The top of each relief is connected to a support beam using two bolted brackets, which were found to be compliant connectors, while the bottom rests on a set of steel plate shims that transfer the weight of the relief onto a horizontal steel support beam.

Fig. 5: Schematic representation of the southern part of the gallery with Assyrian art.
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In a transverse direction, and b longitudinal direction.

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The measurements taken at the slab are referred to as “Floor reference,” where sensors were placed on the exposed concrete using aluminum bases to record acceleration in the vertical direction. Accelerations of the superstructure elements were measured in the horizontal direction at the top and mid-height of the columns, as well as at the bottom of the mezzanine floor support beam, with sensors installed using magnetic mounts. To measure the vibrations of the art, accelerometers were attached to the art’s bracing elements, also using magnetic mounts. To measure art acceleration, the sensors were placed at the top corners of five reliefs, with a few also being positioned at the bottom edge (Fig. 6a, b). The sensors’ placement on the reliefs was based on the preliminary assessment of the reliefs’ mounting conditions, where the partial fixity of both the top lateral brackets and the bottom shims was considered as uncertain boundary conditions. These areas were found to be particularly susceptible to amplified vibration response due to the compliant connections at the top and the shims at the bottom, which allow relative motion of the reliefs. For the lamassu, accelerations were measured in three directions using a tri-axial accelerometer setup, attached using a magnetic mount (Fig. 6c, d).

Fig. 6: Relief and lamassu instrumentation.
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a Instrumented relief showing locations of the sensors in red. b Backside of the instrumented relief affixed to the wall using steel stock. c Tri-axial accelerometer setup on the lamassu, where the x-axis corresponds to the out-of-plane direction, the y-axis to the in-plane direction, and the z-axis to the vertical (gravity) direction. d Backside of the instrumented lamassu. Photographs courtesy of the Metropolitan Museum of Art.

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Results

Ambient vibration

In the first phase, ambient vibrations caused by visitors and staff circulation were recorded to analyze the statistics of the velocities under normal museum operation. The records include primarily the vibration of the building and the art due to foot traffic, mechanical equipment (HVAC, etc.), and the structural response to street traffic from neighboring 5th Avenue, which experiences high density bus and truck traffic. For the statistical analysis, recorded acceleration and integrated velocities were collected over a period of ten days, with the absolute maximum of mean values recorded every 15 min. The records in Table 1 indicate that under normal museum conditions, the absolute maximum velocities of the reliefs did not exceed 0.44 mm/s, while floor vibrations remained below 0.32 mm/s. The lamassu, measured with a tri-axial accelerometer, exhibited a maximum PV in the vertical (z-axis) direction of only 0.18 mm/s.

Table 1 Maximum PVs of the reliefs in horizontal (out-of-plane) direction recorded during normal operation of the museum
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Although the vibration levels were well within the established safe limits, two of the reliefs showed higher velocity levels, on average. This can be attributed to the fact that these reliefs are located farther from the end supports of the main girders that span the gallery in the north-south direction and carry the floor slab. The main girders are framed into a heavy structural masonry wall, which provides significant mass and damping, and is expected to attenuate a substantial portion of the vibrations transferring to the reliefs closest to the girders’ end supports. The lamassu exhibited lower levels of vibration due to its substantial mass, which acts as a mass damper for the art. Figure 7 demonstrates the statistics of the velocities recorded at the slab (floor reference), column next to the relief, and top of the relief. The velocity time histories were sampled, and the relevant statistics (mean, standard deviation, and absolute maximum) for each 15 min bin were estimated. The mean values serve as an error check (near-zero mean indicates functional sensor) while the peak statistics show maximum recorded velocity during each 15 min window.

Fig. 7: Statistics of the absolute mean velocities at Relief 5 recorded during normal museum operation.
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Each data point represents the peak velocity (mm/s) within a 15 min time window.

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The analysis of ambient conditions showed that, during normal museum operations, the vibrations of the art and supporting elements are well within acceptable limits, with no damage expected as a result. To better understand the dynamic amplification of vibrations in the art and structural elements, an investigation was carried out to examine their correlation with floor velocity levels. The amplification factors for the reliefs and the structural elements are presented in Table 2, while those for the lamassu are in Table 3. It is important to note that the amplification factors were computed based on the time histories of the velocities and not the maximum PVs. The reference points for floor vibrations were positioned directly beneath the art being measured.

