1. Introduction
Among the various noises generated in urban areas, neighbor noises in multifamily housing become a primary issue as the acoustic requirements in residences rise [
1,
2,
3]. Notably, floor impact noises (e.g., noises stem from walking, running, and moving furniture) are key detractors of acoustic comfort, with reports indicating that such noises are the main cause of noise complaints in densely populated areas [
4,
5]. In areas where the city saturation has rapidly progressed, multifamily housing adopting wall–slab systems are popular for their ability to provide more housing units vertically and fewer floor plan irregularities [
6]. However, wall–slab system buildings, which are mainly supported by shear walls, are believed to have lower floor impact noise insulation compared to the Rahmen system, which consists of columns and beams, as they allow bending waves generated by floor impacts to transmit through integrated interior walls. The findings of [
7,
8] show that about half of the noise energy in a room surrounded by concrete plates comes from flanking transmission via walls and slabs not directly impacted by the source support this fact.
Due to the characteristic of having many walls that act as mediums for vibration transmission, the vulnerability to noise in wall–slab buildings includes not only the issue of noise level but also the problem related to the propagation of noise, which makes it difficult to locate the source of the noise. For residents of multifamily housing, relieving acoustic annoyance through dialogue with noise-producing residents is challenging when the noise source remains unidentified [
9]. The consistent social demand to identify the noise source in areas heavily supplied with wall–slab multifamily housing implies a need for attention to the propagation of floor impacts [
10,
11].
Indeed, if the vibration induced by the impacts from daily activities can be sufficiently isolated, the vulnerability of wall–slab structures to the propagation of floor impacts might not be significantly highlighted. The floating floor system is a common vibration isolation method used for sound insulation against floor impacts [
12,
13]. It features a resilient layer placed between the walking surface and the structural slab, which plays a significant role in dampening vibrations [
4]. However, recent studies indicate that the floating floor approach encounters limitations in attenuating floor impact noises below 100 Hz, such as heavy impacts from footsteps or children running and jumping, which is crucial in residential noise annoyance control [
14,
15].
Therefore, exploring alternative methods to reduce the propagation of vibration over distance is key to enhancing residential acoustic comfort. One promising option is the use of periodic materials, a type of metamaterial designed to block or reduce wave propagation and vibration based on periodic theory [
16,
17]. The materials which have periodic structure with an elastic modulus and mass density modulated show great potential in suppressing vibrations in civil structures and isolating seismic vibrations [
18,
19,
20]. However, their application in residential buildings has seen limited research, largely due to the structural modifications required in their implementation [
6,
21]. In the study exploring the application of periodic materials in residential buildings [
21], the methodology was confined to affixing fabricated specimens to existing building slabs and assessing their effectiveness in reducing impact noise and vibrations. Therefore, studies focusing on their attenuation efficiency over distance are even scarcer, pointing to an area needing further exploration.
The primary objective of this research is to enhance understanding of the application effects of innovative periodic materials in wall–slab structures, particularly focusing on distance attenuation. This research adopts an experimental approach, retrofitting periodic materials onto existing structures to evaluate improvements in vibration and noise insulation. Such a method allows for an intuitive assessment of the improvements brought by periodic materials and their compatibility with current construction practices.
The first phase of this research explores rebar construction methods in wall–slab structures. After examining structural design guidelines, this research identifies conditions under which periodic materials can be effectively applied. An experimental structure meeting these criteria is then selected for in-depth examination of its natural vibration and noise insulation characteristics. The natural vibration frequencies are investigated using the frequency response function. Also, attention in this research is given to the attenuation of heavy impacts, typically generating noise and vibrations below 100 Hz. To simulate such impacts, rubber ball excitations, as recommended by the International Organization for Standardization, are employed to replicate noises similar to those caused by barefoot walking or children jumping.
Subsequently, this research progresses to the installation of periodic materials within the experimental structure and reassessing its vibrational characteristics and noise insulation performance. The final stage of the study compares the findings before and after applying periodic materials. This comparison not only focuses on distance attenuations and difference reversals but also includes a juxtaposition with a typical wall–slab multifamily housing scenario. Furthermore, the discussion extends to examining the potential role of periodic materials in localizing the source of impact noises.
