Study on Sound Absorption Properties of Polyvinyl Chloride (PVC) Film Multicavity Structure Materials

Since the development of industry, sound absorption and noise reduction have gradually become an urgent problem to be solved. Lightweight polymer flm materials are very efective in response to sound waves, and sound waves can easily cause vibration of the flm, which can convert sound energy into vibration and flm friction to achieve sound absorption. Te application conditions of the flm material are very harsh, that is, a support body is required to fx the flm and the flm needs to be tensioned. Te flm is very thin and easy to damage. Te idea of this research is to transform the flm into a bubble structure and use a large number of flm bubbles to form a cavity structure material. As a unit of the sound absorption structure, bubbles can avoid damage to the flm. In this paper, commercial polyvinyl chloride flm bubble materials are used to prepare two kinds of flm multicavity structure materials, and the sound absorption performance of this flm multicavity structure material is studied. Te research results show that this flm multicavity structure material has very excellent broadband sound absorption performance, which changes the narrow band sound absorption properties of the usual flm single cavity. Te average sound absorption coefcient can reach 0.84 in frequency range from 500Hz to 6400Hz. Tis structural material has a single peak sound absorption curve at the middle and low frequency bands, which is the characteristic of resonance sound absorption. And at the middle and high frequency bands, it exhibits the characteristics of broadband sound absorption. Te flm multicavity structure material has both cavity sound absorption and broadband sound absorption characteristics.


