Sound transmission in sandwich panels takes place via airborne sound and structure-borne sound. Airborne sound transmission takes place when sound waves impinge upon the faces, inducing vibrations, and these are transmitted via the core and then radiated to the other side. On the other hand, structure-borne sound transmission takes place via vibrations generated within the structure, transmitted via elastic waves, and then radiated to the surrounding fluid. Analysis of sound transmission in sandwich panels has been extended beyond classical theories of mass law, coincidence effect, and mass-spring-mass resonance to include the complexities of the core, including periodicity. Advanced theories, such as Bloch waves, the transfer matrix method, and homogenization, have been employed to accurately predict sound transmission loss, and it has been found that sandwich panels do not behave according to mass law due to their flexible and periodic core.

The acoustic performance of sandwich panels is highly dependent on frequency and hence requires special design considerations for various frequency ranges. For low-frequency ranges (0 - 1000 Hz), where the “mass law” is not effective and resonance plays a crucial role in sound transmission through sandwich panels, scientists have attempted to address MSM dip control through optimization of the geometry of sandwich cores [14][15] and design auxetic/hybrid cores for STL enhancement [11][15]. For high-frequency ranges above 1000 Hz, coincidence phenomena and band gap phenomena dominate sound transmission through sandwich panels, and truss lattice cores have shown potential for STL enhancement through partial band gaps. For mid-frequency ranges (1 - 10 kHz), where sound transmission through sandwich panels is difficult to model, scientists have come up with innovative ideas such as compliant mechanism cores for designing attenuation zones [16] and analysis of wave propagation through periodic profiles.

Critical analysis of existing research indicates that there is a need to overcome several limitations. Firstly, there is a gap between the structural and acoustic research communities. For example, many research works on the mechanics of sandwich panel structures often ignore acoustic aspects altogether [4]-[6]. Secondly, various modeling methods are available to solve panel problems, from efficient methods like TMM to accurate methods like FEM. However, there is a lack of systematic validation of the applicability of various modeling methods to various core materials and frequency ranges [17]. Thirdly, material damping and its frequency dependency have not been well developed, although it is critical to controlling resonance peaks [9]. Lastly, scaling laws showing that band gap frequencies vary inversely with length scales have critical implications for scaling laboratory results to full-scale applications. For example, the effects of manufacturing imperfections on scaling laws have not been well understood.

SteelTrusses

Steel truss connectors have traditionally been heavily utilized in the construction of sandwich panels, usually made up of welded wire fabric and steel members. Various steel connector configurations have been reported by Sah et al. [1], including steel truss, I-section, and C-section connectors. Although steel offers high strength and ductility, it has major thermal bridging issues. The research work of Fu et al. [9][18] has shown pyramidal and tetrahedral steel truss core materials in steel sandwich panels, indicating that strut length, radius, and inclination angle have a significant impact on transverse shear stiffness and structure-borne sound transmission paths. The major advantage of steel trusses is their known mechanical properties and design methodologies; however, steel has high thermal conductivity, and hence thermal issues are of major concern in energy-efficient building envelopes.

ShearPins

Discrete shear pin connectors are a minimalist design concept in connecting wythes and usually consist of short and high-strength members located in the insulation layer. Haffke et al. in reference [4] utilized GFRP bar-type shear connectors that act as shear pins with diameters of 12 mm and a ribbed surface to facilitate mechanical interlocking. The shear pin connectors had their ends cut at 30 degrees and free lengths equal to the core thickness to ensure maximum shear resistance and minimum bending action. De Sousa et al. in reference [6] also utilized functional and structural GFRP connectors in micro-concrete sandwich structures, and in this case, structural GFRP bars of 8- and 12-mm diameters act as a primary mechanism of shear transfer between the outer layers of RSFRC and the inner insulation layer. Discrete shear pin connectors allow for strategic placement to ensure maximum composite action.

