# Experimental and Numerical Investigation of Acoustic Performance for Full-Sized SPS

Authors: Yu Gao; Kun Liu; Wenan Jiang; Yubin Fang
Journal: Shock and Vibration
 (2022)

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## Abstract

The sound insulation of a sandwich plate system (SPS) was measured by the sound pressure method in fixed support boundary conditions and reverberation sound field. The results were compared with those obtained using the finite element method. The sound insulation curves obtained via experiments and numerical simulation were observed to be in agreement. This indicates that the numerical simulation method can effectively reflect the sound insulation performance of the structure. In addition, the influence of different parameters on the sound insulation performance of the structure was evaluated using the finite element method, and the weight of each parameter in the influence of sound insulation was ranked by applying the function of “fsrftest” in the software MATLAB. It was found that in the low-frequency domain, the length-to-width ratio of the SPS had the most significant effect on the sound insulation performance of the structure, and the mass ratio of the panel to core exerted the least influence on it. Furthermore, in the medium- and high-frequency domain, the main factors affecting the sound insulation were different in the different frequency ranges, and the frequency range should be considered during the design of the structure. The results can provide technical support for the analysis of the sound insulation performance of SPSs.


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## Body

## 1. Introduction

With the rapid development of aerospace, shipping, transportation, and other industries, the physical and mental health of staff and the requirements of tourists with regard to the comfort experienced while operating equipment has attracted attention [1–3]. Moreover, the comfort level of the working and living environment has become the focus of designers in various industries. As a result, noise reduction technology has become a research hotspot in the fields of shipping, aerospace, and transportation in recent years [4, 5]. As a laminated plate, the SPS has excellent designability and advantages, such as small weight, good sound absorption, anti-vibration performance, convenient processing, and a wide application range [6–10]. It has been widely used in various types of equipment such as ships, aircraft, and high-speed rail [11–15]. Therefore, the acoustic characteristics of SPS are of high significance to the noise reduction design of equipment.In recent decades, lots of researches have been carried out to study the sound insulation performance of laminated plates [16–20]. In the experimental studies, the single cantilever beam vibration test and the standing wave tube method were used to measure the sound insulation performance of the co-cured sandwich composite, which was inserted with special damping material between the lamina [21]. The results showed that the novel damping polymer enhances the damping characteristic and sound insulation performance of laminates significantly. In the field of lightweight sound insulation, graphene oxide was used as the filler to prepare a new type of composite material. After deriving the sound insulation property by the four-channel impedance tube system, it was found that the sound insulation property of the new structure is increased, especially in the low-frequency range [22]. In addition to filling new materials, a new kind of core named face-centered cubic core was also proposed, which demonstrated excellent broadband sound insulation as well as great mechanical property by comparing with the composite quadrilateral honeycomb sandwich structure [23]. To guide the design of real practice for the composite sandwich panels, Huang et al. [24] conducted a quantitative comparison of over ten widely-adopted models and verified the applicability and accuracy of the models in different scenarios, showing the large differences in the sound insulation performance between different finite panel models. In the theoretical studies, the new method based on the space harmonic series and Biot theory [25], the sound velocity potential method [26], and the shear deformation shallow shell method [27] was used to study the sound insulation performance with infinite sandwich panels and compared the results with those in the existing literature to verify the accuracy and reliability of the theoretical model. Based on Kirchhoff’s theory for the elastic faces and Mindlin theory for the core, Assaf et al. [28] and Fu et al. [29] established an analytical model of the sound insulation capacity of a composite laminate plate subjected to plane acoustic excitation and analyzed its sound insulation performance. The feasibility of this method was verified by comparing the test results. Talebitooti et al. [30] carried out an acoustic analysis of a double-curved composite shell with four sides simply-supported constraints, based on the third-order shear deformation theory. The researchers focused on the boundary effect on the structural sound transmission loss and compared the results with those of the infinite shell. Finally, the effects of the transverse displacement configuration and shell size on the structural sound transmission loss were discussed. Based on the research, a new approach was made to consider the number of modes for the finite composite structure treated with a porous material.The above description reveals that the current research on the sound insulation performance of composite laminates addresses structures with panels of small or infinite size under simply-supported constraints and plane acoustic excitation. The structures of all types of equipment are finite in size and subjected to surrounding fixed-support boundary conditions and a reverberant sound field. Therefore, it is essential to conduct acoustic tests on full-sized models to investigate their sound insulation performance when subjected to a surrounding fixed constraint and reverberant sound field.In this study, the sound insulation performance of a full-sized SPS was investigated experimentally in the fixed support boundary conditions and the reverberation sound field. In addition, numerical simulation analysis was carried out. The results show that the numerical calculation results are in good agreement with the experimental results. Moreover, the influence of the geometry and material parameters of the SPS on the sound insulation performance was studied by parameterization and weight analysis.


## 2. Acoustic Test

### 2.1. Test Specimens

The SPS specimen investigated in this paper is spliced by four small panels, as shown in Figure1. The size of two SPSs is 902 w × 2700 (h) × 26 (t) mm3 and the other two is 1032 w × 2700 (h) × 26 (t) mm3. The overall size of the SPS is 3868 w × 2700 (h) × 26 (t) mm3. The top and bottom panels of the four SPSs are made of steel and have a thickness of 4 mm. The core layer is made of polyurethane and has a thickness of 18 mm. The mechanical parameters of the two materials are shown in Table 1. It is worth emphasizing that the internal structure of SPS was firstly designed, which consists of the polypropylene glycol, diphenylmethane, diisocyanate, curing agent, organotin, and the other raw materials which was used to cast the polyurethane core material with the density is ρ=1200 kg/m3.Figure 1
The layout diagram of SPSs: (a) the structural type of SPS; and (b) the geometric parameters.
(a)(b)Table 1
Material parameters of SPS.
SPSDensity (kg∙m−3)Elasticity modulus (GPa)Poisson ratioThe panel78502100.3The core12001.00.44During specimen preparation, the materials for the panel and core layer are first cut to the required size. Then, the surface is pretreated for better connection between the panel and the core layer. Second, the adhesive connections are made between the panel and the core layer. Furthermore, holes are drilled in the four small SPSs along their edges for connecting these SPSs to obtain a large-size SPS (see Figures2(a) and 2(b)). They are connected by built-in square pipes, the joints are fixed with bolts, and the lap gap is sealed with silica gel. The assembled specimen is shown in Figures 2(c) and 2(d).Figure 2
The adhesive and boundary holes of SPS: (a) the adhesive; (b) the holes at the boundary; (c) SPS built-in square pipe connection; and (d) square pipe connection diagram.
(a)(b)(c)(d)