Introduction
Te increasing noise pollution has signifcantly infuenced people's lives since the industrial evolution, ranking the second among all environmental pollution [1][2][3][4].Industrial noise and social life noise will afect human hearing and psychology.At the same time, high intensity noise will cause the aging of mechanical equipment and cause harm to buildings [5][6][7].Terefore, sound absorption and noise reduction have gradually become an urgent problem to be solved [8,9].
During the past few decades, two methods have been widely investigated to alleviate noise pollution: passive and active noise control [10,11].Passive noise control indicates reducing noise by using sound absorption materials and structures [12,13].Sound absorption materials and structures mainly include porous sound absorption materials [14][15][16] (i.e., foam plastics, metal foams, and fber porous materials) and resonance sound-absorbing materials (i.e., microperforated plate sound absorption materials [17,18], membrane sound-absorbing materials [19,20], Helmholtz resonance sound absorption structures [21,22], and flm cavity sound absorption structures).Porous sound absorption materials are composed of a large number of pores, cracks, or cavities, allowing sound waves to enter the material [23,24].Te sound energy is dissipated by the heat loss caused by the friction between air molecules and the pore wall, and the viscosity of the airfow in the material causes the viscosity loss, the sound energy can be greatly reduced, and the porous material exhibits broadband sound absorption at 1000-6000 Hz [25][26][27].Te resonant sound absorption material is mainly a cavity resonance structure, and the sound absorption frequency band is narrow.When the sound wave propagates to the surface of the material, the air inside the material vibrates with the vibration of the sound wave.When the frequency of the incident sound wave is close to the natural frequency of the structure, the air in the cavity vibrates violently and resonates [28][29][30].In the resonant sound absorption material, the flm cavity structure shows the advantages of light weight, low cost, and simple ways of manufacturing.
Under the excitation of sound, the flm causes vibration and absorbs sound waves.Te sound absorption of the flm cavity structure is afected by the flm surface density and cavity depth [31].However, this structure is unlikely to achieve broadband absorption as only a single flm cavity structure is applied.Tus, many recent studies have been carried on in order to achieve broadband sound absorption by the flm cavity structure, such as flm with mass structure [32,33], flm with cavity structure [34,35], and honeycomb flm metamaterial structure [36].Acoustic metamaterials composed of flm and mass block were used to absorb lowfrequency sound waves [37][38][39][40], and the sound absorption coefcient at 100-1000 Hz can reach more than 0.6 [41][42][43][44].Te fnite element method was used to analyze the vibration mode of this structure, and the sound absorption principle was explained [45,46].Te infuence of the geometrical and material factors of the structure on the propagation loss was investigated [47,48].By changing the position and quantity of the masses and the shape, density, and prestress of the flm structure, the position and bandwidth of the sound wave transmission peak can be efectively controlled, improving the sound wave absorption capacity [49][50][51].At the same time, the sound insulation performance of this structure was investigated, the fnite element simulation results showed that this structure can achieve efective sound insulation in the 0-300 Hz frequency band, and the sound insulation can reach 24 dB at 157 Hz [52].Langfeldt proposed that the peak value of sound insulation at antiresonance was more than the corresponding mass-law 25 dB [53,54].And a theoretical analysis model using point coupling analysis method is proposed to analyze the flm with mass structure, and a relationship is obtained, indicating that the sum of the incoming acoustic wave (complex number) pressure amplitudes (averaged over the membrane area) must be equal to the outgoing waves.By using this relationship, and without considering any details of the wave solution, it was shown that the maximum achievable absorption for single side incidence is 50%, while the maximum absorption for back-refecting surfaces is up to 100% [55,56].Te acoustic properties of the flm with cavity structure could be adjusted by compressing the air between two flms.Te study results showed that the sound absorption bandwidth of double layer flm structures with cavities is 400 Hz higher than that of single layer flm structures [57,58].Adhering a flm to the micro-perforated plate was also proposed.Te flm had a signifcant infuence on the acoustic impedance.A higher absorption peak than a single-layer micro-perforated panel can be achieved by adjusting the size of the flm cells, increasing from 0.76 to 0.97 [59].By comparing and analyzing the acoustic performance of honeycomb metamaterials with and without flm, the results showed that the acoustic performance of the flm structure was greater at low frequencies and the sound insulation at 500 Hz-2500 Hz was greater than that of metamaterials without flm.Te frequency position of the acoustic refection peak can be efectively controlled by changing the density parameters and structural parameters of the flm [60,61].A bubble structure of locally resonant acoustic metamaterial that can reach the transmission peak at 1480 Hz was designed [62].And a theoretical model to predict the resonant behavior of bubble-based metamaterials was developed.An analytical expression for resonant frequencies of bubble meta-screens using self-consistent approximation method [63].
In summary, the study of flm materials in sound absorption or sound insulation mainly uses skeletons or supports to form a flm cavity structure recently.Due to the small surface density of the flm, it is easy to cause vibration and change the acoustic performance of the flm structure.Te main research results are that the good narrow frequency band acoustic performance can be found in medium and low frequencies.
Te application conditions of the flm material are very harsh, that is, a support body is required to fx the flm, and the flm needs to be tensioned.Because the flm is very thin and easy to damage, it is difcult to apply the flm to noise control in practice.Te idea of this research is to transform the flm into a small structure, such as a bubble structure, and use a large number of flm bubbles to form a cavity structure material.Te advantage is that the flm can be fexibly used for structural design after the flm is transformed into a bubble structure.As a unit of the sound absorption structure, bubbles can avoid damage to the flm.Even if it is damaged, it is a small number of bubbles that will not afect the structure of the overall flm cavity material.
Commercial packaging polyvinyl chloride (PVC) flm bubbles laid the foundation for this research, which is used for packaging and reducing vibration to prevent damage of products.Tis material will be thrown away as waste after being used, causing environmental pollution.Te second use of this material is conducive to environmental protection.Te structure of this commercial PVC flm bubble is favorable to the response of sound waves, that is, it is easy to convert sound waves into vibrations, thereby eliminating noise.Using this single layer flm bubble, two types of flm cavity materials can be prepared, the multilayer flm PVC bubble structure (PB) and the frame flled by PVC bubble structure (FPB).Tree efects on sound absorption performance are studied, including flm bubble material thickness, bubble diameter and porosity.
Tis flm bubble structure has the advantages of ultralightweight, easy preparation, easy installation, convenient use, and the secondary utilization of discarded commercial bubble materials, which is benefcial to environmental protection.It can realize the application of flm materials in sound absorption materials.It is a new type of sound absorption material with a broad application prospect.

2
Shock and Vibration

Experiment
2.1.Sample Preparation.Two kinds of samples were made with waste PVC flm bubbles used in commercial packaging.
Te frst structure is to cut the ordinary waste PVC bubble material into discs required for the sample, and paste the multi-layer flm PVC bubble (PB) sample, as shown in Figures 1(a) and 1(b).
Te second structure is to cut the packaging bubble material into a single flm bubble, the bubble is intact.Te thickness of the bubble flm is 0.01 mm, and the diameter is 5 mm, 10 mm, and 25 mm.Te design frame is cylindrical, and the front and back are restricted by narrow strips, which width is 2 mm and spacing is 3∼4 mm.Te complete frame is made by 3D printing technology.Te diameter of the frame is 99.6 mm and 29 mm respectively.Te material of the frame is polytetrafuoroethylene resin.Te flm bubbles are packed into the frame to form frame flled by PVC bubble materials (FPB), as shown in Figures 1(c) and 1(d).When preparing FPB samples, the porosity of the sample can be controlled by changing the mass of bubbles flled.Te porosity can be calculated using formula.
where m is the mass of bubbles flled, V is the volume of sample, and ρ PVC is the density of the PVC flm bubbles.