Table 2 Reliefs’ amplification factors relative to the floor reference velocity
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Table 3 Lamassu’s amplification factors relative to the floor reference velocity
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The analysis of the vibration data showed that the lamassu experiences no amplification in any direction, moving synchronously with the floor as a large lumped mass. In contrast, Relief 1 showed a velocity amplification of 3.62 at the top and 2.37 at the bottom. Relief 2 exhibited a stronger amplification from the floor with a factor of 4.89 at the top, and reduced vibration with a factor of 0.75 at the bottom, demonstrating variability in the relief dynamics. Such a strong discrepancy in the motion of the relief suggests that the art is relatively well anchored to the horizontal beam at the bottom and loosely connected at the top with a compliant connector. A compliant connector is a type of connection that allows some degree of flexibility or movement between the connected components. Unlike rigid connectors that provide a fixed, immovable connection, compliant connectors allow relative motion and thermal expansion between parts. The top of Relief 3 experienced velocities 5.40 times stronger than those measured on the floor, indicating significant amplification. This also suggests compliant connections between the relief and the superstructure, as the column showed almost no amplification from the floor. The vibration of a lower part of Relief 4 was amplified by the factor of 4.20, which in fact was not expected since the relief is supported by a horizontal beam at the bottom. Such an amplification implies that the relief is poorly anchored, likely due to deterioration or loosening of the shims responsible for transferring the load from the relief to the beam. Conversely, the top of Relief 5 shows a smaller amplification from the floor motion, which can be explained by a relatively stiffer connection of this relief to the support structure.

Further, using ambient vibration records, the modal characteristics of the reliefs, lamassu and the slab were identified, with the natural frequencies summarized in Table 4. The frequencies are reported along with their standard deviations, which reflect the uncertainty in the estimates due to ambient variability, nonlinearities in the dynamic response, and sensors’ noise. The uncertainties were quantified using multiple acceleration records.

Table 4 Natural frequencies of the art and the floor, with standard deviation indicating uncertainty in the identified values
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The first natural frequency of the lamassu, identified at 2.95 Hz, indicates that it behaves as a rigid body fully coupled with the floor (slab), an observation also supported by the analysis of amplification factors. The coupling stems from the mechanical connection at the base, where the statue rests on the slab through mortar bedding and the anchoring system. Within this coupled system, the dynamic responses of the lamassu and the slab are interdependent, and as a result, the modal characteristics of the statue (i.e., its natural frequencies and mode shapes) are influenced by the dynamic properties of the slab. The first natural frequencies of the reliefs are found to lie within the range of 11–25 Hz, further supporting the presence of flexible connections and loose shims. The relatively low effective stiffness implied by these values points to compliant boundary conditions, particularly at the top supports, where the most vibration amplification was observed.

The measurements collected revealed significant amplification of the art relative to the slab’s motion. The discrepancy in the motion of the reliefs is likely due to the different fixity conditions of the frames into which the art was mounted. The dynamic data underlie visual observations, indicating low connection fixity between the supporting superstructure and the relief panels. The tops of the reliefs experience the most amplification due to compliant lateral brackets that connect the art panels’ backplane with the superstructure. Closer inspection also showed that the edges of a few reliefs have pre-existing hairline cracks at the interface between the art and the plaster infill, while others appear fused with the plaster. This variation in edge fixity could further contribute to the variability of the reliefs’ dynamics. Due to the existing hairline cracks, the reliefs are partially detached from the wall and move with minimal structural damping, losing the mitigating effect provided by the plaster lath composite, which itself has considerably higher internal damping than the steel structure. However, the independence in movement is likely beneficial to the art as it prevents fretting/rubbing between the art and the plaster wall, which may damage the panel edges.

Construction means and methods probes

In the second phase, a series of probing tests were conducted, during which accelerations and integrated velocities were recorded for the analysis. Several construction tools were tested in close proximity to the Assyrian reliefs, with distances to the sensors ranging from 0.2 to 6 m. Accelerations were simultaneously recorded on all instrumented support structures and the art for each tool for a duration of 1–5 min per test. The selection of test locations and methods was tailored to align with the specifics of the renovation project. This approach ensured that the testing would provide relevant information about the art and the superstructure behavior. Table 5 shows a summary of the measured peak velocities during the tests performed.