### 2.2. Test Setup

The acoustic laboratory consists of a sound source room, a receiving room, and a test hole. The sound source room and receiving room are completely separated structurally, both rooms are equipped with echo elimination devices to create a reverberant sound field inside. The size of the test hole can be varied by stacking solid bricks and cement. The test specimen is sealed with cement. The external and internal structure diagrams of the laboratory are shown in Figures3(a), 3(b), and 3(c), respectively. The size of the sound source room is 5400 (L) × 4500 w × 3300 (H) mm3, the size of the receiving room is 4800 (L) × 4350 w × 3250 (H) mm3, and the size of the test hole is 4100 w × 3100 (H) mm2, the height of its lower edge from the ground is 500 mm.Figure 3
The laboratory: (a) external structure of the laboratory; (b) sound source room and specimen assembly drawing; (c) receiving room and specimen assembly drawing; (d) layout of measurement points in sound source room; (e) layout of measurement points in receiving room; and (f) placement of sound source.According to ISO 10140-1 [31] and ISO 10140-2 [32], six measurement points are arranged in both the sound source room and receiving room. Two standard sound sources are installed in the sound source room. The measurement points and sound source are arranged in the field as shown in Figures 3(d), 3(e), 3(f), and 4. Here, S1 and S2 are the locations of the sound sources, and L1 to L6 are those of the measurement points. The floor corner of the sound sources room and receiving room is used as the origin of coordinates. Standing on the ground plane perpendicular to the direction of the specimen as the X-axis positive direction, parallel to the specimen as the Y-axis positive direction, and vertically in the ground direction as the Z-axis positive direction. The position direction of X, Y, Z conforms to the right-hand screw rule. The coordinates of each measurement point and sound source location are listed in Table 2.Figure 4
Diagram of laboratory, the layout of sound sources, and measurement points.Table 2
Coordinates of measurement points and sound source locations.
ChamberPositionX (mm)Y (mm)Z (mm)Sound source roomS1410031001400S2400012001700L1130031801300L2214026001300L3182012001300L4320021701300L534607601300L6350034001300Receiving roomL1115033901300L2254030401300L3150024001300L413009701300L5260012901300L6220033001300


### 2.3. Test Procedures

The impedance tube method (standing wave tube method), the sound pressure method, and the sound intensity method are the three commonly used airborne sound insulation test methods. For the sound insulation test of the impedance tube, the test specimen area is very small (i.e., usually under 0.2 square meters); while for the sound pressure method and the sound intensity method, the test specimens are mainly large structures (i.e., the test specimen area is several square meters). The sound insulation test principle of the sound pressure method is as follows: the specimen is installed in the hole between the two test rooms, the sound source room and the receiving room. The reverberation sound field is generated in the sound source room, which is randomly incident to the surface of the specimen, and the sound pressure through the specimen is received and measured in the receiving room. And then, the sound insulation of the specimen is calculated by measuring the sound pressure of the microphones in both the rooms. However, the sound insulation test principle of the sound intensity method is that: the layout and installation of the sound source room and the receiving room are the same as those of the sound pressure method. The sound insulation of the specimen is obtained by measuring the sound pressure of the microphone in the sound source room and the sound intensity of the receiving room.Based on the existing test conditions, the sound insulation of the SPS is measured by the sound pressure method. One 12-body omnidirectional sound source OS 003 (cooperating with the echo cancellation devices in the sounding room and the receiving room to form a reverberation sound field) and two microphones are placed inside the reverberation room, two microphones are installed in the receiving room, the sound pressure of the reverberation sound field is 1 N/m2. And the test specimen is the SPS prepared in Section 2.1. It is sealed with high-acoustic-insulation sand mud and buried in the test hole. The gap between the specimen and hole is sealed with acoustic insulation rock wool, and all gaps were sealed with acoustic insulation sealant during the field assembly. The layout of the overall acoustic test is shown in Figures 3(b) and 3(c). The test temperature is maintained at 12°C. The relative humidity and atmospheric pressure are 55% and 0.1 MPa, respectively. Furthermore, the speed of sound is c=340.3 m/s, and the density is ρ=1.225 kg/m3.The sound pressure of the SPS is tested in the frequency range 100 Hz–3150 Hz(contains the following 16 center frequency points: 100 Hz, 125 Hz, 160 Hz, 200 Hz, 250 Hz, 315 Hz, 400 Hz, 500 Hz, 630 Hz, 800 Hz, 1000 Hz, 1250 Hz, 1600 Hz, 2000 Hz, 2500 Hz, and 3150 Hz) in accordance with the requirements of the IMO MSC 337 (91) [33] and ISO 10140-2 [32]. During the test, in stage I, the equipment is connected and the parameters are adjusted, then, the microphone MPA 201 is calibrated through the CAL 200 acoustic calibrator, and then, the multi-channel digital vibration and noise analysis system DH 5922 N are connected together after completion. In stage II, the background noise is tested to ensure that the test results of the receiving room are not affected by the intrusion sound, and then, the experimental sound pressure level test is carried out. To ensure that a steady-state continuous sound spectrum can be generated within the measured frequency range (i.e., the sound pressure level data of 12 measuring points), the sound sources are placed at the S1 and S2 positions, respectively, and the power amplifier SWA 100 is connected, as shown in Figure 5. In stage III, after the test is completed, data processing is performed according to ISO 717-1 [34] to obtain the sound insulation test curve of the SPS. It is noted that the detailed information of various instruments and equipment is shown in Table 3, and the schematic diagram of the sound pressure method test is shown in Figure 6.Figure 5
Vibration and noise analysis system.Table 3
The information of various instruments and equipment.
NameModelBrandMulti-channel digital vibration and noise analysis systemDH 5922 NJiangsu DonghuaPower amplifierSWA 100Jiangsu Donghua12-body omnidirectional sound sourceOS 003Jiangsu DonghuaMicrophoneMPA 201Beijing Sheng Wang Acoustic (BSWA)Acoustic calibratorCAL 200BSWAFigure 6
Sound pressure test block diagram.