Results of Sound Absorption Performance of Multilayer Film PVC Bubbles (PB).
A single piece of commercial flm PVC bubble material is used, cut into discs, and PB samples are made by gluing the discs of PVC bubble material.Te average sound absorption coefcient is the average value of the sound absorption coefcient from 150 to 1600 Hz.Te starting frequency is the lowest frequency at which the sound absorption coefcient reaches 0.2.Te sound absorption curve is shown in Figure 2.
It can be seen from Figure 2(a) that the PB structure material has an obvious resonance peak in the frequency range of 150-1600 Hz.Te resonance peak moves to low frequency with the increase of the material thickness, which is similar to the sound absorption characteristics of the cavity resonance structure.Te sound absorption curve has a single peak sound absorption characteristic, which is due to the resonance sound absorption caused by the cavity.
Generally speaking, for cavity sound absorber, the greater the depth, that is, the greater the thickness of the sample, the more the absorption peak moves to low frequencies.
It can be seen from the experimental results that when the thickness of the sample increases, the sound absorption curve of the sample moves to low frequencies.Te average sound absorption coefcient increases, and the starting frequency decreases.When the thickness is 10 mm, the sound absorption coefcient of the PB sample reaches the maximum at 1600 Hz, which is 0.75, and there is no peak; When the thickness is 20 mm, the sound absorption coefcient of the sample reaches its maximum at 1170 Hz, which is 0.99, showing obvious single peak sound absorption characteristics; When the thickness is 30 mm, the sound absorption coefcient of the sample reaches its maximum at 746 Hz, which is 0.98, also showing obvious single peak sound absorption characteristics.Moreover, the single peak at this sample moves 424 Hz to the low frequency, which is caused by the increase in sample thickness.
Te sample thickness of 30 mm is selected, and PB samples with flm bubble diameters of 5 mm, 10 mm, and 25 mm are prepared respectively.It can be seen from Figure 2(b) that in the frequency range of 150-1600 Hz, the three diameter flm bubbles have little efect on the resonance peak of PB material.And the resonance absorption peak is almost at the same position, which means that the thickness of the sample determines the position of the resonance peak.When the thickness is constant, the depth of the cavity has been determined, and the position of the resonant absorption peak has been determined.When the flm bubble diameter is larger, the sound absorption coefcient is higher.When the bubble diameter is 10-25 mm, the average sound absorption coefcient is basically the same, and the sound absorption frequency band is wider; when the bubble diameter is 5 mm, the average sound absorption coefcient is the minimum and the sound absorption band becomes narrower.It can be seen that the diameter of the flm bubble should be larger.

Results of Sound Absorption Performance of Frame Filled by PVC Bubbles (FPB).
Te structure of FPB is to put flm bubbles into a frame, to form a tightly connected structure between the flm bubbles, and the thickness of the FPB is controlled by the outer frame, as shown in Figure 1.Tree efects on sound absorption performance of FPB materials are investigated respectively, including sample thickness, flm bubble diameter and porosity.

Te Efects of Tickness on the Sound Absorption
Performance of FPB.Te flm bubble diameter of 10 mm and porosity of 0.975 are selected, and FPB samples with thickness of 10 mm, 15 mm, 20 mm, 25 mm and 30 mm are prepared respectively.It can be seen from Figure 3(a) that in the frequency range of 150-1600 Hz, a wider resonance absorption peak is occurred obviously in FPB structure.Te resonance absorption peak becomes more complicated, but it is still resonance absorption.Te sound absorption curve of FPB moves to low frequency with the sample thickness Shock and Vibration increases.When the sample thickness is 10 mm, the sound absorption coefcient reaches the maximum at 1600 Hz, which is 0.75, and there is no resonance absorption peak; when the sample thickness is 15 mm, the sound absorption coefcient reaches the maximum at 1600 Hz, which is 0.85, and the resonance absorption peak still does not occur; when the sample thickness is 20 mm, a resonance absorption peak occurs, which frequency is 908 Hz, and the sound absorption coefcient is 0.86; when the sample thickness is 25 mm, the frst resonance sound absorption frequency is 782 Hz, and the sound absorption coefcient is 0.93; when the sample thickness is 30 mm, the sound absorption coefcient of FPB structure can reach 0.94 at 754 Hz.Te sound absorption frequency band moves 154 Hz to low frequency with the sample thickness increases from 20 mm to 30 mm.And the morphology of the peak is basically the same.Compared with the PB structure, the absorption peak morphology of FPB structure is more complex and wider.Te sound absorption coefcient of FPB with a thickness of 30 mm and a flm bubble diameter of 10 mm is 0.54, which is slightly larger than 0.52 of PB.
In Figures 3(b) and 3(c), when the sample thickness increases from 10 mm to 30 mm, the average sound absorption coefcient of sample increases and the starting frequency decreases gradually.