Table 5 Summary of peak velocities recorded during pilot tests
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Circular saws, grinders, and floor sanders produce continuous high-frequency vibrations due to motor rotation and direct transmission of force to the substrate. The DeWalt drill operates at variable speeds (7.5–34 Hz), applying low-frequency cyclic torque and axial force, under pressure. Chipping guns (Hilti TE506, TE800-AVR) deliver mid- to high-frequency impacts (31–58 Hz), inducing strong cyclic loading. In contrast, hand tools like framing hammers and pry bars introduce localized, high-amplitude sustained vibrations when used repeatedly. Based on the authors’ experience, the construction tools evaluated in this study are commonly used in museum renovation projects. Therefore, a detailed assessment of the vibrations generated by these tools during different probes is presented.

A significant effort in this project includes the replacement of existing floor finishes in the galleries that house the Assyrian art. The scope, therefore, requires a probe of the removal of both parquet wooden floors, terracotta floor tiles, and self-leveling mortar bed beneath the tiles. For the latter, the use of hand tools such as a framing hammer to advance a flat pry bar into the mortar bed led to a peak velocity level that surpassed the 3 mm/s threshold for the stone relief nearest to the testing area. This occurrence was due to the substantial impact force applied to the tools during mortar removal. Hand tools, on average, generate high vibration peaks, as they are typically used in combination with a hammer to advance the tool. The impact from the hammer generates energy that goes onto the structure in a series of sharp peaks rather than a large number of lower energy impacts, as in the case of rotating/reciprocating tools such as drills, grinders, and chipping guns. Figure 8a illustrates the effect of the impact force produced by the flat pry bar and the hammer on the velocity level of the nearby relief. The frequency spectrum, which represents the energy distribution of the signal across different frequencies, is described by the Power Spectral Density (PSD), presented in Fig. 8b. The spectrum, estimated from the recorded velocities, indicates that a significant amount of energy over a broad range of frequencies was transferred to the relief during the test of mortar removal, posing a potential risk. On the other hand, the same test of mortar removal performed with the chipping gun resulted in lower vibrations, with the peak velocity not exceeding 0.58 mm/s (Fig. 9(a)). Additionally, as demonstrated in Fig. 9b, the energy content of the relief’s response was lower compared to the same construction procedure performed using the hand tools.

Fig. 8: Mortar removal using a flat pry bar and framing hammer.
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a Velocity time history recorded during the removal. b Frequency spectrum corresponding to the recorded velocity signal.

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Fig. 9: Mortar removal using Hilti TE506 chipping gun.
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a Velocity time history recorded during the removal. b Frequency spectrum corresponding to the recorded velocity signal.

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As shown in Table 5, a relatively high but short-duration PV peak (5.23 mm/s) was measured at the art during the drilling out of rivets holding the metal baseboard, located immediately under Relief 5. This test was necessary since the baseboard removal is a part of the floor renovation plan for the gallery. During the test, the slab and the support structure experienced far lower levels of vibration than the relief and did not exceed 2.15 mm/s (Fig. 10). Thus, the relief was directly excited by the drilling and baseboard removal activity, and the vibrations were likely highly attenuated during transmission from the art to the floor and the support elements.

Fig. 10
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Velocity time histories recorded during the pilot test of drilling out rivets from the baseboard.

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Drilling a hole for the toggle bolt above the same relief also caused an increase in the art’s vibrations, though to a lesser degree, with a maximum PV of 1.98 mm/s registered at the relief. The superstructure experienced larger PVs, reaching 2.3 mm/s at the top and 2.46 mm/s at the column mid-height. The drilling above the relief occurred almost parallel to the top support beam, allowing vibrations to travel a shorter distance and be directly transmitted to the support system. Figure 11 further demonstrates the relief support system and the locations where the tests were performed.

Fig. 11: Support system and testing setup.
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a Support system and instrumentation of Relief 5. b Schematic illustrating drilling tests performed above and below the relief. c The test of drilling a hole for a toggle bolt; the relief is covered by protective plastic sheathing.

