Experimental and Numerical Investigations of the Vibration and Acoustic Properties of Corrugated Sandwich Composite Panels

Abstract

Featured Application

The simulation method in this article is proposed to calculate the vibration properties and sound transmission of a kind of corrugated sandwich panel. The vibration and acoustic tests are performed to validate the simulation method. This work can provide a fundamental support for the comprehensive design of vibration and acoustics of the composite sandwiched panel.

Abstract

To explore the lightweight structures with excellent vibration and acoustic properties, corrugated composite panels with different fiber reinforcements, i.e., carbon and glass fibers, were designed and fabricated using a modified vacuum-assisted resin infusion (VARI) process. The vibration and sound transmission loss (STL) of the corrugated composite panels were investigated via mode and sound insulation tests, respectively. Meanwhile, finite element models were proposed for the verification and in-depth parametric studies. For the vibration properties of the corrugated composite panels, the results indicated that the resin layer on the panel surface, despite the extremely low thickness, showed a significant effect on the low-order bend modes of the entire structure. In addition, the difference in the mode frequency between the panels consisting of different fiber types became more and more apparent with the increase of the frequency levels. For the sound insulation property of the panel, the initial frequency of the panel’s resonant sound transmission can be conveniently increased by increasing the layer thickness of surface resin, and the fraction of fiber reinforcements is the most predominant factor for the sound insulation property, which was significantly improved by increasing the thickness of the fiber cloth. This work can provide fundamental support for the comprehensive design of vibration and acoustics of the composite sandwiched panel.

1. Introduction

Composite sandwiched structures consisting of two thin composite plates with high stiffness in combination with a lightweight core have been widely used in aerospace, automotive, marine, and other engineering fields [1,2,3,4,5], owing to their excellent specific stiffness, specific strength, and multi-functionalization, such as high electromagnetic, stealth characteristics, thermal transport, energy absorption, etc. [6,7,8,9,10]. The lightweight cores are normally made of foam, balsa, and other materials with viscous-elastic properties [11,12,13], which on one hand significantly prevent the structural weight penalty, and on the other hand potentially provide some specific functions, e.g., wave absorption or energy dissipation [14], for the sandwiched structures. However, the pure lightweight cores are basically limited by the low mechanical performance [15], and some spatial configurations, such as corrugated, pyramidal, tetrahedral, and Kagome cores, are proposed to enhance the mechanical properties of the core part [16,17,18,19,20]. Among the different core configurations, composite corrugates combined with lightweight foam provide the superiorities of high stiffness, low cost, and easy processing, which have been widely used in many industrial fields. Vibration and sound insulation are the most typical engineering properties for automotive and aviation structures. It is well-known that these properties are significantly influenced by the structural configurations and the utilized materials. Therefore, to facilitate the industrial applications of composite sandwiched structures, it is necessary to gain an in-depth knowledge of the influence of the design factors on the vibration and acoustic properties. This work can provide fundamental support for the comprehensive design of vibration and acoustics of the composite sandwiched panel.

Researchers have made great efforts to establish the design methodologies of corrugated composite structures to enhance their vibration performance. Peng et al. [21,22,23,24] investigated the free vibration characteristics of sandwiched structures with corrugated, honeycomb, corrugated channel, and graded corrugated lattice cores. The research indicated that the vibration properties can be designed by changing the material components and the configurations of the sandwiched structure. Magnucka et al. [25] studied the stability and vibration of multi-layer sandwiched structures. A mathematical method was proposed to calculate their natural frequencies. Guo et al. [26] proposed a new semi-analytical method for the dynamic homogenization and vibration analysis of sandwiched beams, which provides a good accuracy of natural frequency prediction. Yang [27] investigated the modes of sandwiched structures and proposed a modified damage index based on the mode flexibility curvature variation to identify the damage locations within the sandwiched structures. Based on a refined shear deformation theory, Han et al. [28] proposed an accurate and simple theory method to study the free vibration and buckling behaviors of foam-filled composite corrugated sandwich plates under thermal loading. Arunkumar et al. [29] investigated the influences of electric and magnetic potential on the vibroacoustic response of the different types of truss core and honeycomb core sandwich panels and provided an exact solution for a vibroacoustic response of magneto-electro-elastic (MEE) composite plate and sandwich panels with MEE facings. Mohammadi et al. [30] used the Kirchhoff–Love shell theory to model the kinematic behavior of sinusoidally corrugated panels with a variable radius of curvature and studied the effects of different configurations of carbon nanotubes and various geometrical parameters, such as corrugation amplitude and number of corrugation units. Furthermore, panel aspect ratios were presented on the natural frequency and dynamic response of the sinusoidally corrugated, functionally graded carbon nanotube-reinforced composite panels. From these investigations, it can be found that the mode properties of the composite sandwiched structures are significantly affected by the geometric parameters, process methods, and material properties. This provides designers with various design methods to obtain the desired structural vibration performance. In recent years, to solve the problems encountered in the application of traditional modal testing methods (for example, the sensor must contact the measured object, the force hammer is easy to damage the measured object, etc.), many new modal testing methods and equipment, such as the Laser Doppler Vibrometry system [31,32] and the Digital Image Correlation Technique [33], have been developed. These works present the use of non-destructive, non-contact experimental modal analysis using the single- or multi-point approach for measurement over the surface of the product and enable modal testing to be performed in more working environments.

In addition to the vibration behavior, the acoustic property of structures is also becoming increasingly attractive to both civil and military industries since it has a close relationship with the personnel comfort and equipment stealth. Shen et al. [34] and Tao et al. [35] established theoretical acoustic models of corrugated sandwich panels by using the same simplified method that simplifies the middle layer to springs and analyzed the effects of design factors on the sound transmission loss (STL). The difference is that in the latter investigation, the corrugated panel is filled with porous material. Bartolozzi et al. [36] devoted an equivalent material formulation for simplifying the complex shaped core to an equivalent homogeneous material, which considerably improves the efficiency of finite element calculation and achieves a satisfactory accuracy. Tang et al. [37] and Wang et al. [38] investigated the sound absorption of sandwiched structure panels with micro-holes. Shahsavari et al. [39] presented an analytical study on the sound wave propagation across a sandwich cylindrical shell with a corrugated core filled with porous materials and investigated the vibroacoustic effects of various parameters, such as porosity, types of the porous materials, the thickness of the corrugated core, the structural damping factor, the incident angle, and the Mach number of the external flow. Jin et al. [40] proposed a perforated meta-structure combining fish-belly panels and a corrugated sandwich structure for broadband sound absorption and developed an effective impedance theory to study the relationship between sound absorption performance and geometric factors. Luo et al. [41] designed 49 kinds of aramid honeycomb sandwich panels by the orthogonal test method and tested their sound insulation properties, and furthermore predicted the sound insulation performance of aramid honeycomb sandwich panels based on artificial neural network. The results showed that these properties are influenced by various factors, including different geometric parameters and manufacturing techniques, and some of them are coupled.