Te Efects of Film Bubble Diameter on the Sound
Absorption Performance of FPB.Te thickness of 30 mm and porosity of 0.975 are selected, and FPB samples with flm bubble diameter of 5 mm, 10 mm, and 25 mm are prepared, respectively.It can be seen from Figure 3(d) that the resonance absorption peak in the sound absorption curve changes obviously, when the diameter of the flling PVC flm It can be seen from Figures 3(e) and 3(f ) that as the flm bubble diameter increases, the average sound absorption coefcient and the starting frequency of the sample decrease slightly.When flm bubble diameter is 5 mm and 10 mm, the average sound absorption coefcients of samples are the same, both are 0.54.When the diameter of flm bubble is 25 mm, the FPB sample has better low frequency sound absorption performance.In comprehensive comparison, when the flm bubble diameter is 10 mm, the sample has the most excellent sound absorption performance.Shock and Vibration

Te Efects of Porosity on the Sound Absorption Performance of FPB.
Te thickness of 30 mm and flm bubble diameter of 10 mm are selected, and FPB samples with porosity of 0.975, 0.977, 0.979, 0.981 and 0.983 are prepared, respectively.It can be seen from Figure 3(g) that when the porosity of the FPB structure increases, the resonant absorption peak of the sound absorption curve moves to high frequency.Tat is, the larger the porosity, the worse the low frequency sound absorption performance of the FPB structure.When the porosity is 0.975, the sound absorption coefcient of FPB structure can reach 0.94 at 754 Hz; When the porosity is 0.983, the sound absorption coefcient of FPB structure can reach 0.96 at 1284 Hz.
It can be seen from Figures 3(h) and 3(i) that as the sample porosity increases, the average sound absorption coefcient changes from 0.49 to 0.56, and the starting frequency increases signifcantly.

Comparison of Sound Absorption Performance Results of
PB and FPB Samples.PB and FPB samples with a diameter of 29 mm are prepared.In order to further study the sound absorption performance of the flm cavity structure material, the test is carried out in a wider frequency band, and the test range is 500-6400 Hz.Te average sound absorption coefcient is the average value of the sound absorption coefcient from 500 to 6400 Hz.Te resonance frequency is the frequency at which the sound absorption coefcient reaches its maximum.Te starting frequency is the lowest frequency at which the sound absorption coefcient reaches 0.2.In Figure 4(a), the PB structure material has broadband sound absorption and excellent sound absorption performance.At less than 1600 Hz, the same as the previous test results, the resonance absorption peak frequency is basically the same.In the range greater than 1600 Hz, broadband sound absorption characteristics appear, and there is no obvious resonance absorption peak.For medium and high frequencies, the sound absorption properties of porous materials appear.It can be seen that the average sound absorption coefcient of No. 1 sample with a flm bubble diameter of 10 mm is 0.75, and the average sound absorption coefcient of No. 2 sample with a diameter of 25 mm is 0.72.Terefore, for the PB structure, a flm bubble with a smaller diameter can be selected to improve its sound absorption coefcient.
In Figure 4(b), the FPB structure has broadband sound absorption.Te average sound absorption coefcient of the No. 1 and No. 2 sample is 0.84, while the starting frequency of the No. 2 sample is low, which is 416 Hz.When the sample porosity is 0.98 and the flm bubble diameter is 25 mm, the bubble volume is large, the number of bubbles is less, and the friction between the flm bubbles is less.It can be seen from curve No. 2 that the frst resonance peak is a narrow and smooth single peak.It shows that the contact between the flm bubbles is small, and the friction between the bubbles is less.When the bubble diameter is 10 mm, there are more small bubbles and the frst resonance peak becomes wider, indicating that the contact between the small bubbles is more, the friction between the flms is more, and the sound absorption performance of the middle and low frequency is higher than that of No.2 sample with diameter of 25 mm.
In Table 1 and Figure 4(c), the PB and FPB flm cavity samples both have broadband sound absorption characteristics.When the frequency is less than 1600 Hz, both have resonance sound absorption characteristics, and when it is greater than 1600 Hz, both have porous sound absorption characteristics.Te average sound absorption coefcient of FPB is greater than PB, therefore, the sound absorption performance of FPB is better than PB.Te starting sound absorption frequency of PB is lower than FPB, and the low frequency sound absorption performance of PB is slightly better than FPB.
Te sound absorption properties of flm multicavity structure materials are compared with commonly used sound absorption materials.Te material parameters and sound absorption test results are shown in Table 2, and the sound absorption curve is shown in Figure 5.
It can be seen from Table 2 and Figure 5 that when the thickness of the four materials is 30 mm, the average sound absorption coefcient of FPB structure is the largest, 0.84.Te average sound absorption coefcient of polyurethane foam is the smallest, 0.66.PB and FPB structures exhibit cavity resonance sound absorption characteristics at frequencies below 1600 Hz, with better low frequency sound absorption performance.Te average sound absorption coefcient of melamine foam is 0.82, but its price is expensive.PB and FPB structure is the secondary use of discarded commercial flm bubble materials, which is light and conducive to environmental protection.