FRPConnectors

Fiber Reinforced Polymer (FRP) connectors have emerged as universally accepted alternatives to steel connectors, which provide similar levels of strength while maintaining significantly lower thermal conductivity. The Glass Fiber Reinforced Polymer (GFRP) is identified as the most commonly utilized FRP material, which is generally produced using E-CR glass fibers and vinyl-ester/polyester resin systems [4][5]. Silva and Lameiras [5] have designed PERFOFRP connectors, which are made from perforated GFRP plates of 2.32 mm thickness with strategically placed holes to provide interaction with concrete dowel action through multiple mechanisms, including concrete front bearing, dowel effect via perforations, and frictional resistance. This has emerged as an advanced version of traditional bar connectors, which can potentially provide better load distribution and failure characteristics. Sah et al. [1] have reported the entire range of materials utilized in FRP connectors, which includes GFRP, CFRP, and BFRP materials; it is evident that material selection is critical and significantly influences structural as well as economic viability. The ribbed surface textures and end-conditioning processes, such as 30˚ cuts, generally adopted in FRP connectors [4][6] reflect the construction industry’s adaptation of reinforced concrete principles.

Hybrid andComposite Connectors

Recent emerging research has been carried out to investigate hybrid connector systems, in which several materials or geometries are employed to attain synergistic performance benefits. Sah et al. [1] found that hybrid steel-FRP connectors are an emerging trend, which may help to attain ductility and thermal efficiency simultaneously. Wan et al. [7] and Yan et al. [8] studied GFRP lattice truss structures, in which the connector system is not an individual component but rather an integral three-dimensional woven fabric, where the epoxy resin is infused. Gradient layer structures, such as T1, T2, and T3, were designed, consisting of “8”-shaped piles in the warp direction and “1”-shaped piles in the weft direction, thereby developing orthogonal anisotropy that can be tailored to meet specific requirements. This method of weaving is quite different from the conventional method of inserting discrete connectors, in which delamination may be completely eliminated. Xu et al. [2] reviewed advanced composite connectors such as FMLs and hybrid materials, indicating that future connectors may be developed to utilize the benefits of hybrid materials rather than individual materials.

The main structural function of mechanical connectors is to facilitate the transfer of shear forces from one wythe of concrete to another to obtain composite or partial composite action against gravity and lateral loads. Haffke et al. [4] proved that shear forces are effectively transferred by GFRP bar connectors under combined fire exposure and mechanical loads, though temperature has a major impact on the stiffness of connectors. Silva and Lameiras [5] found that there are three distinct shear force transfer methods from one wythe of concrete to another: concrete bearing at the front of the connector, dowel action through perforations, and frictional resistance at the interface of the connector with concrete. For composite action of panel structures, connectors must be able to withstand not only vertical shear forces but also tension and compression forces from lateral loads such as wind and seismic events [1]. De Sousa et al. [6] proved that the structural performance of FRP connectors is comparable to that of steel connectors when properly designed to obtain composite action in building strengthening. However, whereas mechanical connectors are critical for structural integrity, they inevitably introduce structure-borne sound transmission degradation. Atalla [17] found mechanical links to be the primary source of degradation in double-wall sound transmission, whereby a single connector acts as a preferred transmission path for vibrational energy to bypass the insulating air gap. Franco et al. [19] and Yang et al. [10] found that the geometry of connectors plays a critical role in sound transmission, particularly in terms of angles, cross-sections, and configurations. Moosavimehr and Phani [20] found that core geometries are critical in altering sound transmission loss, regardless of material quantity. Gazzola et al. [14] found that ligament flexural characteristics tune mechanical stiffness, which in turn affects the mass-spring-mass system resonance frequency. Li and Yang [11] found that locally varying stiffness can create stopbands to inhibit vibrational energy transmission.

This tension between the structural and acoustic properties is what poses optimization problems. Kohrs and Petersson [21] proved that periodic truss-like cores can be used to achieve pass and stop bands for waves propagating through the material, and that the configuration of the core fundamentally influences the paths that waves propagate. Dede and Hulbert proposed that the connector’s geometrical properties can be optimized for the reduction of vibrations without affecting load transfer. Wang et al. proved that the material used for the filler has properties that reduce the amplitudes of resonant waves without affecting the material’s stiffness. Quinteros et al. proposed using phononic crystals and optimized the geometrical properties of the unit cell to achieve band gaps for certain frequencies. Yet despite all of these advances, very little research has focused on the explicit optimization of connectors for sandwich structures made of concrete with regard to structural and acoustic performance. While most research on structural-acoustic design has utilized idealized geometries of connectors that vary significantly from actual connectors used in concrete panel structures, the large mass and damping of the concrete wythes compared to the face sheets of most sandwich structures may significantly impact the acoustic penalty of such a design. It is suggested that research be conducted to determine the impact of various connector geometries on sound transmission through a structure, whether it is possible to design a connector layout that has an acoustic stopband with shear transfer capability, and what the quantitative relationship is between composite action and sound loss.