In the vibration and acoustic design of composite sandwich panels, as the coupling relationship between some design variables, the different choice of materials and design processes often leads to changes in the effect of design variables and parameter sensitivity. Therefore, even for the same configuration, slight differences in materials and processes may lead to great changes in the design methods. To establish a useful design method, it is necessary to carry out parametric research on the vibration and acoustic performance of the novel designed composite sandwich panel.

In this research, composite sandwiched panels with pyramid corrugates and lightweight foam were designed and fabricated. Special attention was paid to the effects of different fiber reinforcements, i.e., carbon and glass fibers, on the vibration and acoustic properties of the as-manufactured sandwiched structures. A combination of experimental and numerical methods was applied to investigate the dynamic characteristics of the composite sandwiched panels. Mode and sound insulation tests were conducted to evaluate their vibration behavior and acoustic insulation properties, respectively. In addition, to provide a verification of the experimental analysis, a finite element model for the composite sandwiched panel was proposed. Based on the model validation, a parametric study on the vibration and acoustics properties of the corrugated composite panels was performed. The coupling effect of the vibration and acoustic properties was revealed and the sensitive design factors to the vibration and acoustic properties of the panel were found, which is the main novelty of the present work. This work can provide fundamental support for the comprehensive design of vibration and acoustics of the composite sandwiched panel.

2. The Fabrication of the Corrugated Sandwich Panel

2.1. Materials

In this paper, the corrugated composite panel is a sandwiched panel composed of reinforced fiber cloth, resin, and foam strips. The fiber cloth and foam are bonded together by the resin, and the cured resin is also an important part of the corrugated composite panel. In the research, two types of plain-woven fabric fiber cloths, i.e., T300 carbon fibers and S-PC/EWR400 glass fibers, were utilized to fabricate different corrugated composite panels. The related material properties of the two fiber cloths are listed in Table 1, which were supplied by Hebei Optfilm Composite Co., Ltd., Shijiazhuang, China. The lightweight M60 PVC foam strips were used to maintain the corrugate shape, and they were supplied by Sino Composite. The MERICAN^® 30-200P vinyl epoxy resin was supplied by Sino Polymer, China. The related material properties of the foam and resin are listed in Table 2.

2.2. Panel Fabrication

The corrugated sandwich panel was integrally fabricated using a modified vacuum-assisted resin infusion (VARI) technique, as schematically shown in Figure 1. The details of the manufacturing process are provided in our previous research [42]. Differently, no additional fiber cloths were placed at the top of the corrugated panels in this study. The basic configuration of the corrugates was mainly dominated by the cross-section of the foam strip, as shown in Figure 1f. One should note that due to the closed-cell structure of the foam strips, the epoxy resin cannot thoroughly penetrate the entire foam part but forms an extremely thin resin layer at the surface of the panel after curing, as indicated in Figure 1f. After the sample is made, the edge burrs need to be cleaned and trimmed according to the usage requirements. In this paper, the size of the sample is 0.6 × 0.7 m.

3. Test Procedures

Mode tests and sound insulation tests were conducted in this research to evaluate the vibration and acoustic properties of the as-manufactured corrugated composite panels, respectively.

3.1. Mode Tests

In the mode tests, the corrugated panels were supported by four soft springs to mimic the free boundary conditions. The selection criteria of the soft spring are: the frequency of the vibration system formed by the soft spring and the plate is lower than the first-order natural frequency of the plate; that is to say, the vibration of the panel relative to the soft spring is the movement of the overall panel, and the simulation and experimental results can be compared to verify whether the selection of the soft spring is reasonable. As schematically shown in Figure 2a, the springs are located at the four corners of the rectangular panel. An impact hammer was used to excite the vibration of the panel at the measure points, as shown in Figure 2a. For accuracy, the average data of the three parallel tests were reported. The vibration signal was captured by an accelerometer bonded at point 19 and was finally transmitted to the dynamic signal analysis system developed by Donghua Testing Technology Co., Ltd., Taizhou, China. For the hammering mode test, the governing differential equation of a continuous system excited by a hammer force {F(t)} can be written as [43]:

(1)$\left[M\right]\left\{\ddot{x}\right\}+\left[C\right]\left\{\dot{x}\right\}+\left[K\right]\left\{x\right\}=\left\{F(t)\right\}$

where [M], [C], and [K] are the mass, damping, and stiffness matrices of the continuous system, respectively. {F(t)} is a step input force vector. The frequency response function (FRF) of the system can be written as:

(2)$H(j\omega )=\frac{X(j\omega )}{F(j\omega )}=\frac{1}{-{\omega }^2[M]+j\omega [C]+[K]}$

where F(jω) is the impulse input force generated by the hammer, while X(jω) is the response of the system.

The Poly-reference Least Square Complex Frequency (PolyLSCF) method proposed by Guillaume [44] was used in this research to fit the frequency response function. This method has been widely used to fit the frequency response function in the frequency domain, which has a relatively high recognition accuracy and can generate a clear stable map. The frequency response characteristics diagram of points 34 and 40 is shown in Figure 2b, respectively. The vibration peaks of the two points showed good consistency in the frequency domain, which is beneficial for mode picking.

In this paper, the accelerometer sensor and modal hammer were from Donghua Testing Technology Co., Ltd., Taizhou, China. The accuracy of the accelerometer is 1.075 mV/(m·s²) and the frequency response range is 1–10,000 Hz. The accuracy of the modal hammer is 2.118 mV/N, and the working range is 1–5000 N. The sampling frequency for the modal test is 2000 Hz. The PolyLSCF was used to fit the frequency response function. The dynamic signal, mode shapes, mode frequencies, and damping ratios were obtained using the dynamic signal acquisition and analysis software system, DHDAS, from Donghua Testing Technology Co., Ltd., Taizhou, China.