## 2.1. Test Specimens

The SPS specimen investigated in this paper is spliced by four small panels, as shown in Figure1. The size of two SPSs is 902 w × 2700 (h) × 26 (t) mm3 and the other two is 1032 w × 2700 (h) × 26 (t) mm3. The overall size of the SPS is 3868 w × 2700 (h) × 26 (t) mm3. The top and bottom panels of the four SPSs are made of steel and have a thickness of 4 mm. The core layer is made of polyurethane and has a thickness of 18 mm. The mechanical parameters of the two materials are shown in Table 1. It is worth emphasizing that the internal structure of SPS was firstly designed, which consists of the polypropylene glycol, diphenylmethane, diisocyanate, curing agent, organotin, and the other raw materials which was used to cast the polyurethane core material with the density is ρ=1200 kg/m3.Figure 1
The layout diagram of SPSs: (a) the structural type of SPS; and (b) the geometric parameters.
(a)(b)Table 1
Material parameters of SPS.
SPSDensity (kg∙m−3)Elasticity modulus (GPa)Poisson ratioThe panel78502100.3The core12001.00.44During specimen preparation, the materials for the panel and core layer are first cut to the required size. Then, the surface is pretreated for better connection between the panel and the core layer. Second, the adhesive connections are made between the panel and the core layer. Furthermore, holes are drilled in the four small SPSs along their edges for connecting these SPSs to obtain a large-size SPS (see Figures2(a) and 2(b)). They are connected by built-in square pipes, the joints are fixed with bolts, and the lap gap is sealed with silica gel. The assembled specimen is shown in Figures 2(c) and 2(d).Figure 2
The adhesive and boundary holes of SPS: (a) the adhesive; (b) the holes at the boundary; (c) SPS built-in square pipe connection; and (d) square pipe connection diagram.
(a)(b)(c)(d)


## 2.2. Test Setup

The acoustic laboratory consists of a sound source room, a receiving room, and a test hole. The sound source room and receiving room are completely separated structurally, both rooms are equipped with echo elimination devices to create a reverberant sound field inside. The size of the test hole can be varied by stacking solid bricks and cement. The test specimen is sealed with cement. The external and internal structure diagrams of the laboratory are shown in Figures3(a), 3(b), and 3(c), respectively. The size of the sound source room is 5400 (L) × 4500 w × 3300 (H) mm3, the size of the receiving room is 4800 (L) × 4350 w × 3250 (H) mm3, and the size of the test hole is 4100 w × 3100 (H) mm2, the height of its lower edge from the ground is 500 mm.Figure 3
The laboratory: (a) external structure of the laboratory; (b) sound source room and specimen assembly drawing; (c) receiving room and specimen assembly drawing; (d) layout of measurement points in sound source room; (e) layout of measurement points in receiving room; and (f) placement of sound source.According to ISO 10140-1 [31] and ISO 10140-2 [32], six measurement points are arranged in both the sound source room and receiving room. Two standard sound sources are installed in the sound source room. The measurement points and sound source are arranged in the field as shown in Figures 3(d), 3(e), 3(f), and 4. Here, S1 and S2 are the locations of the sound sources, and L1 to L6 are those of the measurement points. The floor corner of the sound sources room and receiving room is used as the origin of coordinates. Standing on the ground plane perpendicular to the direction of the specimen as the X-axis positive direction, parallel to the specimen as the Y-axis positive direction, and vertically in the ground direction as the Z-axis positive direction. The position direction of X, Y, Z conforms to the right-hand screw rule. The coordinates of each measurement point and sound source location are listed in Table 2.Figure 4
Diagram of laboratory, the layout of sound sources, and measurement points.Table 2
Coordinates of measurement points and sound source locations.
ChamberPositionX (mm)Y (mm)Z (mm)Sound source roomS1410031001400S2400012001700L1130031801300L2214026001300L3182012001300L4320021701300L534607601300L6350034001300Receiving roomL1115033901300L2254030401300L3150024001300L413009701300L5260012901300L6220033001300


## 2.3. Test Procedures

The impedance tube method (standing wave tube method), the sound pressure method, and the sound intensity method are the three commonly used airborne sound insulation test methods. For the sound insulation test of the impedance tube, the test specimen area is very small (i.e., usually under 0.2 square meters); while for the sound pressure method and the sound intensity method, the test specimens are mainly large structures (i.e., the test specimen area is several square meters). The sound insulation test principle of the sound pressure method is as follows: the specimen is installed in the hole between the two test rooms, the sound source room and the receiving room. The reverberation sound field is generated in the sound source room, which is randomly incident to the surface of the specimen, and the sound pressure through the specimen is received and measured in the receiving room. And then, the sound insulation of the specimen is calculated by measuring the sound pressure of the microphones in both the rooms. However, the sound insulation test principle of the sound intensity method is that: the layout and installation of the sound source room and the receiving room are the same as those of the sound pressure method. The sound insulation of the specimen is obtained by measuring the sound pressure of the microphone in the sound source room and the sound intensity of the receiving room.Based on the existing test conditions, the sound insulation of the SPS is measured by the sound pressure method. One 12-body omnidirectional sound source OS 003 (cooperating with the echo cancellation devices in the sounding room and the receiving room to form a reverberation sound field) and two microphones are placed inside the reverberation room, two microphones are installed in the receiving room, the sound pressure of the reverberation sound field is 1 N/m2. And the test specimen is the SPS prepared in Section 2.1. It is sealed with high-acoustic-insulation sand mud and buried in the test hole. The gap between the specimen and hole is sealed with acoustic insulation rock wool, and all gaps were sealed with acoustic insulation sealant during the field assembly. The layout of the overall acoustic test is shown in Figures 3(b) and 3(c). The test temperature is maintained at 12°C. The relative humidity and atmospheric pressure are 55% and 0.1 MPa, respectively. Furthermore, the speed of sound is c=340.3 m/s, and the density is ρ=1.225 kg/m3.The sound pressure of the SPS is tested in the frequency range 100 Hz–3150 Hz(contains the following 16 center frequency points: 100 Hz, 125 Hz, 160 Hz, 200 Hz, 250 Hz, 315 Hz, 400 Hz, 500 Hz, 630 Hz, 800 Hz, 1000 Hz, 1250 Hz, 1600 Hz, 2000 Hz, 2500 Hz, and 3150 Hz) in accordance with the requirements of the IMO MSC 337 (91) [33] and ISO 10140-2 [32]. During the test, in stage I, the equipment is connected and the parameters are adjusted, then, the microphone MPA 201 is calibrated through the CAL 200 acoustic calibrator, and then, the multi-channel digital vibration and noise analysis system DH 5922 N are connected together after completion. In stage II, the background noise is tested to ensure that the test results of the receiving room are not affected by the intrusion sound, and then, the experimental sound pressure level test is carried out. To ensure that a steady-state continuous sound spectrum can be generated within the measured frequency range (i.e., the sound pressure level data of 12 measuring points), the sound sources are placed at the S1 and S2 positions, respectively, and the power amplifier SWA 100 is connected, as shown in Figure 5. In stage III, after the test is completed, data processing is performed according to ISO 717-1 [34] to obtain the sound insulation test curve of the SPS. It is noted that the detailed information of various instruments and equipment is shown in Table 3, and the schematic diagram of the sound pressure method test is shown in Figure 6.Figure 5
Vibration and noise analysis system.Table 3
The information of various instruments and equipment.
NameModelBrandMulti-channel digital vibration and noise analysis systemDH 5922 NJiangsu DonghuaPower amplifierSWA 100Jiangsu Donghua12-body omnidirectional sound sourceOS 003Jiangsu DonghuaMicrophoneMPA 201Beijing Sheng Wang Acoustic (BSWA)Acoustic calibratorCAL 200BSWAFigure 6
Sound pressure test block diagram.