The fundamental concept of a mechanical link forming a “bridge” in a sound transmission problem is well-established in the field of acoustics. Atalla explicitly treats this in his work, using a Transfer Matrix Method (TMM) approach to show the degradation of Transmission Loss (TL) in a DW with the addition of mechanical links. The “bridge” concept provides a direct path of transmission for vibrational energy, effectively “short-circuiting” the spring-like isolation of the air gap. This is especially true in a turbulent boundary layer (TBL) excitation condition, which is conducive to resonance in the transmission through the structure.

The core is essentially the bridge in a sandwich panel. Previous research has shown that various core configurations result in different wave propagation modes. These modes are critical in defining the acoustic behavior of a structure. For instance, Franco et al. [19] showed that regularly spaced truss cores are responsible for directivity in wave propagation. By introducing randomness in the stiffness of these cores, the directivity was disrupted, resulting in reduced vibration levels and acoustic power. This shows that the periodicity of the connector arrangement is critical in defining efficient sound bridges. Additionally, Moosavimehr and Phani [20] showed that various truss lattice cores result in unique wave propagation modes characterized by partial band gaps. These are ranges of frequencies where wave propagation is impeded. This shows that the sound bridge generated by the connectors is not simply on or off but is a function of its geometry.

The mechanical properties of the material used in the connector, especially in terms of its stiffness and density, are of primary importance in establishing the strength of the sound bridge. It should be noted that the connector acts as a dynamic element with impedance matching the facings.

Theoretical and numerical studies have clearly proven these facts. Yang et al., in their research on a DW system with interconnected acoustic cavities, have shown that the stiffness of the connecting element, i.e., the value of Young’s Modulus (E), plays an important role in the calculation of the stiffness ratio (κ) of the structural component and acoustic cavities. It should be noted here that the value of κ plays a crucial role in the calculation of Sound Transmission Loss (STL). It has been found in the research of Yang et al. that a stiffer connecting element would always lead to a lower value of STL compared to a softer one. These findings are in accordance with the research of Atalla et al. [17], in which it was clearly shown that the value of stiffness of the connecting element (k) plays a crucial role in the degradation of TL. Kabiripoor et al. in their research have shown that an increase in static bending stiffness would always lead to a lower value of STL in the stiffness-controlled frequency range.

The role of material density and its distribution is also significant. In their modeling of periodic sandwich structures, Marczak and Jedrysiak [22] proved that an increase in the stiffness ratio of the core (ξ = E2/E1) increases the lower-order synchronous vibration frequencies, whereas an increase in the density ratio of the core (ζ = ρ2/ρ1) reduces all the frequencies. This proves that the connector materials have a significant effect on the modal behavior of the panel, which in turn governs the acoustic radiation and transmission. The difference in the materials of the connector and the facings/core filler is a significant factor. For example, replacing a dense and stiff steel connector with a less dense and less stiff Glass Fiber-Reinforced Polymer (GFRP) connector not only removes the thermal bridging effect [4][5], as discussed earlier, but may also affect the structural dynamics of the sound bridge and hence reduce the efficiency of the sound bridge in transmitting the sound.

Apart from the inherent material properties, the spatial arrangement and the details of the geometry of the connectors play an important role in the vibro-acoustic response. The arrangement of the connectors essentially describes the periodic structure.

The research on randomization of stiffness conducted by Franco et al. [19] may be seen as a tacit recognition of the role of spatial regularity. A regular and periodic arrangement of structures provides a coherent waveguide with high transmission efficiency, whereas the addition of irregularity or “perturbations” can disrupt the coherence of the vibrations and localize them, reducing the effect of the sound bridge. This idea underlies the concept of phononic crystals, as studied in the research conducted by Quinteros et al. [23]. It was shown that the band gap frequency in phononic crystals depends inversely on the length scale (L). If all the parameters of a sandwich panel are uniformly scaled in size, the band gap width remains unchanged. However, if only certain parameters, e.g., the diameter of struts, are changed in a “distorted scaling,” the band gap may be entirely eliminated, changing the transmission characteristics of the sound bridge.