4. Experimental Results
4.1. Changes in Distance Attenuation of Sound Responses
The analysis of the experimental results of periodic material applications commences by assessing the changes in sound responses of the experimental structure.
Figure 4 elucidates the modifications in
SPL within rooms on the first and second floors induced by rubber ball impacts on the roof slab. Measurements are visualized through contrasting lines, with the lighter gray indicating the results prior to the implementation of periodic materials and the darker lines delineating the post-application results.
Figure 4 provides a detailed representation of the average
for each 1/3 octave band in the rooms on both floors, while also explicitly illustrating the attenuation of sound with distance.
The upper portion of the graph presents the individual SPL measurements for each one-third octave band, providing a detailed frequency response profile. The post-application results exhibit a general trend of reduction in SPL. This detailed frequency breakdown allows for a nuanced understanding of the periodic materials’ damping properties and their frequency-specific effectiveness. In addition to showing the average SPL measurements, the lower portion of the figure displays the difference in SPL between the two rooms on the second and first floors across the frequency bands (), both with and without the application of periodic materials. The table below the graph quantitatively summarizes these differences, further underscoring the enhanced sound attenuation achieved through the application of periodic materials. The post-application disparity in SPL between the second and first floors becomes pronounced in the octave bands of lower frequencies, notably in the 50, 63, 100, 125, 200, 250, 315, and 400 Hz ranges. This suggests that the periodic materials’ application has a considerable influence on the transmission of lower-frequency sounds, which are often challenging to mitigate in building environments.
Based on the , before the application of periodic materials, the was uniformly 56 dBA in the rooms on both the second and the first floors. This result indicates a lack of distinct distance attenuation of low-frequency impacts. Post-application, however, the in the second floor room decreases to 53 dBA, while the first floor room registers a further reduction, reaching 52 dBA. Considering the pre-application value (56 dBA) as 1 for comparison, the relative value becomes 0.95 on the second floor with an of 53 dBA, and 0.93 on the first floor with an of 52 dBA. This 5% reduction in the second floor room clearly demonstrates the improvement in impact noise insulation due to the periodic materials, while the greater reduction of 7% in the first floor room also indicates effectiveness in terms of distance attenuation.
4.2. Changes in Distance Attenuation of Vibration Responses
Next, the changes in vibration responses, which act as a medium for the transmission of impact noise, are followed.
Figure 5 represents the experimental results analyzing the effects of applied periodic materials on the natural vibrations of the experimental structure. The figure is arranged with a cross-section of the experimental structure in the center, flanked by a total of six graphs. The cross-section of the experimental structure is marked with the locations of the installed scattering materials and each vibration measuring point. The central black arrow indicates the point of impact force application.
The graphs present the average eigenfrequency response from 10 to 1000 Hz derived through the FRF between the impulse hammer excitation and each measurement point. The graphs are organized in a vertical sequence with different parts of the building represented in each. The top graph shows the vibration response of the ceiling, the middle graph depicts the walls, and the bottom graph illustrates the floor’s response. To understand the location of these responses, see the sides of
Figure 5: the left side of each graph shows the responses on the second floor—these are the points that are closer to the excitation point. On the right side, you will see the responses on the first floor, which are the points that are further away from the excitation point. The vibration response of the walls is expressed as the average of the values measured at two points. In each graph, the lighter lines represent the vibration response before the application of periodic materials, and the darker lines after their application. At the bottom of each graph, the
OA difference in vibration response before and after the application of periodic materials is denoted. Before the application of periodic materials, the experimental structure showed greater vibration responses in all components of the first floor compared to the second floor. This suggests that the members of the first floor are more vulnerable to the roof slab excitation of the experimental structure. As can be seen through a comparison of
OA (light black lines), the vibrations of the ceiling, walls, and floor of the second floor were relatively lower, which is believed to be due to the smaller scale of the experimental structure compared to actual multifamily residences.