## 3. Numerical Simulation Analysis

### 3.1. The Finite Element Models

Finite element analysis is performed on the sound insulation performance of the SPS. The calculations are performed in the finite element software program LMS Virtual Lab, which is divided into three parts: building the calculation model, solving and calculating, and post-processing.Firstly, in order to reduce the complexity of the simulations when building the model, the geometry is a whole plate in the numerical simulation that is equivalent to the SPS specimen assembled in the test (see Figure7(a)). The perimeter of the specimen is treated with high-acoustic-insulation mortar, acoustic rock wool, and acoustic sealant between the specimen and hole during the test, which can predict the sound insulation performance of the SPS accurately. To simulate the boundary constraints of the specimen, the SPS is subjected to fixed support boundary conditions in LMS Virtual Lab, other physical quantities such as material properties are set consistent with the test.Figure 7
The finite element models: (a) the simulation model of SPS; and (b) the element models of sounding room, receiving room, and the positions of measuring points.
(a)(b)Secondly, the tetrahedral mesh is used to discretize the SPS, sound source room and receiving chamber. According to the requirements of the acoustic mesh in the fluid model analysis of the Virtual Lab Acoustic module are as follows [35]:(1)L≤c6fmax,where, L is the element mesh length, c is the speed of sound in the fluid medium, and fmax is the maximum calculation frequency of the model. The maximum calculation frequency of the simulation is 3150 Hz in the present work. According to formula (1), the maximum size of the acoustic mesh should not be greater than 17.9 mm. In order to improve the calculation efficiency and to ensure the calculation accuracy, the mesh size is selected as 17 mm [36]. The number of nodes is 62355, and the number of meshes is 314399. The schematic diagram of the entire finite element model is as shown in Figure 7(b).Finally, in order to simulate the sounding room and the receiving room in the test, the sound insulation of the SPS was calculated by the software LMS Virtual Lab. In stage I, the model (i.e., Figure7(b)) is imported into the acoustic finite element module. In stage II, the parameter settings are defined, such as structural and fluid materials, mesh properties, boundary constraints, AML properties, and reverberation sound sources. In stage III, the direct acoustic-vibration coupling method is used to solve the problem, and the sound insulation frequency characteristic curve can be obtained by post-processing the calculation results.


## 3.1. The Finite Element Models

Finite element analysis is performed on the sound insulation performance of the SPS. The calculations are performed in the finite element software program LMS Virtual Lab, which is divided into three parts: building the calculation model, solving and calculating, and post-processing.Firstly, in order to reduce the complexity of the simulations when building the model, the geometry is a whole plate in the numerical simulation that is equivalent to the SPS specimen assembled in the test (see Figure7(a)). The perimeter of the specimen is treated with high-acoustic-insulation mortar, acoustic rock wool, and acoustic sealant between the specimen and hole during the test, which can predict the sound insulation performance of the SPS accurately. To simulate the boundary constraints of the specimen, the SPS is subjected to fixed support boundary conditions in LMS Virtual Lab, other physical quantities such as material properties are set consistent with the test.Figure 7
The finite element models: (a) the simulation model of SPS; and (b) the element models of sounding room, receiving room, and the positions of measuring points.
(a)(b)Secondly, the tetrahedral mesh is used to discretize the SPS, sound source room and receiving chamber. According to the requirements of the acoustic mesh in the fluid model analysis of the Virtual Lab Acoustic module are as follows [35]:(1)L≤c6fmax,where, L is the element mesh length, c is the speed of sound in the fluid medium, and fmax is the maximum calculation frequency of the model. The maximum calculation frequency of the simulation is 3150 Hz in the present work. According to formula (1), the maximum size of the acoustic mesh should not be greater than 17.9 mm. In order to improve the calculation efficiency and to ensure the calculation accuracy, the mesh size is selected as 17 mm [36]. The number of nodes is 62355, and the number of meshes is 314399. The schematic diagram of the entire finite element model is as shown in Figure 7(b).Finally, in order to simulate the sounding room and the receiving room in the test, the sound insulation of the SPS was calculated by the software LMS Virtual Lab. In stage I, the model (i.e., Figure7(b)) is imported into the acoustic finite element module. In stage II, the parameter settings are defined, such as structural and fluid materials, mesh properties, boundary constraints, AML properties, and reverberation sound sources. In stage III, the direct acoustic-vibration coupling method is used to solve the problem, and the sound insulation frequency characteristic curve can be obtained by post-processing the calculation results.


## 4. Results and Comparisons

The sound insulation performance of the SPS with the sound pressure of the reverberation sound field is 1 N/m2, frequency range of 100 Hz–3150 Hz, and step size of 1/3 octave is studied experimentally and numerically. The sound insulation curves obtained thereby are compared in Figure 8.Figure 8
Comparison of sound insulation curves of SPS obtained through test and simulation.Figure8 reveals that the troughs of the curves are located near the natural frequency of the structure. This is because resonance phenomenon is generated when the frequency of the sound source is close to the natural frequency of the structure, it increases the transmittance of sound waves and thereby causing the sound insulation performance of the structure to deteriorate. Simultaneously, a trough is generated in the sound insulation curve, where the sound insulation becomes smaller. The sound insulation performance is the worst near the first-order natural frequency of the structure of 250 Hz. This is because when the frequency of the sound wave is consistent with the first-order natural frequency of the SPS, which produces the largest resonance response, makes the power of the transmitted sound wave increase sharply, thus, the sound insulation performance of the structure near the first-order natural frequency is the worst. Moreover, with the increase of the natural frequency order, the sound insulation trough moves up, indicating that with the increase of the natural frequency order, the resonance response of the structure gradually weakens, the power of transmitted sound wave gradually decreases.It can be concluded from the comparative analysis of the sound insulation curves obtained by the test and numerical simulation (in Figure8) that within the calculated frequency range of 100 Hz–3150 Hz, the sound insulation troughs of the curves occur at the frequencies of 250 Hz and 630 Hz. These frequencies are close to the natural frequencies of the structure, such as 251.34 Hz and 633.81 Hz. At 250 Hz, the test and simulation values are 8.2 dB and 7.58 dB, respectively, and the sound insulation error is 7.56%. At 630 Hz, the test and simulation values are 17.80 dB and 17.07 dB, respectively, and the sound insulation error is 4.10%. Furthermore, the maximum error of sound insulation in the entire calculated frequency range is 12.23% (<15%).From the above analysis, it can be seen that the test and simulation results are in good agreement, irrespective of the size of the sound insulation, the position of the sound insulation valley, or the change trend of the sound insulation curve. This shows that the numerical simulation method can be used to analyze the sound insulation performance of the structure effectively.