Other geometric parameters are also significant. For example, Yang et al. [10] have shown that an increase in the inclined angle θ of the connecting beam results in improved sound insulation. This result can be interpreted in terms of an impact on the transmission of out-of-plane motion, either facilitating or hindering it. Fu et al. [9][18] have shown that an increase in core height (h_c) and radius (r) shifts the positions of the natural frequencies and affects the amplitude of STL. For example, an increase in height results in an increase in natural frequency, shifting the dips in STL to higher values. Fu et al. have also shown that an increase in core radius results in a decrease in natural frequency but can increase STL. Li and Yang have shown that an inhomogeneous core, achieved by varying the cell angle θ, can be used to shift dips in STL, thus optimizing sound transmission. Finally, the number of unit cells [15] and the ligament dimensions of the core [14] are also significant, with changes leading to performance fluctuations and shifts in key resonances.

The sound bridge effect is naturally frequency-dependent and is seen most prominently in certain resonant frequencies. The literature has consistently pointed out certain critical frequency regimes where the effect is seen to be particularly acute.

The most fundamental is the mass-spring-mass (MSM) resonance, in which the two facings vibrate out-of-phase on the stiffness of the core/connectors. Gazzola et al. [14] explicitly related the geometry of an elastic ligament to this phenomenon, showing that a decrease in ligament thickness causes the MSM resonance dip to occur at lower frequencies (e.g., 187 Hz for their configuration). This is a dip in frequency for drastically reduced insulation, where the sound bridge is most effective. Wan et al. [7] found a similar resonance dip at 160 Hz for all tested woven lattice truss panels, irrespective of thickness, highlighting its fundamental origin from the interaction between the two facings on the stiffness of the connectors.

Aside from this basic resonance effect, the connector geometry defines the entire modal response of a panel, which is a series of transmission paths that vary as a function of frequency. Most studies have measured natural frequencies for different cores [9][11][13][18][22][24], which directly relate to maxima in vibration response [12][24] and minima in STL [8][10][11]. For example, different topologies of truss cores, such as pyramidal, kagome, or tetrahedral topologies, result in different first resonance frequencies [9], which are also evident from corresponding minima in the STL curves [15]. Higher-order resonances, like that of the frame flexural mode at 630 Hz reported by Gazzola et al. [14], provide additional transmission paths for sound. Periodic structures also have band gaps, which are ranges of frequencies where wave propagation is inherently forbidden. Dede and Hulbert [16] designed a compliant mechanism core that had a broadband attenuation zone starting from 2320 Hz, where the top layer vibration is significantly reduced. Moosavimehr and Phani [20] reported coincidence frequencies and double-wall resonances that vary depending upon the topology of cores, which results in the enhancement of STL by up to two orders of magnitude at band gap frequencies.

Table 1 summarizes the key literature research results on the acoustic bridging effect of mechanical connectors, including connector parameters, observed effects on sound transmission, and relevant frequency ranges.

Table 1. Summary of key literature findings on the sound bridge effects of mechanical connectors.

Finite Element Modeling appears to be the most widely accepted numerical method for the vibro-acoustic characterization of sandwich panels’ performance, with ABAQUS, ANSYS, LS-DYNA, and COMSOL Multiphysics being the most popular commercially available software packages widely utilized for the purpose [1][2][20]. While the development of a valid FE model may result in more realistic predictions compared to simplified analytical approaches and may minimize the need for extensive experimentation, the available numerical studies are mostly limited to the individual component performance evaluation instead of system performance evaluation. The choice of finite elements plays a critical role in the accuracy of the solution. For sandwich panels, shell elements are often used for the face sheets, beam elements for the core struts, and acoustic elements for the fluid regions, along with the corresponding damage criteria such as the Hashin failure criteria and Cohesive Zone Models. However, computational costs become prohibitively expensive with large-scale models or high-frequency calculations, and validation against experimental results rather than numerical results remains an important tool in ensuring the reliability of predictive calculations across the studies reviewed [2][12].