Result Analysis of Sound Absorption Performance of the PB
Structure.Te flm bubble structure is mainly composed of a cavity and a flm, the cavity occupies a large volume, and the flm occupies very little volume.Te function is that the bubble cavity provides the refection space of the sound wave, the flm generate heat and dissipate sound energy by vibration and friction with sound waves.Te structure of PB is neat, as shown in Figure 1(a).It is made up of multiple layers flm bubbles and the porosity remains unchanged.Te bubbles are independent of each other and have less interaction.Te external appearance is similar to periodic structure.It exhibits typical sound absorption characteristics of flm cavities below 1600 Hz.As shown in Figure 2, the sound absorption coefcient curve presents a smooth resonant single peak morphology.
When the sound wave radiates to the surface of the PB structure, it causes the flm with a small area density to vibrate, which converts the sound energy into the flm vibration and consumes a part of the sound energy.At the same time, the sound wave radiates into the inside of the PB material due to the flm vibration, and the sound wave encounters each surface of the flm will refect causing cavity resonance and flm friction will consume sound energy.When the flm bubble layer increases, the efect between the flm bubble and the sound wave increases, so the sound absorption coefcient increases.Te thicker the PB, the

Shock and Vibration
deeper the cavity and the more the resonant absorption peak moves to the low frequency.When the thickness of PB is constant, the flm bubble diameter has no signifcant efect on the resonance frequency.Tis is because no matter how the diameter of the flm bubble changes, the overall cavity volume changes little, the movement of resonance absorption peak is not significant, and the average sound absorption coefcient changes little.
When the frequency is greater than 1600 Hz, the sound absorption curve exhibits broadband sound absorption characteristics, that is, the sound absorption characteristics of porous materials.When the acoustic waves enter the inside of the PB structure, due to the number of flm cavities increases, the area of action between the flm and the sound waves increases.During the process of sound wave multiple refections, the sound energy consumed by the flm friction also increases, and the sound absorption performance is improved.It can be seen from Figure 2(b) that when the diameter of the flm bubbles is small, the number of bubbles per unit volume will increase, and the area of the flm will increase, and the efect between flm and sound waves will increase.
In summary, the sound absorption characteristics of the PB structure are cavity sound absorption characteristics in the middle and low frequencies, broadband sound absorption characteristics in the middle and high frequencies, and the PB structure generally exhibits broadband sound absorption characteristics.Te required resonance peak frequency can be obtained by controlling the thickness of the PB structure, so that the low frequency sound absorption characteristics can be designed.At medium and high frequencies, a broadband sound absorption efect can be obtained by controlling the diameter of the flm bubble, and a smaller bubble diameter is benefcial to improve the sound absorption coefcient.
Tree ways for PB structure to dissipate sound energy are concluded, including flm vibration, cavity resonance, and friction between sound waves and the flm surface.