3.2. Acoustic Tests

A sound intensity test was conducted to evaluate the sound transmission loss (STL) of the composite panels [45,46]. The tests were performed in a reverberation room and a semi-anechoic room, which were connected by a sound insulation wall, as shown in Figure 3a. The samples were placed in an open window, in the center of the wall. The size of the window was around 0.6 × 0.7 m (see Figure 3b). Due to the large error of the low-frequency test, this test was performed in the frequency range of 400 to 8000 Hz.

The incident sound intensity level ($L_{Ii}$) on the source side of the panel can be expressed as:

(3)$L_{Ii}=L_{pi}-6$

where $L_{pi}$ is the measurements of the space-averaged sound pressure level in the reverberation room. Regarding the receiving side of the panel, the transmitted intensity was directly measured by using two microphones in the anechoic room [47]. The STL of the corrugated composite panel was then calculated as:

(4)$ST{L}_{\exp }=L_{pi}-L_{It}-6$

where $L_{It}$ is the transmitted sound intensity level.

4. Numerical Simulation

To provide verification for the experimental study, the dynamic characteristics, i.e., vibration behavior and acoustic properties, of the corrugated composite panels were also investigated through the finite element (FE) method.

4.1. Mode Analysis

As shown in Figure 4a, the FE models of the corrugated composite panels investigated in this research were established by using a commercial software UG NX, and the specific parts of the panel model are shown in Figure 4b. Both the fiber cloth and the resin layer were meshed with CQUAD4 elements, whereas the foam strips were meshed with CHEXA8 elements. The components were assembled by using a merge technique which makes the joint surface between components have common nodes. According to the literature [48], at least ten elements per local wavelength were ensured at the highest frequency in the simulation analysis. Therefore, the element size was set to be 2 mm to guarantee the precision of the analysis. Material properties of the considered parts were obtained from the data listed in Table 1 and Table 2. Corresponding to the mode tests, a free boundary condition was used for the panel model to calculate the modes.

4.2. Sound Transmission Level Analysis

The STL properties of the corrugated composite panels was numerically evaluated by using the commercial FE software COMSOL Multiphysics^®. Different from the test processes, both the reverberation and anechoic rooms were not built in the model. Instead, an ideal diffuse field was directly added on the source side of the composite panels, while an ideal anechoic termination was added on the receiver side. The model of the tested composite panel was consistent with that in Figure 4, with the same material properties obtained from Table 1 and Table 2. By solving the vibroacoustic problem, the incident and transmitted sound intensity can be calculated by [45,46]:

(5)$I_{x,in(tr)}=\frac{1}{2}\mathrm{Re}\left(p_{in(tr)}{\mathrm{v}}_{x,in(tr)}^{*}\right)$

where $p_{in}$ and ${\mathrm{v}}_{x,in}$ are, respectively, the sound pressure and velocity of the incident wave on the source side of the panel, $p_{tr}$ and ${\mathrm{v}}_{x,tr}$ are, respectively, the sound pressure and velocity of the transmitted wave on the receiver side, x is the normal direction of the panel, * represents the sign of the conjugate, and Re is the real part of a complex number. The STL of the panel is then written as:

(6)$ST{L}_{sim}=L_{Ii}-L_{It}$

The simulation was performed in the frequency range of 100 to 7000 Hz under the assumption of fixed-constrained boundaries.

5. Results and Discussion

5.1. Mode Analysis

The first four mode shapes combined with the corresponding natural frequencies of the glass fiber corrugated panels (GFCPs) and carbon fiber corrugated panels (CFCPs) are shown in Figure 5a. To provide a clear comparative study, the comparison results, i.e., glass fiber vs. carbon fiber and experiments vs. simulation, are plotted in Figure 5b–e, respectively. The error between two results is expressed by:

(7)$Error=\frac{M_i-Mre{f}_i}{Mre{f}_i}$

where $Mre{f}_i$ is the i-th mode frequency, which is used as the reference value for comparison, and $M_i$ is the i-th mode frequency which is compared to the reference frequency.

As shown in Figure 5b, the experimental mode of GFP is the reference value, and it can be found that the mode frequencies of CFP were larger than those of the GFP, and the fourth experimental mode error was the highest. The simulation mode analysis is shown in Figure 5c, and the simulation mode of GFP is the reference value. The simulation results show the same law as the experimental results. In Figure 5d,e, the experimental modes of panels are the reference values. The errors between the experimental and the simulation modes were all less than 6%, which indicates that the results obtained from the proposed FE model showed very good agreement with the experimental results.

Comparing the mode characteristics of the two panels, it was found that for the first four modes, the GFCPs and the CFCPs provided similar mode shapes, i.e., bending deformation, as shown in Figure 5a. It is worth noting that the first mode shapes of the corrugated panels were diagonally bent rather than perpendicular to the direction of the foam strip, which is consistent with those of the homogeneous panels. This indicates that the foam is not a main factor for influencing the first mode, i.e., the bending stiffness, of the corrugated panels, even though the foam strips have a clear direction in the panel structures. This is mainly attributed to their low Young’s modulus and closer location to the inside of the panel compared to the fiber reinforcements and epoxy resin.

Comparing the experimental modes of GFCP and CFCP, as shown in Figure 5b,c, it was found that the mode frequency of the CFCP was basically greater than that of the GFCP. Although the difference was neglected in the lower-order vibration, it became more obvious for the higher mode levels. One should note that the bending stiffness of composite panels is predominantly affected by the outer layer material [47]. The surface resin layer and the fiber cloth are subjected to tension and compression and play predominant roles in the low-order vibration. The surface resin layer and fiber cloth can be considered as two springs in series, and the Young’s modulus of the fiber is much greater than that of the resin. Therefore, the bending stiffness of the surface layer, and finally, of the entire panel, is mainly determined by the resin. Since the main difference between the GFCP and CFCP is the fiber rather than the surface resin layer, the difference in natural frequencies of GFCP and CFCP is small. It should be noted that carbon fiber has a lower density than that of glass fiber, which is likely the main contributing factor for the slightly higher mode frequency of the CFCP compared to the GFCP counterparts. As the frequency increases, the mode shape of the sandwiched panel becomes complex, and both the fiber on the surface and the core parts begin to contribute to the mode deformation, which makes the mode frequency difference between GFCP and CFCP more noticeable.