## 5. Parameter Analysis

In this part, the influence of the ratio of panel mass to core mass, panel size, core thickness, and core material on the sound insulation performance of the SPS is studied by the finite element acoustic software LMS Virtual Lab, on the basis of calculating the natural frequency and modal characteristics of the structure. And for the convenience of research, the size of the SPS in this part is 500 × 500 × 15 mm3. The specific form and parameters are shown in Table 4. The mechanical parameters of the materials are identical to those in Table 1. The sound source is vertically incident by the plane wave, the sound pressure of the sound field is 1 N/m2, the calculated frequency range is 100 Hz–3150 Hz, and the step length is 1/3 octave. The description of the legend in the figure is shown in Table 5.Table 4
Structural forms and parameters of SPS.
Structural formStructural parametersTop and bottom panel:Length × width: 0.5 m × 0.5 mThickness: 1.5 mmCore materials:Thickness: 12 mmTotal structural mass: 9.4875 kgTable 5
Legend description.
Parameter abbreviationParameter full nameMPCMass ratios of panel-to-core layerLWRatio of length-to-widthPTPanel thicknessCTCore layer thicknessCMCore layer material


### 5.1. Mass Ratio of SPS

According to the existing research [37–39], the sound insulation performance of the sandwich panel structure is affected by its structural parameters, and the sound insulation performance can be affected by changing the mass of the sandwich panel. However, for a sandwich panel of the same quality, if the ratio of panel mass to core mass is different, the sound insulation properties may also be affected.Based on the above reduced structural size of SPS, the overall structural mass, length, and width of the SPS are maintained constant, whereas, the thickness of the panel and core are varied. Numerical simulation analysis is conducted on the sound insulation performance of SPSs with panel-to-core layer mass ratios of 1, 1.64 (original model), and 2. The calculation results are shown in Figure9.Figure 9
Influence of different panel-to-core layer mass ratios on sound insulation curve of SPS.It is evident from Figure9 that under the condition of equal mass, the sound insulation trough of the structure shifts toward the lower frequencies with the increase in the panel-to-core layer mass ratio. Furthermore, the trend becomes apparent gradually. The density of the sound insulation trough of the sound insulation curve increases gradually, and the change is obvious. This is because the natural frequency of the SPS decreases with the increase in the panel-to-core layer mass ratio, and the resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) increases gradually. Thus, the higher the panel-to-core layer mass ratio, the higher is the density of the sound insulation trough of the sound insulation curve of the structure.In the middle- and high-frequency range of 1500 Hz–3150 Hz, the sound insulation of the structure is minimum when the panel-to-core layer mass ratio is 2, maximum when it is 1.64, and in the middle position when it is 1. Therefore, it is necessary to determine the optimal panel-to-core layer mass ratio to optimize the sound insulation performance of the structure.


### 5.2. Length-to-Width Ratio of SPS

In addition to the ratio of panel mass to core mass, other structural parameters of the SPS will also affect its sound insulation characteristics.Based on the above structural size of the SPS and with the width of the structure maintained at 500 mm, the sound insulation performance of SPSs with lengths of 500 mm, 1000 mm, and 1500 mm, that is, the length-to-width ratio of 1, 2, and 3 are analyzed by numerical simulation method. The calculation results are shown in Figure10.Figure 10
Influence of length-to-width ratio on sound insulation curve of SPS.The structure does not display the coincidence effect under the action of a plane wave source with vertical incident. Figure10 reveals that the sound insulation curve of the SPS in the frequency range of 100 Hz–3150 Hz consists of the stiffness control area and resonance control area. In the stiffness control area, the structural sound insulation decreases with the increase of sound frequency. In the resonance control area, the sound insulation of the SPS sandwich plate is affected mainly by its natural frequency and the structural mode. The frequencies corresponding to the troughs of the sound insulation curve are located near the natural frequencies of the structure. This is because the structural resonance near the natural frequencies of each order causes an abrupt increase in the transmission sound wave. Thereby, the sound insulation performance of the structure is minimum here, which results in the sound insulation trough.The calculation curve in Figure10 shows that when the width of the structure remains constant, the natural frequency of the structure decreases with the increase in the length of the panel, and the sound insulation trough of the sound insulation curve gradually shifts towards lower frequencies. As the length of the panel increases, the acoustic valley density of the sound insulation curve increases gradually. This is because the natural frequency of the structure decreases with the increase in the length of the panel, and the resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) increases gradually. Therefore, there is an increase in the density of the acoustic valley of the sound insulation curve of the structure with the increase in the length-to-width ratio.In the calculated frequency range, the sound insulation curve of the structure shifts downward with the increase in the length-to-width ratio of the panel, the sound insulation decreases gradually, the frequency range of the sound insulation trough is narrowed, and the sound insulation performance deteriorates.


### 5.3. Panel Thickness of SPS

Based on the above structural dimensions of SPSs, the sound insulation performance of SPSs having top and bottom panels with thicknesses of 1.5 mm, 3.5 mm, and 5.5 mm is analyzed by numerical simulation. The core layer thickness is maintained constant at 15 mm. The calculation results are shown in Figure11.Figure 11
Influence of panel thickness on sound insulation curve of SPS.Figure11 shows that the sound insulation trough gradually shifts towards higher frequencies with the increase in the SPS panel thickness. The trend is gradually obvious. This is because the natural frequency of the structure would increase with the increase in the panel thickness when other parameters remain constant. The density of the acoustic valley on the sound insulation curve reduces gradually with the increase in the thickness of the panel. This is because the natural frequencies of SPS increase with the increase in the thickness of the panel. Furthermore, the resonance frequency of the structure reduces gradually within the same frequency range (100 Hz–3150 Hz). Thus, the larger the panel thickness of the structure, the smaller is the density of the acoustic valley of the sound insulation curve.In the calculated frequency range, the structures with the panel thicknesses of 1.5 mm and 5.5 mm display the smallest and the largest sound insulation performance, respectively. That is, the sound insulation curve of the structure shifts upward with the increase in the panel thickness, the sound insulation performance is enhanced, and the trend slows down gradually. Therefore, the sound insulation performance of the structure can be improved by increasing the thickness of the panel appropriately while maintaining the structural weight within the permitted range.