Result Analysis of Sound Absorption Performance of FPB Structure 4.2.1. Te Efects of Tickness on the Sound Absorption
Performance of FPB.Te FPB structure is more complicated, which is consisted of the multiple individual flm bubbles flled into the frame.Te bubbles are no longer independent, and the flms between the bubbles squeeze each other, as shown in Figure 1(c).Te efect of the flm increases, so the sound absorption peak becomes more complicated.As shown in Figure 3, the resonance absorption peak is not a smooth single peak, but a broad resonance absorption peak at the frequency range less than 1600 Hz.Te morphology of the absorption peak is related to the flm bubble cavity structure.Te sound absorption curve of the PB structure is a smooth single peak, indicating that the cavity is invariant in the sound wave radiation.Te bubbles in the PB structure are independent of each other, therefore, it can be ensured that the cavity of the entire structure will not change.In the FPB structure, the bubbles are mutually squeezed, and the interaction between the flm and bubbles is strong.When the sound wave radiates to the surface of the FPB, the flm will vibrate due to the sound pressure, which will cause the deformation of the bubble cavity, so the resonance absorption peak changes in morphology.
As the thickness of the FPB sample increases, the sound absorption curve of the sample shifts to low frequencies, and the starting frequency gradually decreases.As the cavity depth increases, the volume of a Helmholtz resonator increases, and the resonance frequency shifts to low frequencies.
As the thickness of the FPB increases, the average sound absorption coefcient increases.Tis is because the number of flm bubble cavities in the sample increases with the thickness increases, the interaction area of sound waves with the flm increases, the propagation channel becomes more complicated, the sound wave attenuation increases, and the sound absorption performance improves.

Te Efects of Film Bubble Diameter on the Sound
Absorption Performance of FPB.Te FPB structure is more complicated, the flm bubbles squeeze each other, and the flm vibration is more complicated.When the thickness is constant, the diameter of the flm bubble decreases.When the diameter of the flm bubble is 5 mm, it is the smallest bubble diameter in this set of experiments.At this time, the number of flm bubbles flled is the largest, the squeezing area between the flms is the largest, the friction between the flms is the strongest, the resonance absorption peak is widened, and the complex single-peak characteristics are presented, as shown in the sound absorption curve of Figure 3(d).Tis is because the existence of both the cavity efect and the friction between the flms at this time.So, the sound absorption coefcient is the highest.
When the thickness of the FPB is constant, the resonance peak frequency is related to the size of the flm bubble cavity.Te larger the flm bubble cavity, that is, the larger the diameter, the more the resonance peak moves to the low frequency.Tis is because large bubbles have a large volume and the flled FPB structure has a larger cavity.So, the resonance peak moves to a low frequency as the bubble diameter increases.When the diameter of the flm bubble changes from 5 mm to 25 mm, the resonance absorption peak frequency of the FPB structure drops from 1162 Hz to 672 Hz and moves to the low frequency by 490 Hz.It can be seen that the diameter of the flm bubble can change the resonance sound absorption frequency of the FPB structure.
Te larger flm bubble diameter can improve the low frequency sound absorption performance, but it is not good for the improvement of the sound absorption coefcient.Tis is because the friction between the flms is reduced, and the sound energy consumption is decreased.In summary, a middle flm bubble diameter can be selected.