Periodic materials were applied only to the intermediate slab. Nevertheless, a reduction in vibration response was observed throughout the structure, with an average reduction of about 11.21 dB based on the averaged OA. The vibration response on the second floor mainly decreased in the area above 200 Hz, and the vibration rebound on the first floor decreased uniformly across all areas. Particularly noteworthy is the vibration response of the walls (W2) on the second floor. If one considers the in-plane waves propagating along the structure, despite there being no section with applied periodic materials between the excitation point and the two points W2a and W2b, a significant reduction of 8.27 dB was observed. This suggests that the distance attenuation effects resulting from the application of periodic materials in buildings cannot be simply interpreted.
After the application of periodic materials, the phenomenon of larger vibration responses at points farther from the excitation than those closer was improved in the experimental structure. Specifically, lower vibration responses were observed in the ceiling and floor of the first floor compared to the second floor, indicating that the effects of periodic materials contributed to the reduction in vibration propagation throughout the structure. These results demonstrate that periodic materials are highly effective in controlling vibration propagation.
Let us delve deeper into the effectiveness of periodic material applications in terms of distance attenuation.
Table 4 illustrates the distance attenuation changes in
OA resulting from the application of periodic materials. This table distinguishes the difference between pre- and post-application of periodic materials, displaying the
OA at each vibration response measurement point. For each structural member group, it contrasts the differences between points that are nearer and further from excitation. By presenting this data, the table also compares the changes in distance attenuation for each member at specified measurement points, both before and after the application of periodic materials.
In the column ‘OA without periodic material applications’, attenuation values for the ceiling, walls, and floors are shown at points near (2F, A) and far (1F, B), with the difference between these two values presented as (A–B). The ‘OA with periodic material applications’ column presents data in the same manner, allowing for a comparison of the effects of periodic material applications at each measurement point.
When comparing before and after the application of periodic materials, it is evident that the difference in vibration attenuation between near and far points has increased for the ceiling, walls, and floors. This suggests that periodic materials effectively reduce the propagation of vibration energy and that this effect increases with distance.
For example, for the ceiling, before the application of periodic materials, the near point shows 201.80 dB and the far point 204.89 dB in
OA vibration response. This shows a difference of −3.09 dB, with a larger vibration response at the far point. After the application of periodic materials, the near point showed 199.75 dB and the far point 185.70 dB in attenuation, with the difference increasing significantly to 14.05 dB. A similar pattern is observed in walls and floors, confirming that the effect of periodic materials on vibration attenuation is consistent throughout the structure. In
Table 4, it is confirmed that the average attenuation difference changed from −5.35 dB to 9.26 dB. In other words, the difference in vibration response between points near to and far from the excitation point shifted from negative to positive, indicating that the experimental structure transformed into one where lower vibration responses are seen at further distances. When comparing to the pre-application
OA values, members on the second floor showed an average vibration response decrease of about 2%, while members on the first floor exhibited a reduction of approximately 9%. In other words, after the application of periodic materials, the reduction in vibration response was more pronounced at points further from the excitation source.
The results described in
Section 4.1 and
Section 4.2 indicate that before the application of periodic materials, the experimental structure did not exhibit distance attenuation characteristics for impact noise and vibration. After the application, the environment transformed to clearly show distance attenuation for both impact noise and vibration. In terms of vibration, the change from negative to positive in the difference between points near to and far from the excitation point confirms a clear change in distance attenuation. However, the improvements in distance attenuation for impact noise were relatively less pronounced, suggesting that it is more challenging to achieve as clear an effect on noise distance attenuation as on vibration. Despite this, the application of periodic materials still brought about consistent improvements in distance attenuation across the entire structure for both impact noise and vibration aspects. These results imply that the use of periodic materials can play a significant role in the development of strategies for the management and control of impact noise within buildings.
5. Discussions
This study examines the impact noise and vibration response of structures undergoing change through the application of periodic materials in wall–slab structures, from the perspective of distance attenuation. The attenuation effect of plane wave propagation through periodic materials is well known through applications in civil engineering, such as pile barriers [
20,
36,
37]. Although there has been research on the application of periodic materials in wall–slab structures [
21], the focus has often been on the magnitude of impact noise, resulting in limited consideration of the propagation of in-plane waves related to the localization of impact source where multiple plates are combined.