### 5.4. Core Layer Thickness of SPS

Based on the above structural size of SPS, the sound insulation performance of SPSs with core thicknesses of 12 mm, 22 mm, and 32 mm is analyzed by numerical simulation. The panel thickness is constant at 1.5 mm. The calculation results are shown in Figure12.Figure 12
Influence of core thickness on sound insulation curve of SPS.As is evident from Figure12, the structure with the core thickness of 12 mm has the first sound insulation trough near 400 Hz, the minimum sound insulation is 17.78 dB, and the sound insulation is the smallest; The core thickness of 32 mm has the first sound insulation trough near 630 Hz, the minimum sound insulation is 33.03 dB, the sound insulation is the maximum. That is, the sound insulation curve of the structure shifts upward with the increase in the core thickness, the sound insulation performance is enhanced, and the trend slows down gradually.In the calculated frequency range, the sound insulation trough would gradually shift to higher frequencies with the increase in core thickness, and the density of sound insulation trough would decrease gradually. This is because the increase in core thickness results in an increase in the natural frequency of the SPS. Then, the resonance frequency of the structure would decrease gradually in the same frequency range (100 Hz–3150 Hz). Therefore, the larger the core thickness, the smaller is the density of the sound insulation trough of the sound insulation curve.From the above analysis, it can be seen that when designing the sandwich panel structure, the sound insulation performance of the structure can be improved by increasing the core thickness appropriately.


### 5.5. Core Layer Material of SPS

The core material is also an important part that affects the sound insulation properties of the structure. Therefore, polyurethane, aluminum alloy, and a composite material are used as the core materials, and the core thickness is 12 mm. The other structural parameters are consistent with the SPS mentioned above. The material parameters of each core are shown in Table6, and the calculation results are shown in Figure 13.Table 6
Properties of core materials.
Core materialDensity (Kg∙m−3)Elasticity modulus (GPa)Poisson ratioPolyurethane120010.44Aluminum alloy269863.820.35Composite material1900180.15Figure 13
Influence of core material on sound insulation curve of SPS.Figure13 shows that the sound insulation trough of the structure shifts toward higher frequencies with the increase in the elastic-modulus-to-density ratio of the core material, the trend gradually slows down. Furthermore, the density of the sound insulation trough of the sound insulation curve decreases gradually, and the change is significant. This is because the increase in the elastic-modulus-to-density ratio of the material results in the increase in the natural frequency of the SPS. The resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) is reduced gradually. Thus, the higher the ratio of elastic modulus to density of the material, the lower is the density of the sound insulation trough of the structural sound insulation curve.In the middle and high frequencies (1500 Hz–3150 Hz) of the calculated frequency range, the elastic-modulus-to-density ratio and sound insulation are minimum when the core material of the structure is polyurethane and maximum when it is aluminum. That is, in the medium- and high-frequency parts, the sound insulation curve of the structure shifts upward with the increase in the ratio of elastic modulus to density, the sound insulation trough frequency range is widened, and the sound insulation performance is improved significantly.In summary, it can be concluded that the influence of the core material should be considered when designing SPS, and appropriate materials should be selected.


### 5.6. Parameter Weights Analysis

The above part discusses the influence of different parameters on the sound insulation of the structure, and further research of the weight of each parameter in the influence of the sound insulation has the most significance for the design and application of the structure in practical engineering. The “fsrftest” function in the software MATLAB is applied in this part to obtain the univariate feature ranking for regression using F-tests. It is a test that the statistics follows theF-distribution under the null hypothesis, and is usually used to analyze statistical models that use more than one parameter to determine whether all or some of the parameters in the model are suitable for estimating the parent. The calculation results are shown in Figures 14 and 15.Figure 14
The weight of each parameter in the low-frequency domain of (a) 100 Hz; (b) 630 Hz; and (c) 1000 Hz.
(a)(b)(c)Figure 15
The weight of each parameter in the medium- and high-frequency domain of (a) 2000 Hz; (b) 2500 Hz; and (c) 3150 Hz.
(a)(b)(c)In the low-frequency range of 100 Hz–1500 Hz, three central frequency points of 100 Hz, 630 Hz, and 1000 Hz are taken, and the weights of the mass ratio of panel-to-core layer, geometric size of the panel, core thickness, and core material parameters in the influence of the sound insulation of the structure are calculated as shown in Figure14.From the analysis of Figure14, it can be seen that in the low-frequency range, the length-to-width ratio of SPS has the largest weight in the sound insulation of the structure, which is the main factor affecting; the mass ratio of panel-to-core layer has the smallest weight, and the least impact on the sound insulation. This is because in the low-frequency domain, the sound insulation of the structure is mainly affected by the stiffness, and the length-to-width ratio of SPS is the main factor affecting the stiffness of the structure. Therefore, the length-to-width ratio of SPS is the main factor affecting the sound insulation.In the medium- and high-frequency range of 1500 Hz–3150 Hz, three center frequency points of 2000 Hz, 2500 Hz, and 3150 Hz were taken, and the mass ratio of panel-to-core layer, panel geometric size, core thickness, and core material parameters in the influence of the sound insulation of the structure are calculated as shown in Figure15.From the analysis of Figure15, it can be seen that in the medium- and high-frequency domain, the weight of the length-to-width ratio of SPS gradually decreases, which is not the main factor affecting the sound insulation of the structure. Near the frequency of 2000 Hz, the main factor affecting the sound insulation of the structure is the core thickness; near the frequency of 2500 Hz, the mass ratio of panel to core is the main factor affecting the sound insulation; and near the frequency of 3150 Hz, the thickness of panel has the largest weight in the influence of the sound insulation, which is the main factor in the sound insulation. And the main factors affecting the sound insulation are different in different frequency range, because the structure is affected by resonance in the medium- and high-frequency domain, and the factors affecting the sound insulation are complex. Therefore, in practical engineering applications, the design should be considered in different frequency ranges to meet the sound insulation requirements of different frequency ranges of the structure.