Te Efects of Porosity on the Sound Absorption Performance of FPB.
In the FPB structure, the flm bubbles squeeze each other, and the flm vibration is more 8 Shock and Vibration complicated.When the porosity of FPB structure increases, the number of flm bubbles flled in the frame decreases, the squeeze between the flms weakens, the efect of friction between the flms changing to sound energy weakens, and the resonance absorption peak becomes a smooth single peak.Tis is similar to the absorption peak of the PB structure, which is a smooth single peak, as shown in the curve of Figure 3(g).When the porosity is 0.983, the single peak of sound absorption curve is similar to the absorption peak of the PB structure.Tis is because when the porosity increases to above 0.981, the number of flled bubbles decreases, the friction between the bubbles disappears, and the bubble cavity relatively independent, the cavity resonance absorption peak becomes a smooth single peak.When the porosity is 0.975, the absorption peak morphology is complicated and the sound absorption coefcient increases.Tis is because as the porosity decreases, the number of flm bubbles flled in the frame increases, the friction between the flms increases, and the bubbles are no longer independent of each other.So the resonance absorption peak transforms into a wide and complex morphology.When the porosity is small, the density of flm bubbles flled in the frame is high, the bubbles are compressed, and the contact area between the flm bubbles increases.When the sound wave radiates to the surface of the FPB material, it dissipates more sound energy, so the sound absorption coefcient increases.When the porosity is large, the density of flm bubbles flled in the frame decreases, the efect between the flms decreases, the dissipation of sound energy decreases, so the sound absorption coefcient decreases.It can be seen from the change of the sound absorption coefcient that in the FPB structure, the porosity has a suitable value, which should not be greater than 0.980.Tis can increase the density of flm bubbles flled in the frame and the contact area between the bubble flms.When the sound wave radiates to material, the dissipation of sound energy can be increases by increasing the friction between the flms, and there is also a sound absorption efect of the flm cavity at the same time.Te FPB structure with excellent sound absorption performance can be obtained with such a joint efect.
In summary, the sound absorption characteristics of the FPB structure are cavity sound absorption characteristics in the middle and low frequencies, broadband sound absorption characteristics in the middle and high frequencies, and the FPB structure generally exhibits broadband sound absorption characteristics.Te resonance absorption peak is related to the thickness.Te greater the thickness, the more the sound absorption curve moves to low frequencies.When the total thickness is constant, it is related to the size of the flm bubble diameter.Te larger the flm bubble diameter, the more the resonance sound absorption frequency moves to low frequencies.
Te morphology of the resonance sound absorption curve is related to the porosity.Te smaller the porosity, the more the number of flm bubbles flled in the frame, the greater the degree of the bubbles squeezing, the larger the contact area of the flms and the wider and more complex resonance peaks.When the porosity increases to a certain value (greater than 0.981), the number of flm bubbles flled in the frame is small, the bubbles are independent of each other, and the resonance peak becomes a smooth single peak.
Four ways for FPB structure to dissipate sound energy are concluded, including flm vibration, cavity resonance, friction between sound waves and the flm surface, and friction between the flms.

Comparison of Sound Absorption Performance of PB and FPB.
From the PB and FPB structure, PB structure dissipates sound energy in the following ways: flm vibration, cavity resonance, friction between sound waves and the flm surface, while FPB structure dissipates sound energy in the following ways: flm vibration, cavity resonance, friction between sound waves and the flm surface, and friction between the flms.It can be seen that FPB dissipates sound energy in one more way than PB, that is, the friction between the flms.Te ability of FPB structure to dissipate sound energy is greater than that of PB structure, so the sound absorption performance of FPB structure is better than that of PB structure.It can be seen that under the same parameter conditions, the average sound absorption coefcient of FPB structure is 0.84, the average sound absorption coefcient of PB structure is 0.75, and the sound absorption performance of FPB structure is better than that of PB structure.In the middle and low frequencies, the resonant peak of PB structure is a smooth curve, and the resonant peak of FPB structure is wide.Tis is because the bubble distribution in the two structures is diferent.Te bubbles in the PB structure are independent of each other and arranged regularly, forming a fxed cavity structure, and the resonance peak is a smooth single peak.In the FPB structure, the bubbles are in a squeezed state, and the bubbles are not independent.When the sound wave radiates to material, friction between the bubble flms will occur and the shape of the cavity will be changed, so the resonance peak becomes wider and more complicated.Te peak-valley value of PB structure is deeper than FPB structure, the resonance peak is more obvious, and the cavity sound absorption characteristics of PB structure are more prominent than FPB structure.Both PB and FPB structure exhibit broadband sound absorption performance at medium and high frequencies, and have a high sound absorption coefcient.Tis is due to the various ways of dissipating sound energy, such as the friction between the sound waves and the flm surface, the friction between the flms, and the cavity resonance, etc. Tere are many ways to transform sound energy, and the sound absorption mechanism is complex, which results in broadband sound absorption characteristics.Te summary of the performance comparison between the PB structure and the FPB structure is as shown in Table 3.
In general, both PB and FPB structure have broadband sound absorption performance.It presents the cavity sound absorption characteristics in the middle and low frequencies, and broadband sound absorption characteristics in the middle and high frequencies, and the sound absorption frequency band can be controlled by adjusting the structure

Shock and Vibration
where ρ 0 is the density of air, 1.29 kg/m 3 .c is the sound speed in air, 340 m/s.M 0 is the areal density of the flm, which is equal to the product of the flm thickness and the flm density.h is the air layer thickness between the flm and the rigid wall.Te density of the PVC flm is 1.38 × 10 3 kg/m 3 , the thickness of the flm is 1 × 10 −4 m.