Coupled fluid-structure interaction models have also been proposed to simultaneously address structural vibrations and acoustic radiation using specialized software packages such as ACTRAN and LMS Virtual. Lab, and COMSOL Multiphysics with periodic boundary conditions implemented in the code [9][14]. These methods generally employ equivalent core representations of complex geometries involving honeycomb or truss cores modeled as an orthotropic material using infinite baffle approximations and Perfectly Matched Layer techniques in the acoustic domain [9][24]. The Transfer Matrix Method provides a computationally efficient method, but is restricted to flat panel geometries and high-frequency solutions where modal effects are negligible in the acoustic domain [17]. In contrast, validation of these methods against experimental results appears to be surprisingly absent in the literature, with most studies only comparing results with other numerical models or theoretical results, with simplifying assumptions in the core modeling potentially masking important local effects critical in accurate transmission loss calculations [9][14][24].

Simplified analytical methods, from one-dimensional spectral elements to two-dimensional equivalent plate approaches, have been proposed for the compromise between solution accuracy and computational efficiency for optimization and parameter studies [11][13][15]. Spectral beam elements with the Wittrick-Williams method are useful for efficient eigenvalue extraction without any mode skipping, and equivalent single-layer approaches based on Third-order Shear Deformation Theory are exact for simply supported boundary conditions [11][13]. Averaging of tolerances is useful for microstructure changes by redefining the periodic cell function rather than redefining the entire model, though accuracy is sacrificed for higher vibration modes [22]. However, all simplified methods universally suffer from a compromise in solution accuracy, whether through two-dimensional approximations, “hard” core approximations, or inability to capture joint continuity effects, and generally validate against other numerical methods rather than experimental data, thus limiting confidence in predictive capabilities [10][13][16].

However, determining the right type of numerical technique for sound-bridge analysis depends greatly on balancing detail and efficiency within particular frequencies. FEM is best used for low-frequency analysis in that it can describe specific modal behavior through shell and beam element details, but it is typically limited to individual components due to the prohibitive computational costs of large-scale, high-frequency simulations. Coupled vibro-acoustics modeling addresses the middle frequency transition by considering both fluid and structure at once, but it uses simplified core structures and infinite baffles, in that it fails to take into consideration important localized effects. The Transfer Matrix Method (TMM) provides high efficiency for high-frequency solutions where modal effects are negligible, but it is strictly restricted to flat panel geometries and captures only average acoustic trends. Lastly, simplified analytical and hybrid models such as 1D spectral element method and 2D equivalent plates are ideal for quick parameterization in low to middle frequencies, but make use of idealized boundary conditions (simply supported), and do not consider joint continuity and higher vibration modes. However, all these methods currently suffer from a notable lack of experimental validation, specifically regarding concrete sandwich systems.

In the context of vibro-acoustic coupling, the core acts as a “connector,” and its properties are crucial in influencing the dynamic interaction between the two face sheets. The core’s stiffness and damping properties directly influence the energy transfer from the excited face sheet to the other. Research based on completely coupled fluid-structure interaction models has investigated various core materials. For example, Fu et al. [9] and Fu et al. [18] have analyzed metallic cores, such as aluminum and steel truss structures, under various conditions, showing the core’s elastic modulus to be a significant factor in influencing the dynamic response of the panel and its sound radiation. However, the use of lighter and stiffer materials, such as aluminum, as in most research [10][11][15][16], is intended to increase the specific stiffness, but at the expense of internal damping, possibly resulting in reduced damping of the structural vibrations at resonance.

The advent of advanced composites has added a further dimension to core material properties. Arunkumar et al. [13] studied a magneto-electro-elastic (MEE) composite core material, where the intrinsic coupling between electric and magnetic fields in the core material was shown to be used to control vibrations and hence sound radiation. This is a step change from passive material behavior to active material behavior. Additionally, the advent of polymer-based cores such as Nylon PA12 used in the 3D-printed panel studied by Gazzola et al. [14] has shown that there is scope to leverage base material damping. The work by Gazzola et al. was experimentally validated and showed that the viscoelastic properties of the polymer had considerable scope to contribute to acoustic insulation, especially with a periodic structure. However, there is a major gap in knowledge that needs to be filled: whereas the impact of core material effective properties is well understood, there is a lack of work on how the impact of the material’s intrinsic damping coefficient used in the connector affects STL, especially in relation to geometry effects.