## 5.1. Mass Ratio of SPS

According to the existing research [37–39], the sound insulation performance of the sandwich panel structure is affected by its structural parameters, and the sound insulation performance can be affected by changing the mass of the sandwich panel. However, for a sandwich panel of the same quality, if the ratio of panel mass to core mass is different, the sound insulation properties may also be affected.Based on the above reduced structural size of SPS, the overall structural mass, length, and width of the SPS are maintained constant, whereas, the thickness of the panel and core are varied. Numerical simulation analysis is conducted on the sound insulation performance of SPSs with panel-to-core layer mass ratios of 1, 1.64 (original model), and 2. The calculation results are shown in Figure9.Figure 9
Influence of different panel-to-core layer mass ratios on sound insulation curve of SPS.It is evident from Figure9 that under the condition of equal mass, the sound insulation trough of the structure shifts toward the lower frequencies with the increase in the panel-to-core layer mass ratio. Furthermore, the trend becomes apparent gradually. The density of the sound insulation trough of the sound insulation curve increases gradually, and the change is obvious. This is because the natural frequency of the SPS decreases with the increase in the panel-to-core layer mass ratio, and the resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) increases gradually. Thus, the higher the panel-to-core layer mass ratio, the higher is the density of the sound insulation trough of the sound insulation curve of the structure.In the middle- and high-frequency range of 1500 Hz–3150 Hz, the sound insulation of the structure is minimum when the panel-to-core layer mass ratio is 2, maximum when it is 1.64, and in the middle position when it is 1. Therefore, it is necessary to determine the optimal panel-to-core layer mass ratio to optimize the sound insulation performance of the structure.


## 5.2. Length-to-Width Ratio of SPS

In addition to the ratio of panel mass to core mass, other structural parameters of the SPS will also affect its sound insulation characteristics.Based on the above structural size of the SPS and with the width of the structure maintained at 500 mm, the sound insulation performance of SPSs with lengths of 500 mm, 1000 mm, and 1500 mm, that is, the length-to-width ratio of 1, 2, and 3 are analyzed by numerical simulation method. The calculation results are shown in Figure10.Figure 10
Influence of length-to-width ratio on sound insulation curve of SPS.The structure does not display the coincidence effect under the action of a plane wave source with vertical incident. Figure10 reveals that the sound insulation curve of the SPS in the frequency range of 100 Hz–3150 Hz consists of the stiffness control area and resonance control area. In the stiffness control area, the structural sound insulation decreases with the increase of sound frequency. In the resonance control area, the sound insulation of the SPS sandwich plate is affected mainly by its natural frequency and the structural mode. The frequencies corresponding to the troughs of the sound insulation curve are located near the natural frequencies of the structure. This is because the structural resonance near the natural frequencies of each order causes an abrupt increase in the transmission sound wave. Thereby, the sound insulation performance of the structure is minimum here, which results in the sound insulation trough.The calculation curve in Figure10 shows that when the width of the structure remains constant, the natural frequency of the structure decreases with the increase in the length of the panel, and the sound insulation trough of the sound insulation curve gradually shifts towards lower frequencies. As the length of the panel increases, the acoustic valley density of the sound insulation curve increases gradually. This is because the natural frequency of the structure decreases with the increase in the length of the panel, and the resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) increases gradually. Therefore, there is an increase in the density of the acoustic valley of the sound insulation curve of the structure with the increase in the length-to-width ratio.In the calculated frequency range, the sound insulation curve of the structure shifts downward with the increase in the length-to-width ratio of the panel, the sound insulation decreases gradually, the frequency range of the sound insulation trough is narrowed, and the sound insulation performance deteriorates.


## 5.3. Panel Thickness of SPS

Based on the above structural dimensions of SPSs, the sound insulation performance of SPSs having top and bottom panels with thicknesses of 1.5 mm, 3.5 mm, and 5.5 mm is analyzed by numerical simulation. The core layer thickness is maintained constant at 15 mm. The calculation results are shown in Figure11.Figure 11
Influence of panel thickness on sound insulation curve of SPS.Figure11 shows that the sound insulation trough gradually shifts towards higher frequencies with the increase in the SPS panel thickness. The trend is gradually obvious. This is because the natural frequency of the structure would increase with the increase in the panel thickness when other parameters remain constant. The density of the acoustic valley on the sound insulation curve reduces gradually with the increase in the thickness of the panel. This is because the natural frequencies of SPS increase with the increase in the thickness of the panel. Furthermore, the resonance frequency of the structure reduces gradually within the same frequency range (100 Hz–3150 Hz). Thus, the larger the panel thickness of the structure, the smaller is the density of the acoustic valley of the sound insulation curve.In the calculated frequency range, the structures with the panel thicknesses of 1.5 mm and 5.5 mm display the smallest and the largest sound insulation performance, respectively. That is, the sound insulation curve of the structure shifts upward with the increase in the panel thickness, the sound insulation performance is enhanced, and the trend slows down gradually. Therefore, the sound insulation performance of the structure can be improved by increasing the thickness of the panel appropriately while maintaining the structural weight within the permitted range.


## 5.4. Core Layer Thickness of SPS

Based on the above structural size of SPS, the sound insulation performance of SPSs with core thicknesses of 12 mm, 22 mm, and 32 mm is analyzed by numerical simulation. The panel thickness is constant at 1.5 mm. The calculation results are shown in Figure12.Figure 12
Influence of core thickness on sound insulation curve of SPS.As is evident from Figure12, the structure with the core thickness of 12 mm has the first sound insulation trough near 400 Hz, the minimum sound insulation is 17.78 dB, and the sound insulation is the smallest; The core thickness of 32 mm has the first sound insulation trough near 630 Hz, the minimum sound insulation is 33.03 dB, the sound insulation is the maximum. That is, the sound insulation curve of the structure shifts upward with the increase in the core thickness, the sound insulation performance is enhanced, and the trend slows down gradually.In the calculated frequency range, the sound insulation trough would gradually shift to higher frequencies with the increase in core thickness, and the density of sound insulation trough would decrease gradually. This is because the increase in core thickness results in an increase in the natural frequency of the SPS. Then, the resonance frequency of the structure would decrease gradually in the same frequency range (100 Hz–3150 Hz). Therefore, the larger the core thickness, the smaller is the density of the sound insulation trough of the sound insulation curve.From the above analysis, it can be seen that when designing the sandwich panel structure, the sound insulation performance of the structure can be improved by increasing the core thickness appropriately.