Based on the comparison of experimental and numerical results shown in Figure 5d,e, it can be seen that the results obtained from the proposed FE model showed a very good agreement with the experimental results. The maximum relative deviation was approximately 5.86%. In addition, the mode shapes shown in Figure 5a also provided a consistency between the experimental and numerical results. Therefore, the model results were fully validated and can be utilized for the discussion on the effects of the related parameters on the dynamic properties of the composite corrugated panels.

5.2. Sound Transmission Analysis

The experimental and numerical results of the STL property of the two types of corrugated panels are plotted in Figure 6. Firstly, the results of the experiment and simulation had good consistency in the trend, and the maximum error was about 3 dB. The discrepancies between the simulation and experiment may be attributed to the fact that the boundary condition in the simulation is simply supported, but in the sound insulation tests it may not exactly be simply supported [49].

Regarding the evolution of the STL property as a function of the sound frequency, the entire curves of the corrugated composite panels can be divided into four phases based on the investigations conducted on the traditional homogeneous panels [49], as indicated in Figure 6.

In Stage Ⅰ (<200 Hz), which is named the Stiffness Controlled Zone, the STL is proportional to the stiffness of the corrugated panel, showing a monotonous decrease as the frequency increases. After that, the curve steps into Stage II, which is called the Damping Control Zone. The dip that occurs at around 200 Hz corresponds to the resonant frequency of the corrugated panel (${\mathrm{f}}_{\mathrm{r}}$), and ${\mathrm{f}}_{\mathrm{n}}$, characterized by the curve depression points, represent the other resonant frequencies of the corrugated panel corresponding to different orders. One should note that the resonant frequencies of the GFCP and CFCP are almost the same, which indicates that they have similar mode frequencies.

In Stage III, which is named the Mass Control Stage, the discrepancy of the STL between the two types of composite panels results from the difference of their densities. The surface density of the GFCP (5080.9 g/m²) is higher than that of the CFCP (4602.8 g/m²), which leads to relatively higher STL values. Due to the complex structures compared to homogeneous panels, the STL curves of the sandwiched panels containing different fibers present a nonlinear behavior in this stage.

In Stage IV, which is named the Coincidence Effect Zone, the STL decreases at a critical frequency value and then increases with the increasing frequency. The critical frequency, ${\mathrm{f}}_{\mathrm{c}}$, shown in Figure 6, can be obtained by [34]:

(8)${\mathrm{f}}_{\mathrm{c}}=\frac{{\mathrm{c}}^2}{2\mathsf{\pi }}\sqrt{\frac{\mathrm{M}}{\mathrm{D}}}$

where $\mathrm{c}$ is the sound velocity, and $\mathrm{M}$ and $\mathrm{D}$ are the surface density and stiffness of the panel, respectively.

As depicted in Figure 6, it was found that the critical frequencies of the CFCP and GFCP were almost similar. Additionally, the surface density of the GFCP was slightly higher than that of the CFCP. Therefore, considering Equation (8), the stiffness of the GFCP was also slightly higher than that of the CFCP, which finally resulted in a higher STL of the former in Stage I (Stiffness Control Zone).

5.3. Parametric Analysis

Based on the analysis in Section 3 and Section 4, the numerical results were validated by the experimental data. To gain an in-depth insight into the effects of the related material properties on the vibration and acoustic properties of the corrugated composite panels, this section presents a parametric study based on the validated FE models. The parametric matrix was designed based on a single variable principle, and the related parameters for discussion are listed in Table 3. When a parameter is discussed, the values of the other parameters are kept as the basis values, as indicated in Table 3. To focus on the effects of the related material properties, the parametric studies were only performed on the CFCPs.

5.3.1. Parametric Analysis of Vibration Properties

The effects of the density and Young’s modulus of the PVC foam on the mode of the composite sandwiched panels are indicated in Figure 7a,b, respectively. It was found that the mode frequency of the composite panels can be improved by either decreasing the foam density or increasing the Young’s modulus. However, it is known that the material’s density is often contradictory to its Young’s modulus, and hence it is difficult to find a foam with both low density and high Young’s modulus in engineering applications.

The effects of epoxy resin properties on the structural mode are plotted in Figure 7c,e. The density of resin had almost no effect on the modes of the composite panels (see Figure 7c) due to the low mass portion of the epoxy resin inside the panels. However, the high Young’s modulus of resin can significantly increase the mode frequency of the composite panels because of the increase of their bending stiffness (Figure 7d). Based on a similar reason, a higher mode frequency could also be achieved by increasing the thickness of the surface resin layer, as shown in Figure 7e. In addition, as the thickness of the surface resin layer was extremely thin (about 0.2 mm), even if the thickness of the surface resin was doubled, the total weight of the corrugated panel did not increase significantly.

The effects of the fiber volume fraction, represented by the fiber cloth thickness, on the mode of the corrugated panels are shown in Figure 7f. The increasing volume fraction of the fiber cloth decreased the mode frequencies of the corrugated panel. It is known that the natural frequency of the composite panel is determined by the mass and Young’s modulus of its components. In the corrugated sandwich panels, owing to the low weight portion of resin as well as the low density of PVC foam, the fraction of fiber reinforcements is considered as a dominant role for the weight of the entire panel structure. Therefore, increasing the fiber fraction will result in an increase of the entire structural weight. However, this will not affect the bending stiffness of the panel, which is mainly determined by the surface resin layer according to the mode analysis. Consequently, the natural frequency of the corrugated panels is reduced by increasing the fiber volume fraction.

In summary, the layer thickness of the surface resin is the most sensitive design factor to the vibration properties of the sandwich corrugated panel, and changing the layer thickness of surface resin is easy to operate in engineering.