The geometry of the core, whether a truss, honeycomb, or corrugated configuration, is the most extensively studied parameter in vibro-acoustic coupling. The geometry of the core determines the paths of the structure-borne sound and the frequencies at which the panel is most efficient in radiating noise.

Significant research has been dedicated to the study of truss lattice cores. Moosavimehr & Phani [20] have successfully validated their models using historical data on shear panels, providing a framework for understanding the impact of core geometry on STL. Fu et al. [9] and Kabiripoor et al. [15] both investigated the impact of geometry on the truss core, with the latter also demonstrating the potential for optimizing a truss-like geometry for improved STL in broadband low-frequency domains. This is a fundamental aspect in understanding the impact of geometry on STL, as the dimensions of the unit cell and strut angles directly impact the position of the stop band and the coupling stiffness. Guo et al. [12] also used the core geometry for the attachment of resonant shunt circuits, directly impacting the acoustic radiation of specific modes. This is a fundamental aspect in understanding the impact of geometry on STL, as the geometry is not simply a medium for wave propagation but also a medium for impact.

Other geometric configurations exhibit alternative coupling characteristics. For example, Yang et al. in reference [10] studied a double-wall structure with interconnected trapezoidal acoustic cavities. This geometry, in itself, inherently promotes a more complex FSI due to the presence of acoustic cavities that resonate. Another study on woven lattice truss structures was conducted by Wan et al. in reference [7] and Yan et al. in reference [8]. This study promotes an even more intricate geometry, whereby the geometry of the core is multifunctional, promoting load-carrying and sound absorption characteristics. It is, however, interesting to note that in all these studies, the method of coupling was dictated by the geometric complexities. For simpler geometries, particularly those that are periodic, the Rayleigh integral method was adequate in determining sound radiation characteristics, as was shown in references [11][13][19][24]. For more complex geometries, such as those involving interconnected cavities [5] and intricate trusses [14][20], coupled FE models were necessary in determining sound radiation characteristics. This, therefore, suggests that the method of coupling is not independent of the geometric parameters under investigation.

Aside from that, the total configuration of the panel itself, along with its boundary conditions, layering, and the presence of facing layers, greatly impacts its acoustic signature. The literature shows that a range of modeling assumptions as well as experimental configurations is employed, which is difficult to compare directly but is also enlightening.

Boundary conditions are a key aspect of a configurational parameter that plays a significant role in the acoustic response. Research covers a broad spectrum from the assumption of infinite panels to the assumption of simply supported edges. A considerable number of analytical and numerical studies, particularly those dealing with method development, employ simply supported edges [9]-[11][13][17][18] and clamped edges [3][12][16][24], assuming infinite rigid baffle boundary conditions [12][13][24]. This is done to facilitate a comparison with the classical solution. However, as Wang in [3] explicitly compared the boundary conditions (CCCC and SSSS), the boundary conditions significantly affect the stiffness of the panel and the mode shapes, which in turn affect the sound radiation and STL. In the case of experiments, the panels are necessarily placed in a test hole between reverberation chambers [7] and impedance tubes [2][8][14]. The disparity between the numerical boundary assumptions and the actual boundary assumptions is a critical drawback. For instance, the assumption of a rigid baffle does not consider the effect of sound radiation from the edges and the possibility of leakage.

The configuration of the panel in multiple layers is another important parameter. While the traditional sandwich concept consists of only three layers, there have been some investigations into more complex configurations. Franco et al. in reference [19] have investigated a top and bottom composite sheet, which represents the most basic configuration. Atalla, in reference [17], has developed an extensive modeling framework for complex multilayered configurations, including those with noise control materials, showing that each additional layer has an impact on the transfer matrix and hence on the transmission loss. Recent research on gradient and multi-layer woven structures in reference [7][8] takes this concept even further, showing that by modifying the properties in each layer, it is possible to create multifunctional materials that can meet both structural and acoustic requirements. The research on wave propagation in profile strips in reference [21] by Kohrs & Petersson suggests that even the periodicity of the core itself can be considered an important configurational parameter, where any variation in periodicity can be an important tool in influencing vibro-acoustic behavior, an aspect that is also related to phononic crystals and metamaterials, as described in reference [23].