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The vibrations caused by the baseboard removal and the hole drilling for a toggle bolt had a localized effect, as the rest of the monitored reliefs did not experience velocities higher than 0.24 mm/s, and their floor reference velocities remained well below 0.12 mm/s.

As part of the renovation project, a bracing structure will be installed to maintain the lateral stability of the support system holding the Assyrian reliefs in the new structural configuration. This alteration will require the welding of connection plates to the existing support structure to accept connections to the new stiffening assembly. This operation requires removal of the existing yellow paint from the columns. Consequently, a test of paint removal using a mechanical grinder with a steel wire brush wheel was staged on one of the support columns. The procedure generated substantial intensification of the vibrations, reaching 2.99 mm/s at the column top and 4.13 mm/s at the column mid-height. However, the velocities of the art during the test did not exceed 0.8 mm/s. The smaller effect on the reliefs was most likely due to the lower fixity of this particular relief to the support column, through compliant connections, which allowed a significant portion of the energy to dissipate when transmitted to the relief. The grinder generated high vibrations on the structure primarily because it was directly exciting the support column.

The demolition of the structural masonry wall is an essential part of the construction project and had to be tested by means of different tools. The probe was performed with a 23-lb Hilti TE800-AVR chipping gun and a Milwaukee 10-1/4” electric circular saw, followed by manual removal of the bricks by a construction worker. The wall planned for demolition is located 3 meters from the art on the southern perimeter of the gallery. The test conducted with the chipping gun resulted in intense sustained vibrations in one of the reliefs (Fig. 12a). The use of the circular saw was found to cause lower amplitude sustained vibrations but had relatively high transitory impacts on the relief (Fig. 12b). It was also observed that the measured responses were location-specific; the most amplified response during the chipping was recorded in the relief located relatively far to the west. In contrast, when the saw was used to cut the brick, the highest velocity was recorded in the relief located closest to the impact source. This discrepancy in the locations is likely due to multiple factors: the variable fixity of the reliefs to the support structure that transmitted the vibration to the art, and the structural wall’s dynamic transmission of the vibration to the support structure.

Fig. 12: Velocity levels recorded during the test of the masonry structural wall demolition.
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Record of the probe performed with a Hilti TE800-AVR chipping gun, and b Milwaukee 10-1/4” circular saw.

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While the velocities occasionally approached the PV of 1.5 mm/s during the trial demolition, this typically resulted from short but intense impacts rather than sustained vibrations. However, it is important to note that sustained vibrations pose a greater risk to art than short impacts. Damage tends to accumulate over time and requires prolonged, consistent vibration for stress to accumulate in the object, potentially leading to fractures and/or delamination. Therefore, the most harmful vibrations for the art would be those that are sustained and of high magnitude, approaching or exceeding 3 mm/s.

The highest response in the art and the structural system was recorded during the probe of drilling the floor next to the support column (Fig. 13a). The probe was performed as a trial for the future installation of the new support system that will require drilling of the bolts inside the concrete slab. Drilling was executed with the DeWalt hammer drill with 3/4-in. bit, that has both rotational and percussive frequencies. The hammer drill produces high-energy pulses with a broad frequency content, creating high-frequency stress waves that travel across the gallery and induce vibration in the nearby objects. The frequencies of these waves are highly dependent on the solid materials through which they travel.

Fig. 13: Drilling the slab with a hammer drill next to the steel support column.
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a Photograph documenting the probe setup. b Acceleration time history measured on the floor, with a non-zero mean signal evident in the 5-8 s range. c Frequency spectrum of the measured acceleration.

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The accelerations measured during this test went beyond the practical range, especially those recorded by a sensor located on the floor, immediately adjacent to the drilling location. The drilling caused this sensor to rock, resulting in non-stationary signal readings. Such data causes drift during numerical integration, producing unreliable velocity values. As a result, the velocities recorded during this test were discarded. Consequently, the vibration levels measured during this test are presented in terms of accelerations rather than integrated velocities (Table 6).