5.3.2. Parametric Analysis of Acoustic Properties

Figure 8 illustrates the parametric studies on the effects of the related design parameters on the STL of the CFCPs. Based on the numerical results, it is interesting to see that when the density of foam increased, the ${\mathrm{f}}_{\mathrm{r}}$ (the first dip frequency) moved to a lower frequency; nevertheless, the STL at ${\mathrm{f}}_{\mathrm{r}}$ increased, as shown in Figure 8a. In contrast, when increasing the Young’s modulus of foam, the dip will move to a higher frequency, while the STL at ${\mathrm{f}}_{\mathrm{r}}$ will remain at the same level (see Figure 8b). Combining Figure 8a,b, it can be seen that before the first resonance dip, the STL property of the sandwiched panels was proportional to the Young’s modulus, whereas it was inversely proportional to the foam density. After the first dip, however, the trend was converse. Regarding the Mass Control Zone, when the high-density foam is used in the corrguated sandwich panel, the nonlinearity of the STL caused by the structural complexity is obviously weakeded (see the blue curve in Figure 8a, in the frequency range of 1000–4000 Hz). On the contrary, this nonlinearity became increasingly obvious with the increase of the Young’s modulus (see Figure 8b), which will provide difficulties in the design of STL in the high-frequency range.

The effects of the resin density and its Young’s modulus on the STL are shown in Figure 8c,d), respectively. Similar to the effects of the foam density, the first resonance dip (${\mathrm{f}}_{\mathrm{r}}$) moved to a lower frequency while increasing the resin density; nevertheless, the STL at ${\mathrm{f}}_{\mathrm{r}}$ increased. In addition, it can be seen that in the Damping Control Zone (about 300–1000 Hz), the STL fluctuated sharply with the frequency increase, which is likely owing to the change of the resin density, which significantly affects the mode vibration properties of the sandwiched panels. A similar effect of the resin density was also found in the Mass Control Zone; nevertheless, this effect gradually decreased with the increasing frequency (see Figure 8c).

In Figure 8d, it can be seen that the Young’s modulus of resin greatly affected the STL in the Stiffness Control Zone and the Damping Control Zone, which is consistent with the observations obtained in the mode analysis. Different to the effect of foam modulus, the first dip (${\mathrm{f}}_{\mathrm{r}}$) will move to a higher frequency, while the STL at ${\mathrm{f}}_{\mathrm{r}}$ will also increase. When E = 3.4 × 10² MPa, the effect of the mode changing blurs the boundary between the Stiffness Control Zone and the Damping Control Zone. Compared to the basis modulus value (E = 3.4 × 10³ MPa), both increasing and decreasing the resin modulus can enhance the STL in the medium- and high-frequency range (except for E = 3.4 × 10⁴ MPa in the middle-frequency band).

Regarding the effects of the fiber volume fraction, as depicted in Figure 8e, a lower fiber fraction provided a higher STL in the initial stage, i.e., the Stiffness Control Zone. However, a lower fiber fraction tended to shift the bottom point of the curve to the high-frequency range, which resulted in a relatively lower STL during the following stages. The reason is that the increase in the fiber volume fraction caused a significant increase in the weight of the corrugated panel, while the stiffness of the corrugated panel did not change significantly; hence, the mode frequencies of the corrugated panel decreased, which made the first natural dip shift to the left. In addition, increasing the volume fraction of the fiber cloth can obviously increase the STL of the corrugated panel in the Mass Control Zone, which eventually improves the STL at the first dip. Based on the above analysis, it can be found that increasing the fiber volume fraction or the fiber layer thickness is an effective approach to enhance the STL of the corrugated panels at the middle- and high-frequency bands.

In summary, the modulus of resin is the most sensitive factor to the initial frequency of the panel’s resonant sound transmission, which can be easy to operate by changing the layer thickness of surface resin in engineering. The thickness of the fiber cloth is the most sensitive factor to the STL of the sandwich corrugated panel, which can be easy to operate by changing the layer number of the fiber cloth in engineering.

6. Conclusions

In this study, the mode and sound insulation properties of two types of composite corrugated panels fabricated with carbon and glass fibers were experimentally and numerically investigated. Based on the observations, some conclusions can be drawn, as follows:

• (1). Low-order mode frequencies were greatly influenced by the resin layer on the panel surface, despite the extremely low thickness.

• (2). The density of fiber was the main factor affecting low-order modes of composite sandwiched panels. In contrast, the effect of the fiber modulus on the low-order modes was slight.

• (3). The layer thickness of the surface resin was the most predominant factor affecting the initial frequency of the panel’s resonant sound transmission.

• (4). The sound transmission loss (STL) of the sandwiched panel mainly followed the mass law. Increasing the fiber volume fraction or the fiber density can significantly increase the STL property of the corrugated panels. However, this is achieved at the cost of a decrease of the resonance frequency. Fortunately, this can be compensated by increasing the layer thickness of the surface resin. Increasing the foam density also improves the STL, while this tends to significantly increase the weight of the entire panels.

In summary, the thickness of fiber cloth, the fiber density, and the layer thickness of the surface resin are the most sensitive design factors to the vibration and acoustic properties of the lightweight sandwich corrugated panel, and the vibration and acoustic properties of composite panels can be flexibly designed by different parameter combinations.

Author Contributions

Z.W. and T.Z. designed and carried out the experimental method; Z.W. analyzed the data and wrote the paper; Y.L. (Yaoguang Liu) carried out the acoustic simulation and R.G. carried out the vibration simulation; X.C., H.W., Y.L. (Ying Li) and F.Y. reviewed and revised the paper. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Acknowledgments

Thanks to the magazine editors for their careful work, and to the reviewers for their valuable comments.

Conflicts of Interest

The authors have no conflict of interest concerning this manuscript.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. The manufacturing process of the corrugated-core sandwich panel. (a) Arranging the bottom foam. (b) Laying the fiber cloth. (c) Arranging the top foam. (d) Injecting the resin. (e) The curing of the resin and the molding of the panel. (f) Removing the burr on the edge.

Figure 2. (a) Experimental equipment of mode testing. (b) Typical frequency response based on PolyLSCF.

Figure 3. (a) Schematic diagram of sound insulation measurement by sound intensity tests. (b) The size of the tested composite panel.

Figure 4. The FE model of the corrugated sandwich panel. (a) The assembly of the FE model. (b) Typical components of the FE model.

Figure 5. (a) Experimental and numerical mode results of the studied GFCPs and CFCPs. (b) Comparison of experimental modes of different corrugated panels. (c) Comparison of numerical modes of different corrugated panels. (d) Comparison of experimental and numerical modes of the GFCPs. (e) Comparison of experimental and numerical modes of the CFCPs.