## 5.5. Core Layer Material of SPS

The core material is also an important part that affects the sound insulation properties of the structure. Therefore, polyurethane, aluminum alloy, and a composite material are used as the core materials, and the core thickness is 12 mm. The other structural parameters are consistent with the SPS mentioned above. The material parameters of each core are shown in Table6, and the calculation results are shown in Figure 13.Table 6
Properties of core materials.
Core materialDensity (Kg∙m−3)Elasticity modulus (GPa)Poisson ratioPolyurethane120010.44Aluminum alloy269863.820.35Composite material1900180.15Figure 13
Influence of core material on sound insulation curve of SPS.Figure13 shows that the sound insulation trough of the structure shifts toward higher frequencies with the increase in the elastic-modulus-to-density ratio of the core material, the trend gradually slows down. Furthermore, the density of the sound insulation trough of the sound insulation curve decreases gradually, and the change is significant. This is because the increase in the elastic-modulus-to-density ratio of the material results in the increase in the natural frequency of the SPS. The resonance frequency of the structure in the same frequency range (100 Hz–3150 Hz) is reduced gradually. Thus, the higher the ratio of elastic modulus to density of the material, the lower is the density of the sound insulation trough of the structural sound insulation curve.In the middle and high frequencies (1500 Hz–3150 Hz) of the calculated frequency range, the elastic-modulus-to-density ratio and sound insulation are minimum when the core material of the structure is polyurethane and maximum when it is aluminum. That is, in the medium- and high-frequency parts, the sound insulation curve of the structure shifts upward with the increase in the ratio of elastic modulus to density, the sound insulation trough frequency range is widened, and the sound insulation performance is improved significantly.In summary, it can be concluded that the influence of the core material should be considered when designing SPS, and appropriate materials should be selected.


## 5.6. Parameter Weights Analysis

The above part discusses the influence of different parameters on the sound insulation of the structure, and further research of the weight of each parameter in the influence of the sound insulation has the most significance for the design and application of the structure in practical engineering. The “fsrftest” function in the software MATLAB is applied in this part to obtain the univariate feature ranking for regression using F-tests. It is a test that the statistics follows theF-distribution under the null hypothesis, and is usually used to analyze statistical models that use more than one parameter to determine whether all or some of the parameters in the model are suitable for estimating the parent. The calculation results are shown in Figures 14 and 15.Figure 14
The weight of each parameter in the low-frequency domain of (a) 100 Hz; (b) 630 Hz; and (c) 1000 Hz.
(a)(b)(c)Figure 15
The weight of each parameter in the medium- and high-frequency domain of (a) 2000 Hz; (b) 2500 Hz; and (c) 3150 Hz.
(a)(b)(c)In the low-frequency range of 100 Hz–1500 Hz, three central frequency points of 100 Hz, 630 Hz, and 1000 Hz are taken, and the weights of the mass ratio of panel-to-core layer, geometric size of the panel, core thickness, and core material parameters in the influence of the sound insulation of the structure are calculated as shown in Figure14.From the analysis of Figure14, it can be seen that in the low-frequency range, the length-to-width ratio of SPS has the largest weight in the sound insulation of the structure, which is the main factor affecting; the mass ratio of panel-to-core layer has the smallest weight, and the least impact on the sound insulation. This is because in the low-frequency domain, the sound insulation of the structure is mainly affected by the stiffness, and the length-to-width ratio of SPS is the main factor affecting the stiffness of the structure. Therefore, the length-to-width ratio of SPS is the main factor affecting the sound insulation.In the medium- and high-frequency range of 1500 Hz–3150 Hz, three center frequency points of 2000 Hz, 2500 Hz, and 3150 Hz were taken, and the mass ratio of panel-to-core layer, panel geometric size, core thickness, and core material parameters in the influence of the sound insulation of the structure are calculated as shown in Figure15.From the analysis of Figure15, it can be seen that in the medium- and high-frequency domain, the weight of the length-to-width ratio of SPS gradually decreases, which is not the main factor affecting the sound insulation of the structure. Near the frequency of 2000 Hz, the main factor affecting the sound insulation of the structure is the core thickness; near the frequency of 2500 Hz, the mass ratio of panel to core is the main factor affecting the sound insulation; and near the frequency of 3150 Hz, the thickness of panel has the largest weight in the influence of the sound insulation, which is the main factor in the sound insulation. And the main factors affecting the sound insulation are different in different frequency range, because the structure is affected by resonance in the medium- and high-frequency domain, and the factors affecting the sound insulation are complex. Therefore, in practical engineering applications, the design should be considered in different frequency ranges to meet the sound insulation requirements of different frequency ranges of the structure.


## 6. Conclusion

This study investigates the sound insulation performance of an SPS through experimental study and numerical simulation analysis. Firstly, the preparation of the SPS specimen is described, and the acoustic test is carried out. Secondly, the obtained sound insulation curve is compared with the numerical simulation curve. The comparison verifies the feasibility of the numerical simulation technology. Finally, the influence of each parameter on the sound insulation performance of the SPS is discussed by employing the finite element software program LMS Virtual Lab, and its weight is ranked by using the function of “fsrftest”. The following conclusions are drawn:(1)
The numerical simulation curve of sound insulation of the SPS structure is in good agreement with the test curve. This implies that the numerical simulation method can effectively reflect the sound insulation performance of the structure.(2)
The overall variation trend of the sound insulation curve is consistent between the acoustic test and numerical simulation. The sound insulation trough occurs at the frequencies of 250 Hz and 630 Hz, which are located near the natural frequencies of the structure. The maximum error of sound insulation in the entire frequency range is 12.23%, which is within the permissible error range of 15%.(3)
The study on the influence of the panel-to-core layer mass ratio, panel geometry size, core thickness, and material on the sound insulation performance of the SPS indicates that in the low-frequency domain, the mass ratio of panel-to-core layer and the length-to-width ratio of SPS, respectively, have the lowest and the highest effect on the sound insulation of the structure. And the larger the length-to-width ratio of SPS is, the worse the sound insulation performance is. With the increase in the length-to-width ratio, this disadvantage will no longer be obvious. Moreover, in the middle- and high-frequency domain, the main factors affecting the sound insulation are different in different frequency ranges, and the frequency range should be considered during the design of the structure.(4)
For the full-sized SPS structure, the influence of geometric parameters on the sound insulation performance is much greater than that of the core material properties in the low-frequency domain, indicating that the sound insulation performance of the SPS mainly depends on the change of the geometric parameters. Therefore, cost-effective materials can be selected for preparation in engineering applications to realize the large-scale application of SPS in the field of sound insulation performance.



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*Source: 9398988-2022-06-27.xml*