Table 6 Acceleration levels recorded during the test of drilling next to the support column
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The floor reference sensor registered a peak acceleration of 2.42 g, as demonstrated in Fig. 13b, while a sensor attached to the nearby relief recorded a lesser value of 0.98 g. The lower acceleration levels of the relief compared to the structural elements indicate that some energy was dissipated when transmitted to the art. However, the relief still experienced substantial vibration, which according to Thickett5, can be damaging to the art. In this particular case, the repeated exposure of the relief to such a high level of vibrations can weaken the adhesive bonds and cause delamination of the relief’s repair materials. This is an undesirable scenario and should be avoided. The frequency content of the acceleration recorded on the slab, shown in Fig. 13c, indicates that the maximum energy is concentrated around 690 Hz. Such a high frequency can be explained by the short distance between the applied force and the sensor. High-frequency waves tend to attenuate rapidly as they travel through the material due to internal friction and scattering28.

To confirm that the acceleration data measured during this test accurately depicts the structural response of the system, the test was repeated under laboratory conditions using a hammer drill with similar rotational and percussive characteristics. The measurements taken during this test were recorded by an accelerometer located at a distance of 25 cm from the drilling pit. The test results, shown in Fig. 14, indicated that the frequency content in the acceleration data is realistic, confirming the reliability of the acceleration data from the probe at the museum.

Fig. 14
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Energy distribution in acceleration data when heavy and light pressure were applied to the hammer drill during the concrete slab drilling test.

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The analysis also revealed that the pressure applied to the mechanical tool significantly affects the magnitude and frequencies of the vibration. Light pressure on the hammer drill resulted in a lower vibration response in the concrete floor. The definition of light and heavy pressure is obviously a highly subjective, operator-specific quantity. Ongoing live instrumentation during active construction will provide warnings and alarms when rotating/percussive tools are used with excessive force. To reduce the risk of the high amplitude vibrations, a high-speed core drill is recommended as a safer alternative to a conventional hammer drill. It was found in a previous study7 that a coring drill can reduce vibration of the art objects by more than two-fold compared to a conventional hammer drill of the same size. The proximity of the construction zone to the Assyrian reliefs underlines the importance of this tool choice.

Live-load tests

During the third phase, two in-service dynamic load scenarios were performed: 1) the worst-case scenario of a heavy vehicle traversing the gallery and 2) a highly dynamic small crowd of people jumping and dancing in the vicinity of the art. The MMA employs scissor lifts for a variety of facilities maintenance tasks, and it is expected that the lifts will be used for the upcoming renovation project and also serve as a surrogate for other wheeled construction equipment. From the perspective of dynamic effects, scissor lift can be idealized as a large lumped mass traveling across the gallery. The lifts can create a powerful impact force during the raising and lowering of the working platform, which produces strong structural system response. To investigate the potential impact on the art and the support structure, an UpRight 20 N scissor lift was used to simulate typical trade traffic in the gallery that would occur during construction work. The lift was operated within 1 m of the reliefs, driven, extended, and retracted in several locations. Based on the analysis of the measured data, the vibration levels were moderate with high levels (up to 2.48 mm/s) produced only during the rapid retraction of the lift platform into its full down/docked position. Driving the lift across the gallery generated sustained vibrations that did not exceed 1 mm/s. Figure 15a shows the record of the velocities measured at the top of Relief 2, where the highest peaks correspond to the velocities recorded during the rapid raising and lowering of the lift platform.

Fig. 15: Velocity time history recorded at the top of Relief 2.
figure 15

During (a) UpRight 20 N scissor lift driving and docking, b spirited dancing and jumping of thirteen museum staff.

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In the second dynamic test, the vibrations were measured while thirteen museum staff members imitated dancing and jumping activities within a distance of 1-2 m from the reliefs. The effect on the art produced by this activity was substantial, with one of the reliefs registering a PV of 4.8 mm/s. Figure 15b demonstrates that the crowd’s active movements had a far more detrimental effect on the art vibrations compared to the scissor lift operation, an interesting result when considering the impact of museum social events on nearby art objects.

The velocity levels showed that the slab, superstructure, and the art were all highly excited by the small crowd activity, reaching peaks of 2.86 mm/s, 2.27 mm/s, and 4.79 mm/s, respectively. These levels are considerable and, if sustained, could lead to stress accumulation within the art and subsequent development of cracks or other forms of damage to the reliefs, compromising their structural integrity.