Figure 6. The experimental and numerical results of the STL of different types of corrugated composite panels.

Figure 7. Parametric studies on the effects of the related design parameters on the vibration properties of the CFCPs. (a) The effect of foam density. (b) The effect of foam’s Young’s modulus. (c) The effect of resin density. (d) The effect of resin’s Young’s modulus. (e) The effect of layer thickness of surface resin. (f) The effect of the fiber cloth thickness.

Figure 8. Parametric studies on the effects of design parameters on the STL of the CFCPs: (a) the effect of foam density, (b) the effect of foam modulus, (c) the effect of resin density, (d) the effect of resin modulus, and (e) the effect of fiber thickness.

Table 1

The material properties of the carbon fiber cloth (CFC) and the glass fiber cloth (GFC). The data were provided by the manufacturers.

Material Properties of CFC
Parameter	E11 (GPa)	E22 (GPa)	µ12	E33 (GPa)	µ23	µ13
Value	60.0	60.0	0.042	6.7	0.25	0.25
Parameter	G12 (GPa)	G23 (GPa)	G13 (GPa)	α11	α22	α33
Value	3.7	3.5	3.5	1.7 × 10−6	1.7 × 10−6	7.9 × 10−6
Material Properties of GFC
Parameter	E11 (GPa)	E22 (GPa)	µ12	E33 (GPa)	µ23	µ13
Value	22.0	22.0	0.3	9.0	0.45	0.3
Parameter	G12 (GPa)	G23 (GPa)	G13 (GPa)	α11	α22	α33
Value	4.0	8.0	4.0	1.7 × 10−6	1.7 × 10−6	7.9 × 10−6

Table 2

The material properties of the used PVC foam and epoxy resin. The data were provided by the manufacturers.

	Density (kg/m3)	Young’s Modulus (MPa)	Poisson’s Ratio
PVC foam	56	75	0.3
Epoxy resin	1200	3400	0.3

Table 3

The parameter discussion of the corrugated sandwich panel.

Component	Density (kg/m3)	E—Young’s Modulus (MPa)
Foam	8, 56 (basis), 200	5 × 10−3, 5, 50 (basis), 500
Resin	60, 600, 1200 (basis)	3.4 × 10−1, 3.4 × 102, 3.4 × 103 (basis), 3.4 × 104, 3.4 × 105
	The thickness of the carbon fiber cloth (mm)
Fiber cloth	0.2, 1 (basis), 2

References

1. Zhang, Q.; Yang, X.; Li, P.; Huang, G.; Feng, S.; Shen, C.; Han, B.; Zhang, X.; Jin, F.; Xu, F. et al. Bio-Inspired Engineering of Honeycomb Structure-Using Nature to Inspire Human Inno-vation. Prog. Mater. Sci.; 2015; 74, pp. 332-400. [DOI: https://dx.doi.org/10.1016/j.pmatsci.2015.05.001]

2. Wadley, H.N.G. Multifunctional periodic cellular metals. Philos. Trans. R. Soc. A; 2005; 364, pp. 31-68. [DOI: https://dx.doi.org/10.1098/rsta.2005.1697] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/18272452]

3. Côté, F.; Deshpande, V.; Fleck, N.; Evans, A. The compressive and shear responses of corrugated and diamond lattice materials. Int. J. Solids Struct.; 2006; 43, pp. 6220-6242. [DOI: https://dx.doi.org/10.1016/j.ijsolstr.2005.07.045]

4. Xiong, J.; Mines, R.; Ghosh, R.; Vaziri, A.; Ma, L.; Ohrndorf, A.; Christ, H.-J.; Wu, L. Advanced Micro-Lattice Materials. Adv. Eng. Mater.; 2015; 17, pp. 1253-1264. [DOI: https://dx.doi.org/10.1002/adem.201400471]

5. Xu, S.; Beynon, J.; Ruan, D.; Lu, G. Experimental study of the out-of-plane dynamic compression of hexagonal honeycombs. Compos. Struct.; 2012; 94, pp. 2326-2336. [DOI: https://dx.doi.org/10.1016/j.compstruct.2012.02.024]

6. Bai, X.; Zheng, Z.; Nakayama, A. Heat transfer performance analysis on lattice core sandwich panel structures. Int. J. Heat Mass Transf.; 2019; 143, 118525. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.118525]

7. Solyaev, Y.; Lurie, S.; Koshurina, A.; Dobryanskiy, V.; Kachanov, M. On a combined thermal/mechanical performance of a foam-filled sandwich panels. Int. J. Eng. Sci.; 2018; 134, pp. 66-76. [DOI: https://dx.doi.org/10.1016/j.ijengsci.2018.10.010]

8. Qin, Q.; Zhang, W.; Liu, S.; Li, J.; Zhang, J.; Poh, L. On dynamic response of corrugated sandwich beams with metal foam-filled folded plate core subjected to low-velocity impact. Compos. Part A Appl. Sci. Manuf.; 2018; 114, pp. 107-116. [DOI: https://dx.doi.org/10.1016/j.compositesa.2018.08.015]

9. Vignjevic, R.; Campbell, J.; Hughes, K.; Orłowski, M.; Garcea, S.; Withers, P.; Reed, J. Soft body impact resistance of composite foam core sandwich panels with uni-directional corrugated and tubular reinforcements. Int. J. Impact Eng.; 2019; 132, 103320.1. 103320.17. [DOI: https://dx.doi.org/10.1016/j.ijimpeng.2019.103320]

10. Yu, R.-P.; Wang, X.; Zhang, Q.-C.; Li, L.; He, S.-Y.; Han, B.; Ni, C.-Y.; Zhao, Z.-Y.; Lu, T.J. Effects of sand filling on the dynamic response of corrugated core sandwich beams under foam projectile impact. Compos. Part B Eng.; 2020; 197, 108135. [DOI: https://dx.doi.org/10.1016/j.compositesb.2020.108135]

11. Taghizadeh, S.; Farrokhabadi, A.; Liaghat, G.; Pedram, E.; Malekinejad, H.; Mohammadi, S.F.; Ahmadi, H. Characterization of compressive behavior of PVC foam infilled composite sandwich panels with different corrugated core shapes. Thin-Walled Struct.; 2018; 135, pp. 160-172. [DOI: https://dx.doi.org/10.1016/j.tws.2018.11.019]