The research by [
37] on the feasibility of using periodic materials in the form of pile barriers as an earthquake wave mitigation measure shows results related to distance attenuation. According to this research, the magnitude of vibrations decreases by approximately 15%, 40%, and 75% with the addition of one, two, and three rows of pile barriers, respectively, compared to before the application of periodic materials. Also, the slope of the decrease with distance increases. However, compared to before the application, this distance attenuation effect is observed only after the plane wave passes through the section of the periodic material arrangement. Near the center of the section in which periodic material is applied, the vibration response is rather increased by approximately 40–50%, as the section of periodic materials absorbs the vibrational energy of the plane wave.
In contrast, in the experimental structure of this research, the average vibration reduction in all measurement points was 9%, with the largest decrease observed at point F1 by about 14%, compared to before the application of periodic materials. However, the results also show suppressed amplification of vibration response in members where periodic materials were applied (C1, F2).
The most significant difference between the propagation of environmental vibrations commonly addressed in civil engineering and vibration propagation in architectural structures such as wall–slab configurations lies in the complexity of the transmission paths. As noted by [
26], in wall–slab structures, there are multiple flanking paths through which in-plane waves can travel between the same impact and observation points, rather than just a single path. The most influential is the shortest first-order path connecting the two points, but the impact of lower-order paths can also be significant.
The observation results of the noise and vibration response of the experimental structure before the application of periodic materials align well with this explanation. In the experimental structure without periodic materials, the distance attenuation of noise and vibration responses is not observed. Rather, vibration responses are more pronounced at observation points farther from the excitation point. This fact can be interpreted as being due to the overlapping of vibrational energy caused by the influence of multiple flanking paths in wall–slab structures.
The change in average vibration response at points W2a and W2b before and after the application of periodic materials also highlights the characteristic of wall–slab structures having numerous flanking paths. In this research, periodic materials were applied only to the intermediate slab of the experimental structure. Therefore, there are no sections with applied periodic materials on the shortest path from the excitation points to these two wall observation points. It seems unlikely that the point directly below the excitation point, C0, would be significantly affected by the periodic materials. Nevertheless, a reduction in the OA at C0 (2.05 dB) and W2 (8.27 dB) was observed, with a more significant decrease at W2. This indicates that even if the application of periodic materials does not affect the first-order path, the effect of in-plane wave attenuation by periodic materials in a wall–slab structure can be more pronounced due to the presence of numerous flanking paths.
From the perspective of the excitation location, the application of periodic materials not only reduced the vibration response in the section in front of the application but also suppressed vibration amplification in the slab where periodic materials were applied. This led to a more noticeable decrease in vibration response further away from the excitation location, and the experimental structure was able to achieve distance attenuation characteristics in both noise and vibration aspects.
Furthermore, the application of periodic materials to the intermediate slab resulted in improved sound insulation against heavy impacts for the room on the second floor, reducing
from 56 dB to 53 dB. Considering that floating floors—extensively studied for sound insulation—show limited performance against low-frequency, heavy impacts, alternative solutions were constantly explored [
4,
27]. These solutions involved changes in structural type [
6], plan configuration [
14], and junction conditions [
33], with the incorporation of periodic materials [
21] being one of them. Therefore, while the focus of this research was on distance attenuation, confirming heavy-impact sound insulation improvements in the room beneath the impacted floor is notably significant. This finding greatly contributes to enhancing acoustic comfort in wall–slab residential buildings.
In summary, architectural structures such as wall–slab configurations, which involve a complex combination of multiple plates, tend to observe the phenomenon of reversed distance attenuation characteristics due to the numerous flanking paths in vibration transmission. When periodic materials are applied to wall–slab structures, compared to the straightforward transmission direction of plane waves with periodic materials in the form of pile barriers in soil, the presence of numerous flanking paths brings about several differences: First, it is relatively challenging to achieve a significant distance attenuation effect in terms of vibration transmission. Second, however, side effects such as amplification of the applied area due to vibrational energy absorption are mitigated. Third, the application to specific sections can still achieve an overall reduction in structural vibration, which also positively affects the insulation of impact noises.