It is also important to highlight that the dynamic response of lamassu was relatively high when compared to the other tests, reaching 1.98 mm/s during the scissor lift movements and 1.39 mm/s during the crowd jumping, both recorded in the vertical direction (z-direction). The floor reference velocities for the lamassu were almost identical, with 1.97 mm/s and 1.41 mm/s, respectively, which reinforces our previously stated observation that the statue moves synchronously with the floor. Table 7 presents a comparison of the live-load tests’ impact on the lamassu and the reliefs’ velocity levels.

Table 7 Summary of vibration levels recorded during dynamic (live) load pilot tests, PV (mm/s)
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The tests showed that the sudden lowering of the scissor lift platform can generate a strong impact, transmitting vibration energy to the art. While this is undesirable, it is not particularly dangerous since the energy quickly dissipates due to the high damping characteristics of the slab. In contrast, spirited dancing by a small crowd resulted in high, sustained vibrations that exceeded the recommended safe limits for the art.

Simulated relief dynamics

To thoroughly explore the relief dynamics and confirm its expected behavior, a numerical simulation was undertaken. This simulation focuses on one of the larger reliefs and was conducted using the Finite Element Method (FEM) via Abaqus software (CAE 2024) on a CPU E5-2620 processor (24 GB RAM). FEM is a computational technique widely employed to predict how objects respond to external forces, vibrations, heat, and other physical effects. The integration of on-site measurements with FEM modeling is critical in art preservation studies, as it enables the interpretation of observed responses and supports structural analysis for condition assessment10,29,30. This approach is especially valuable in cases where analytical solutions are difficult to derive, offering insights into the structural and dynamic behavior of the system under investigation.

As an example, Relief 3 was used for the simulation, with a height of 2362 mm, a width of 1778 mm, and a thickness of 108 mm. The combined weight of the art and the steel frame to which it is mounted totals 1235 kg. The relief rests on a horizontal steel beam using a combination of steel shims and two steel angle brackets imitating pinned supports, and therefore is modeled as simply supported at the bottom (Fig. 5b). At the top, the corners of the relief frame are attached to the steel support beam using two L-shaped steel angles secured with bolts, one extends vertically and the other horizontally, forming a 90° connection between the beam and the relief. Here, it is important to note that the reliefs are not fixed at the top but rather attached to the support beam that provides lateral support to the relief by means of the bolted connections. Thus, the lateral support of the relief is modeled using two springs, representing these compliant connections, with their stiffness values treated as parameters for the model updating (calibration) routine. The objective function for the model updating was formulated using Bayesian inference31,32,33, which was found to be appropriate in other cultural heritage studies34. For the inference, the priors were taken as the combined stiffnesses of the structural components supporting the relief, rather than the yield strength of the connectors. The basis for this configuration is that the system response to construction-induced vibration typically occurs at low acceleration levels, which would not stress the material to yield. In contrast, the dynamic analysis of systems under seismic loading considers materials reaching their yielding limit. In the simulation of the relief dynamics the yield strength of the material can be neglected, and the system can be modeled relying only on stiffness of the connections. This setup aims to simulate realistic conditions to predict the behavior of the relief under various loading scenarios. For the simulation, we assume that the relief acts as a solid body since no delamination was observed between repaired components during visual inspection of this particular relief (delamination would constitute significant damage). The existing inner fractures have been thoroughly repaired using an epoxy compound (of unknown formulation), and the relief is well-fixed within the steel frame. Therefore, the relief was assumed to remain intact and behave as a solid, rigid diaphragm. A detailed analysis of potential crack growth is beyond the scope of this study, as the focus is primarily on the relief’s general dynamics, for which the assumptions made are reasonable. The objective function is formulated to enable inference of the springs’ stiffnesses from the observed input–output dynamics. Similar to the likelihood-based model updating in study33, we consider the inverse problem, where the discrepancy between the measured acceleration and the model output must be minimized with respect to the stiffness values, leading to maximization of the likelihood of the observed time-history of vibration data conditional on the stiffness values.

To generate artificial measurements, the external force resulting from the scissor lift platform docking (i.e., in its fully lowered position) was applied to the base of the relief. This particular type of loading was chosen as the lift platform snapping into docked position closely resembles an ideal impulse, an impact force that excites the majority of the relief’s dynamic modes. The simulated model output was collected at the top corner node in the FEM model, at the same place as the accelerometer on the actual relief. Figure 16 illustrates the force applied and the spectrum of the model output compared with the measured acceleration records.