12. Sayahlatifi, S.; Rahimi, G.H.; Bokaei, A. The quasi-static behavior of hybrid corrugated composite/balsa core sandwich struc-tures in four-point bending: Experimental study and numerical simulation. Eng. Struct.; 2020; 210, 110361. [DOI: https://dx.doi.org/10.1016/j.engstruct.2020.110361]

13. Gupta, A.; Panda, S.; Reddy, R.S. Improved damping in sandwich beams through the inclusion of dispersed graphite particles within the viscoelastic core. Compos. Struct.; 2020; 247, 112424. [DOI: https://dx.doi.org/10.1016/j.compstruct.2020.112424]

14. Xiong, J.; Ma, L.; Wu, L.; Wang, B.; Vaziri, A. Fabrication and crushing behavior of low density carbon fibre composite pyramidal truss structures. Compos. Struct.; 2010; 92, pp. 2695-2702. [DOI: https://dx.doi.org/10.1016/j.compstruct.2010.03.010]

15. PeterNilsson, M.A.; Seyed, R.A. Transverse shear stiffness of corrugated core steel sandwich panels with dual weld lines. Thin-Walled Struct.; 2017; 117, pp. 98-112.

16. Kazemahvazi, S.; Zenkert, D. Corrugated all-composite sandwich structures. Part 1: Modeling. Compos. Sci. Technol.; 2009; 69, pp. 913-919. [DOI: https://dx.doi.org/10.1016/j.compscitech.2008.11.030]

17. Kazemahvazi, S.; Tanner, D.; Zenkert, D. Corrugated all-composite sandwich structures. Part 2: Failure mechanisms and experimental programme. Compos. Sci. Technol.; 2009; 69, pp. 920-925. [DOI: https://dx.doi.org/10.1016/j.compscitech.2008.11.035]

18. Fan, H.; Fang, D.; Chen, L.; Dai, Z.; Yang, W. Manufacturing and testing of a CFRC sandwich cylinder with Kagome cores. Compos. Sci. Technol.; 2009; 69, pp. 2695-2700. [DOI: https://dx.doi.org/10.1016/j.compscitech.2009.08.012]

19. Liu, J.; Kan, T.; Lou, J.; Xiang, L.; Zhu, X.; Tang, Y. Localized damage response of carbon fibre reinforced polymer composite sandwich panel after thermal exposure. Polym. Test; 2016; 50, pp. 33-40. [DOI: https://dx.doi.org/10.1016/j.polymertesting.2015.12.006]

20. Hao, W.; Liu, Y.; Zhou, H.; Chen, H.; Fang, D. Preparation and characterization of 3D printed continuous carbon fibre reinforced thermo-setting composites. Polym. Test; 2018; 65, pp. 29-34. [DOI: https://dx.doi.org/10.1016/j.polymertesting.2017.11.004]

21. Peng, L.-X.; Yan, S.-T.; Mo, G.-K.; Zhang, X. Free vibration analysis of corrugated-core sandwich plates using a meshfree Galerkin method based on the first-order shear deformation theory. Int. J. Mech. Sci.; 2014; 78, pp. 8-18. [DOI: https://dx.doi.org/10.1016/j.ijmecsci.2013.10.009]

22. Wang, Y.-J.; Zhang, Z.-J.; Xue, X.-M.; Zhang, L. Free vibration analysis of composite sandwich panels with hierarchical honeycomb sandwich core. Thin-Walled Struct.; 2019; 145, 106425. [DOI: https://dx.doi.org/10.1016/j.tws.2019.106425]

23. Wang, X.; Zhao, Z.Y.; Li, L.; Zhang, Z.J.; Zhang, Q.C.; Han, B.; Lu, T.J. Free vibration behavior of Ti-6Al-4V sandwich beams with corrugated channel cores: Ex-periments and simulations. Thin Wall Struct.; 2019; 135, pp. 329-340. [DOI: https://dx.doi.org/10.1016/j.tws.2018.11.008]

24. Xu, G.-D.; Zeng, T.; Cheng, S.; Wang, X.-H.; Zhang, K. Free vibration of composite sandwich beam with graded corrugated lattice core. Compos. Struct.; 2019; 229, 111466. [DOI: https://dx.doi.org/10.1016/j.compstruct.2019.111466]

25. Magnucka-Blandzi, E.; Walczak, Z.; Wittenbeck, L.; Jasion, P.; Rodak, M.; Szyc, W.; Lewiński, J. Stability and vibrations of a metal seven-layer rectangular plate with trapezoidal corrugated cores. Thin-Walled Struct.; 2017; 114, pp. 154-163. [DOI: https://dx.doi.org/10.1016/j.tws.2016.11.025]

26. Guo, J.; Xiao, Y.; Zhang, S.; Wen, J. Bloch wave based method for dynamic homogenization and vibration analysis of lattice truss core sandwich structures. Compos. Struct.; 2019; 229, 111437. [DOI: https://dx.doi.org/10.1016/j.compstruct.2019.111437]

27. Yang, J.-S.; Liu, Z.-D.; Schmidt, R.; Schröder, K.-U.; Ma, L.; Wu, L.-Z. Vibration-based damage diagnosis of composite sandwich panels with bi-directional corrugated lattice cores. Compos. Part A Appl. Sci. Manuf.; 2020; 131, 105781. [DOI: https://dx.doi.org/10.1016/j.compositesa.2020.105781]

28. Han, B.; Qin, K.-K.; Zhang, Q.-C.; Zhang, Q.; Lu, T.J.; Lu, B.-H. Free vibration and buckling of foam-filled composite corrugated sandwich plates under thermal loading. Compos. Struct.; 2017; 172, pp. 173-189. [DOI: https://dx.doi.org/10.1016/j.compstruct.2017.03.051]

29. Arunkumar, M.; Bhagat, V.; Geng, Q.; Li, Y.; Pitchaimani, J. An exact solution for vibro-acoustic response of smart sandwich panels with MEE composite Layer. Compos. Struct.; 2022; 286, 115201. [DOI: https://dx.doi.org/10.1016/j.compstruct.2022.115201]

30. Mohammadi, H.; Setoodeh, A.; Vassilopoulos, A. Isogeometric Kirchhoff–Love shell patches in free and forced vibration of sinusoidally corrugated FG carbon nanotube-reinforced composite panels. Thin-Walled Struct.; 2022; 171, 108707. [DOI: https://dx.doi.org/10.1016/j.tws.2021.108707]

31. Scislo, L.; Guinchard, M. Non-invasive measurements of ultra-lightweight composite materials using Laser Doppler Vi-brometry system. Proceedings of the 26th International Congress on Sound and Vibration; Montréal, Canada, 7–11 July 2019.