However, it is difficult to claim that periodic materials could entirely substitute conventional approaches such as floating floors. The transition of the surface material from high-density to low-density in our experiment might adversely affect airborne noise insulation. Our focus was on low-frequency wave attenuation from heavy impacts, so we did not extensively discuss tapping machine impact results in
Section 3 and
Section 4. The single numerical rating values,
, resulting from tapping machine impacts are benchmarks for assessing noise insulation against light and hard impacts. The
values, measured similarly to rubber ball impact sound responses, showed no significant difference pre- and post-application of periodic materials (70 dBA on the second floor and 71 dBA on the first floor). The lack of noticeable effects on higher frequency impacts indirectly suggests a vulnerability in the airborne noise insulation capability of this method. Nonetheless, the noise insulation against light impacts could be managed with floating floors or modifications to the flooring material. Therefore, integrating periodic materials with existing soundproofing strategies could better secure acoustic comfort in multifamily housings.
As mentioned in the introduction, the localization of impact sources in multi-dwelling residences is a research area of significant social demand [
10,
11]. The approach of identifying impact sources through the sensing of structural vibrations offers a non-intrusive method, which is not only beneficial for improving acoustic comfort but is also promising in the study of human behavior recognition [
45]. However, the practical application of such localization techniques is limited to short-range sensing at the individual plate level, not extending beyond the junctions between structural members [
46,
47]. As observed in the vibration response of the experimental structure before the application of periodic materials, the wall–slab structure does not readily exhibit the distance attenuation effect of vibrations. Consequently, estimating the distance to the excitation location based solely on the magnitude of the vibration response presents significant challenges. Therefore, by applying periodic materials to enhance the discernibility of vibration response differences due to distance changes in a wall–slab structure, it can contribute to overcoming the limitations of short-range sensing in impact source localization. This approach can aid in achieving the same objectives with fewer sensors, offering a practical solution to the challenges highlighted earlier.
6. Conclusions
This research applied periodic materials, promising in controlling in-plane waves and previously used mainly in civil engineering for environmental vibration control. This research applied periodic materials to the intermediate slab of a wall–slab experimental setup. The experiment involved delivering impacts to the roof slab of a two-story experimental structure and measuring the indoor sound pressure levels and overall amplitude of natural vibration of each member before and after the application of periodic materials. The experimental structure, before the application of periodic materials, was a structure where distance attenuation of impact vibration was not observed, with members further from the impact location exhibiting an average vibration response 5.4 dB higher than those closer, based on OA. However, compared to the pre-application, after applying periodic materials, impact noise and vibration decreased by 5% and 2%, respectively, in points closer to the impact location, and by 7% and 9% in farther points. These findings indicate not only the emergence of distance attenuation characteristics but also a reduction in impact noise and vibration responses across all rooms and members. This is a notable result, as unlike applications in civil engineering, vibration amplification was suppressed even in the sections where periodic materials were applied.
In the experimental setup of this research, the application of periodic materials was executed by perforating the existing structure. The consideration of potential side effects on airborne noise transmission due to perforation was, however, limited in this study. Moreover, this research did not perform a sensitivity analysis of various parameters, which could be explored using analytical models. Therefore, further research is necessary before practical application, specifically on application zones, arrangement methods, and material properties. Future studies should also evaluate integrating this method with conventional approaches, like floating floors, to mitigate any potential side effects.
This research contributes to the potential application of promising in-plane wave control materials in architecture. It was confirmed that periodic materials can suppress side effects such as vibration amplification in sections where they are applied in wall–slab structures and enhance distance attenuation characteristics. Should the proposed future research be undertaken, our findings could facilitate the development of impact source localization techniques. Such advancements could enhance acoustic satisfaction and mitigate neighbor noise conflicts, contributing to more sustainable urban residential environments.