Figure 3. summarizes the quantitative data from 25 studies: distribution in terms of (a) the method for the coupled problem (not addressed, one-way, two-way FSI); (b) the type of boundary condition (not specified, simply supported, clamped); (c) the core geometric parameter (not specified, truss/lattice, honeycomb, corrugated/woven); and (d) the validation method (not addressed, numerical only, experiments). The bars in the figure show the number of studies for a specific category. The figure offers a general view of the overall trends in the literature regarding vibro-acoustic coupling in sandwich panels.

The axial stiffness of these connectors is arguably the fundamental parameter that is critical to sound bridging, as stiffer connectors are more efficient in transferring vibrational waves between the facings. Steel-based connectors are known to cause severe acoustic short circuits owing to their high modulus of elasticity. On the contrary, Fiber-Reinforced Polymer (FRP) connectors are seen to offer considerable advantages over steel-based connectors owing to their lower stiffness. Silva and Lameiras [5] found that the longitudinal modulus for GFRP-based connectors is 12.56 GPa. This is much lower than that of steel, which is 210 GPa. de Sousa et al. [6] found that this modulus varied from 10.4 GPa to 58.4 GPa for various fiber architectures. This allows for the optimization of stiffness for thermal as well as acoustic purposes, as FRPs are known to be poor thermal conductors, hence minimizing thermal bridging while possibly enhancing acoustic bridging. However, Sah et al. [1] found in their exhaustive review that the acoustic behavior of FRP-based connectors is seldom quantified.

Figure 4. Key design parameters affecting sound bridging in sandwich panels.

The mass law creates a framework through which the aforementioned aspects may be understood. As emphasized by Atalla [17], the stiffness of the connector (k) is a critical parameter in the case of a double-wall system. A stiffer connector results in a larger degradation of transmission loss due to the elevation of the resonance frequency of the double wall into the problem zone. However, the relationship between the connector stiffness and the acoustic performance is not as clear-cut. For instance, the connector must not only provide adequate decoupling from the acoustic performance but must also maintain structural integrity. Haffke et al. [4] observed that although the GFRP connector retains structural integrity during fire exposure, the acoustic performance of the connector when subjected to extreme loading conditions remains uninvestigated. It is apparent that the entire field of FRPs is yet to be fully explored in terms of the acoustic performance of the connector over the entire range of achievable moduli. Such a gap represents a critical area of research. It is proposed that future studies must be devoted to the characterization of sound bridging for moduli below 10 GPa, as this represents the area with the highest potential for optimization.

Apart from the material properties of the connectors, the geometry of the connectors’ arrangement and their orientation also provides scope for controlling the sound bridging. The effect of the inclination of the connectors has been investigated. Yang et al. [10] showed that an increase in the inclination of the connectors improves the sound insulation due to an added stiffness effect. Fu et al. [9] varied the inclination angle of the pyramidal cores between 30 and 60 degrees. They showed that the inclination of the connectors changes the stiffness of the core and, therefore, must be affecting the sound bridging. A more advanced method of controlling the STL curve is the use of hybrid cores. Li and Yang varied the angle of the cells within the core. This method was employed to tune the STL curve by shifting the dips of the curve. They showed that the optimization of the angle distribution improves the STL performance compared to the uniform angle case.

Moreover, it has been shown by Moosavimehr and Phani [20] that topology itself determines wave propagation properties by comparing tetrahedral, pyramidal, double pyramidal, Kagome, hexagonal honeycomb, and shear panel cores. The results indicate that topology has a major effect on wave propagation properties, coincidence frequencies, and ultimately STL; thus, Kagome has a good compromise between high stiffness and high STL. Kabiripoor et al. [15] also found that core height and aspect ratio are important parameters affecting STL; conversely, the effect of the interior angle is negligible. However, it is obvious that not all parameters are equally important. The effect of periodicity is a bit more complicated; Kohrs and Petersson [21] have shown that periodic length determines fundamental wavenumber as well as spacing of space harmonics; moreover, purposeful periodicity perturbations can cause a smearing effect of wavenumber spectra and thus disturb sound bridging paths. The problem is that it is difficult to apply this knowledge to practical design; thus, Gazzola et al. [14] proposed optimization of periodic cores for specific acoustic phenomena while taking into account manufacturing constraints. The effect of different geometric parameters interacting with each other should be studied more thoroughly; thus, hybrid structures should be analyzed more systematically.