32. Scislo, L. Quality Assurance and Control of Steel Blade Production Using Full Non-Contact Frequency Response Analysis and 3D Laser Doppler Scanning Vibrometry System. Proceedings of the 2021 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS); Cracow, Poland, 22–25 September 2021; pp. 419-423. [DOI: https://dx.doi.org/10.1109/idaacs53288.2021.9661060]

33. Di Lorenzo, E.; Mastrodicasa, D.; Wittevrongel, L.; Lava, P.; Peeters, B. Full-field modal analysis by using digital image correlation technique, Rotating Machinery. Opt. Methods Scanning LDV Methods; 2020; 6, pp. 119-130.

34. Shen, C.; Xin, F.; Lu, T. Theoretical model for sound transmission through finite sandwich structures with corrugated core. Int. J. Non-Linear Mech.; 2012; 47, pp. 1066-1072. [DOI: https://dx.doi.org/10.1016/j.ijnonlinmec.2011.09.014]

35. Fu, T.; Chen, Z.; Yu, H.; Wang, Z.; Liu, X. An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material. Compos. Part B Eng.; 2018; 151, pp. 161-172. [DOI: https://dx.doi.org/10.1016/j.compositesb.2018.06.010]

36. Bartolozzi, G.; Pierini, M.; Orrenius, U.; Baldanzini, N. An equivalent material formulation for sinusoidal corrugated cores of structural sandwich panels. Compos. Struct.; 2013; 100, pp. 173-185. [DOI: https://dx.doi.org/10.1016/j.compstruct.2012.12.042]

37. Tang, Y.; He, W.; Xin, F.; Lu, T.J. Nonlinear sound absorption of ultralight hybrid-cored sandwich panels. Mech. Syst. Signal Process.; 2019; 135, 106428. [DOI: https://dx.doi.org/10.1016/j.ymssp.2019.106428]

38. Wang, D.-W.; Wen, Z.-H.; Glorieux, C.; Ma, L. Sound absorption of face-centered cubic sandwich structure with micro-perforations. Mater. Des.; 2019; 186, 108344. [DOI: https://dx.doi.org/10.1016/j.matdes.2019.108344]

39. Shahsavari, H.; Kornokar, M.; Talebitooti, R.; Daneshjou, K. The study of sound transmission through sandwich cylindrical shells with circumferentially corrugated cores filled with porous materials. Compos. Struct.; 2022; 291, 115608. [DOI: https://dx.doi.org/10.1016/j.compstruct.2022.115608]

40. Jin, Y.; Yang, Y.; Wen, Z.; He, L.; Cang, Y.; Yang, B.; Djafari-Rouhani, B.; Li, Y.; Li, Y. Lightweight sound-absorbing metastructures with perforated fish-belly panels. Int. J. Mech. Sci.; 2022; 226, 107396. [DOI: https://dx.doi.org/10.1016/j.ijmecsci.2022.107396]

41. Luo, Z.; Li, T.; Yan, Y.; Zhou, Z.; Zha, G. Prediction of sound insulation performance of aramid honeycomb sandwich panel based on arti-ficial neural network. Appl. Acous.; 2022; 190, 108656. [DOI: https://dx.doi.org/10.1016/j.apacoust.2022.108656]

42. Zhao, T.; Jiang, Y.; Zhu, Y.; Wan, Z.; Xiao, D.; Li, Y.; Li, H.; Wu, C.; Fang, D. An experimental investigation on low-velocity impact response of a novel corrugated sandwiched composite structure. Compos. Struct.; 2020; 252, 112676. [DOI: https://dx.doi.org/10.1016/j.compstruct.2020.112676]

43. Wang, X.; Li, X.; Yu, R.-P.; Ren, J.-W.; Zhang, Q.-C.; Zhao, Z.-Y.; Ni, C.-Y.; Han, B.; Lu, T.J. Enhanced vibration and damping characteristics of novel corrugated sandwich panels with polyurea-metal laminate face sheets. Compos. Struct.; 2020; 251, 112591. [DOI: https://dx.doi.org/10.1016/j.compstruct.2020.112591]

44. Guillaume, P.; Verboven, P.; Vanlanduit, S.; Auweraer, H.V.D.; Peeters, B. A poly-reference implementation of the least-squares complex frequency-domain estimator. Proceedings of IMAC: A Conference & Exposition on Structural Dynamics, Society for Experimental Mechanics; Kissimmee, FL, USA, 3–6 February 2003.

45. Crocker, M.J.; Raju, P.K.; Forssen, B. Measurement of Transmission Loss of Panels by the Direct Determination of Transmitted Acoustic Intensity. Noise Control Eng.; 1981; 17, 6. [DOI: https://dx.doi.org/10.3397/1.2832181]

46. Cops, A.; Minten, M. Comparative Study Between the Sound Intensity Method and the Conventional Two-Room Method to Calculate the Sound Transmission Loss of Wall Construction. Noise Control Eng. J.; 1984; 22, 104. [DOI: https://dx.doi.org/10.3397/1.2827632]

47. Bies, D.A.; Hansen, C.; Howard, C. Engineering Noise Control; 5th ed. CRC Press: Boca Raton, FL, USA, 2017.

48. Ji, H.; Han, B.; Cheng, L.; Inman, D.J.; Qiu, J. Frequency attenuation band with low vibration transmission in a finite-size plate strip embedded with 2D acoustic black holes. Mech. Syst. Signal Process.; 2021; 163, 108149. [DOI: https://dx.doi.org/10.1016/j.ymssp.2021.108149]

49. Gibson, R.F. Principles of Composite Material Mechanics; 4th ed. CRC Press: Boca Raton, FL, USA, 2016.