Fig. 16: Simulation results.
figure 16

a Applied force, and b frequency content of the simulated and the measured responses at the top of Relief 3, estimated from the acceleration records.

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The alignment between the simulated and measured data in the frequency domain (Fig. 16b) confirms that the assumptions made for the computational model are consistent with the actual behavior of the relief. The inferred stiffnesses of the spring connections, estimated as 1230 kN/m and 1100 kN/m, are consistent with the expected range for semi-rigid bolted connections, such as angle brackets used to secure the relief to its supporting frame. These values reflect the compliant nature of the relief top connections, which provide lateral support without fully constraining the system. Further, the modal analysis indicates that the relief’s first fundamental modes correspond to the rigid body motion, bending, and torsional behavior (Fig. 17).

Fig. 17: The first four mode shapes of the relief.
figure 17

a 1st mode, b 2nd mode, c 3rd mode, and d 4th mode. Red corresponds to maximum displacement and blue to minimum displacement.

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The application of FEM in the context of relief dynamics demonstrates its value as a predictive tool in cultural heritage conservation, providing a foundation for further research and application in similar scenarios, particularly when the number of sensors is limited due to project constraints. The simulation results confirm that the relief moves according to the observations and offer insights into its structural and dynamic characteristics. The identified mode shapes explain the observed hairline cracks between the wall and the relief, as would be expected from a rigid body motion. These results can guide the development of appropriate conservation and monitoring strategies to ensure the long-term preservation of the Assyrian reliefs at the museum. It is important to note, however, that the simulation is based on a simplified assumption in which the relief is modeled as a solid body exhibiting linear elastic behavior. This idealization does not account for the inherent complexities of the relief, such as microcracking, material inhomogeneity, and nonlinearity, or nonlinear interactions at the support interfaces. While the presented approach effectively captures the dominant dynamic characteristics and allows for meaningful comparison with the observations, it potentially overlooks localized effects and the nonlinear structural behavior of the art. Nevertheless, it provides valuable information for art conservation purposes, such as the relief’s mode shapes and especially the stiffnesses of the compliant connectors, which play a significant role in vibration transmission.

Discussion

The recorded accelerations and velocities revealed a strong localized impact of construction activities, with a notable exception during the demolition of the structural masonry wall, where vibrations were also amplified in the distant reliefs. This phenomenon likely stems from the amplified reliefs’ relatively robust connection to the support structure, which transmitted vibrations from the wall to the art. Further, during the probe of drilling out the rivets, another relief showed a significant increase in vibration levels, while the supporting structure exhibited only half the amplitude. This discrepancy suggests a relatively compliant connection between that relief and the support structure. The transmission of energy from the art to the structure largely depends on the nature and quality of their connection. For instance, if a column and a relief are rigidly connected, vibrational energy from any mechanical impact on the column (such as drilling) is transferred directly to the relief. Conversely, less rigid connections, or those with high damping properties, can act as a buffer, dissipating some of the energy and thereby shielding the attached objects from the full impact.

The type of the reliefs’ support connections—steel brackets at the top and shims at the bottom, which we choose to refer to as “legacy connections” due to their installation in the 1980s—were found by the authors to be common in U.S. museums, particularly on the East Coast, where seismic isolation was not typically considered at the time. The challenge with this type of connections is their compliance that results in the amplified motion of the supported art, particularly under dynamic loading from construction or ambient sources travelling through the floor. Compliant connectors introduce flexibility into the system, reducing the overall stiffness of the supports. If the wall-mounted art is loosely connected, it will vibrate more freely relative to the rigid structural frame (or any other support system), especially at those unconstrained locations, as this decoupling allows larger relative motion. The absence of vibration mitigation in the art mounting elements increases the vulnerability of art pieces to vibrations generated by nearby construction activities and routine visitor circulation within the museum. Without isolation or damping details, even low-level, repeated vibrations can lead to long-term structural degradation and damage initiation in art. The use of single bolts for these connections means that each bracket will essentially lose its stiffness if only a single bolt is not fully tightened. Further, disparities in connection stiffness cannot be quantified by visual inspection. This challenge highlights the critical need for site-specific assessments and the implementation of proactive vibration control strategies to ensure the protection and longevity of cultural heritage objects in such environments.