While the stiffness of a connector and its layout influence the path that vibrational waves take, damping treatments affect the efficiency with which vibrational waves are dissipated once they are introduced into those paths. In a more systematic approach, Franco et al. [19] showed that as structural damping is increased from 0.01 to 0.1, it smooths out the transmission loss curve by minimizing deep troughs that are associated with resonant sound bridging. The importance of this is that sound bridging is most likely to be a problem at particular resonance frequencies; by incorporating a damping effect, it is possible to smooth out resonances to ensure that acoustic properties are more uniform. Wang [3] has shown that it is possible to enhance a damped effect by incorporating absorption materials into the core of a connector. These materials can include PUF foams or wood-based materials; wood-based materials have equivalent insulation properties to synthetic foams while also having sustainability advantages. Air flow resistivity was found to be a significant factor.

The source and method of damping have significant implications in practical applications. Wang, Dai, and Hu in [24] determined that filler materials have significant effects on resonance peaks and STL. Triangle-shaped cores provided optimal results when combined with wood-based fillers. This study suggests that the geometry between core materials and fillers has significant implications for damping. Active methods provide further opportunities, as demonstrated in Guo, Jiang, and Xu in [12], in which shunt circuits can be utilized to provide frequency-dependent complex impedances, thereby achieving significant additional damping up to 0.0407. This method can control individual vibration modes. This method specifically targets those modes that are most likely involved in sound bridging, unlike general damping. Another significant source of damping is between the connector and the facing, where Fu et al. in [18] suggest that shear foundation stiffness could be more significant than translation stiffness in sound bridging. Atalla [17] stresses that damping treatments should be considered as an integrated package that takes into account the combined effect of facings, connectors, and core materials since the poroelastic properties of the fill material control the combined effect of the airborne and structural paths. Future research should be conducted on interface treatments and their durability. Additionally, the optimal placement of damping material within the core and the connectors should be studied.

To synthesize the literature in a manner that provides useful design recommendations, it is necessary to understand both what is known and what is not known. With regard to the material science of the problem, FRP connectors have clear advantages over steel in reducing sound bridging; however, the range of possible moduli (10 - 60 GPa) means that the choice of material must be considered carefully, with softer moduli likely more beneficial in acoustic terms but stiffer options potentially necessary in terms of structural performance. Hybrid solutions in which the stiffness of the material is varied along the length of the connector or in a hybrid fiber arrangement have yet to be explored in acoustic terms but represent an interesting avenue of future work. Geometrically, inclined connectors and truss structures have been shown to have benefits in acoustic terms; however, there is no clear agreement in the literature regarding the optimal angle of the connectors, with angles of 30˚ - 60˚ having been explored. Similarly, the concept of a hybrid core in which angles vary across the panel represents a promising avenue of future work.

The biggest gap in existing design standards is that no requirements are given for acoustic behavior within existing standards for connectors or building codes. Sah et al. [1] already stated that the material used for cores is primarily considered to be important for thermal and fire behavior within existing standards, whereas acoustic behavior is seen as secondary. This is now changing as multifunctional design is becoming more accepted [6]-[8], but no requirements are given within major international standards regarding acoustic behavior for connectors. Future research should be aimed at experimental determination of sound bridging behavior for various types of connectors, development of models to describe sound bridging behavior considering various effects such as stiffness, layout, and damping, and integration of research outcomes into design standards. For now, however, designers should apply fundamental principles such as minimizing stiffness, optimizing layout for certain ranges of interest, and providing adequate damping. Verification of acoustic behavior through testing is then required. The future is seen in multifunctional design, where acoustic behavior must be provided in combination with structural behavior, thermal behavior, fire behavior, and durability behavior.