In many cases, relocating certain art objects during construction activities is not feasible due to the substantial risk of damage associated with transportation. This is particularly true for large, fragile, and structurally integrated pieces. Moving such objects will introduce unintended mechanical stresses, result in microcracking, and potentially lead to delamination of repair materials. Consequently, the most viable preservation strategy is often to leave the art in place and focus on managing the surrounding construction environment to minimize vibration transmission to the art objects. In these situations, the construction work in the gallery spaces should be guided by three key principles: (1) avoiding resonance by selecting construction tools whose dominant excitation frequencies do not coincide, within a confidence interval, with the natural frequencies of the nearby art and their mounting systems (including shelves and display cases); (2) selecting tools that inherently generate lower vibration levels, or that incorporate vibration-reducing technologies such as Active Vibration Control (AVC) systems; and (3) implementing isolation or mitigation strategies based on a thorough assessment of the art support structures and mounting conditions to minimize vibration transmission. Further, the selection of construction tools for renovation work at the museums should be discussed with contractors during the project design and bidding phases. This proactive coordination will significantly reduce the risk of damaging the art and provide the construction team with clear guidance for carrying out the work safely.

To determine safe vibration content for various artworks, it is essential to assess their physical and mechanical properties, including material type, support configuration, and pre-existing damage such as cracks and delamination. Next, it is important to understand the objects’ dynamics using experimental or in situ vibration testing. To fully characterize the structural response, time-history measurements of the vibration environment should be collected using accelerometers or other suitable sensors. If the physical testing is constrained by conservation protocols or limited access, numerical modeling (e.g., FEM analysis) can be employed to estimate spectral properties such as resonant frequencies, mode shapes, and damping ratios. Finally, the stability of the art must be evaluated by assessing their geometric properties and mounting conditions.

The present case study on vibration levels within the gallery has provided the construction and conservation teams with critical insights into the potential impact of different construction methods and activities performed near the Assyrian art at the Metropolitan Museum of Art. The Assyrian reliefs illustrate a common challenge in object conservation, as they have been previously fragmented and repaired, resulting in a highly fractured set of objects. The most probable damage scenario due to vibrations is the delamination or rupture of the bond between the repair materials, leading to the further damage of the art. The long-term effects of sustained vibrations can be significant and cumulative, even when the vibration levels are within commonly accepted limits. Vibrations can loosen mechanical fasteners, degrade adhesives, and induce fatigue in compliant connectors that support the art, potentially increasing the objects’ susceptibility to amplified response under dynamic loading. During the construction probes, the vibrations of the reliefs exceeded safe levels on several occasions. The highest vibration levels were recorded during drilling near the support structure using a hammer drill and during rivet removal from the baseboard directly under the relief. Relatively high velocity levels were also recorded during mortar removal using hand tools such as flat pry bar and framing hammer. Additionally, during the live-load tests, a small crowd of thirteen people jumping and dancing resulted in vibrations magnitudes that would be dangerous to the art if sustained over an extended period of time. In contrast, the lamassu do not appear to be endangered by any of the simulated construction activities. However, the data revealed a noticeable increase in the statue vibrations due to the strong vertical impact generated by the scissor lift lowering/docking its platform. The high-amplitude vibrations observed in the support structure during several tests could also pose a risk. The hazard stems from the differential movement between the structure, which carries the plaster lath, and the art. In cases where the two systems are not adequately air-gapped, as some are, there is a potential risk of fretting damage at the edges of the relief panels.

The findings and observations from the pilot test series are intended to inform both the construction phase and the design of a new support structure. The analysis of the vibrations due to different applied loads and test locations helps to quantify the dynamics of the various support structures, as well as the energy propagation within the gallery space. The correlation between the locations of the work performed and the impact on the art can be used to design a safer construction environment, helping to preserve the art during the gallery renovation. This study provides an assessment framework applicable to similar projects in various museums, offering a comprehensive understanding of how different construction methods and support structures affect the dynamics of the art they house. We demonstrate that the specific structural details, down to the fixity of each mounting bracket, can substantially influence the dynamic response of the art. As such, the findings highlight the critical importance of detailed assessments of structural systems and their dynamic interactions with the exhibited art objects. The results and discussion presented here can serve as a reference for developing effective vibration management through informed construction practices in similar renovation projects across different museums.