Calculation of Resonance Frequency of PB Structure.
According to formula (2), the resonant frequency of the PB flm cavity structure is calculated.It can be seen from Table 4 that when the thickness is less than 0.025 m, the theoretical calculation of the PB structure resonance absorption peak frequency is not much diferent from the experimental measurement results, and the PB structure conforms to the theoretical calculation of the flm cavity structure.Terefore, it can be seen that when the thickness is less than 0.025 m, the flm bubbles in the PB structure have little efect on the structure.However, when the thickness is 0.03 m, the diference between the theoretical calculation result and the experimental measurement result is about 210 Hz.And as the thickness increases, the resonance peak moves, and the frequency of the movement is basically a same value with the increase in thickness.Terefore, the calculation formula is revised.After the revision, the formula for calculating the resonance frequency of the PB structure is shown below.
It can be seen from Table 4 that the resonant sound absorption peak frequency of the PB structure calculated using the revised formula (3) is not much diferent from the experimental measurement result.

Calculation of Resonance Frequency of FPB Structure.
According to formula (2), the resonant frequency of the FPB flm cavity structure is calculated.It can be seen from Table 5 that the theoretical calculation of the FPB structure resonance absorption peak frequency is quite diferent from the experimental measurement result, because the FPB structure is more complicated than the PB structure.Te air bubbles in FPB are randomly flled into the frame, and the air bubbles squeeze each other, and the flm has a stronger efect, which makes the resonance peak of FPB structure more complicated.At the same time, the resonance peak frequency does not arithmetic change with the increase of thickness, so the formula can be revised.Te revised formula is shown below.
After the revision, the theoretical calculation of the FPB structure resonance absorption peak frequency is not much diferent from the experimental measurement result.Tis formula can predict the resonance absorption peak frequency of the FPB structure.
Formulas (3) and ( 4) are obtained, which have practical guiding role in the prediction of the PB and FPB structures resonance frequency, and have guiding signifcance for the design of PB and FPB sound absorption structure materials.

Conclusion
(1) Commercial flm bubble materials are used to make a flm multicavity structure, which can achieve broadband sound absorption characteristics.Tis structure greatly improves the ability of the flm to absorb sound waves and provides a method for the design of flm sound absorption materials.(2) Te PB structure is a multi-layer bubble periodic structure, which is characterized in that each layer of flm bubbles are independent of each other, the flm bubbles between the layers are bonded to each other, and there are gaps between the bubbles.Tree ways for PB structure to dissipate sound energy are concluded, including flm vibration, cavity resonance, and friction between sound waves and the flm surface.Te FPB structure is randomly flled with flm bubbles in the frame, the bubbles are squeezed each other, and the bubble flms are close to each other.Four ways for FPB structure to dissipate sound energy are concluded, including flm vibration, cavity resonance, friction between sound waves and the flm surface, and friction between the flms.

Figure 2 :Figure 1 :
Figure 2: (a) Sound absorption curve of PB samples with diferent thicknesses and (b) sound absorption curve of PB samples with diferent flm bubbles diameters.

Figure 3 :
Figure 3: (a) Sound absorption curve of FPB samples with diferent thicknesses, (b) the efect of thickness on average sound absorption coefcient, (c) the efect of thickness on starting frequency, (d) sound absorption curve of FPB samples with diferent flm bubbles diameter, (e) the efect of flm bubbles diameter on average sound absorption coefcient, (f ) the efect of flm bubbles diameter on starting frequency, (g) sound absorption curve of FPB samples with diferent porosities, (h) the efect of porosity on average sound absorption coefcient, and (i) the efect of porosity on starting frequency.

Figure 4 :
Figure 4: (a) Te sound absorption curve of PB samples, (b) the sound absorption curve of FPB samples, and (c) comparison of sound absorption curve of PB and FPB samples.

Figure 5 :
Figure 5: Te sound absorption curve of four materials.

Table 1 :
Comparison of sound absorption performance of PB and FPB samples.

Table 2 :
Comparison of sound absorption properties of four materials.

Table 3 :
Performance comparison of PB and FPB structure.

Table 4 :
Comparison of the resonance frequency theory and experimental results of the PB structure.

Table 5 :
Comparison of resonance frequency theory and experimental results of the FPB structure.
Te sound absorption performance of FPB structure is better than that of PB structure.(3) Te sound absorption of PB and FPB structures has two characteristics.It has cavity resonance sound absorption characteristics at medium and low frequencies.In PB and FPB structures, the cavity occupies a very large volume, and the resonance sound absorption of the cavity is single peak characteristics.Te sound absorption characteristics are related to Shock and Vibration thickness.It has broadband sound absorption characteristics at medium and high frequencies.PB and FPB dissipate sound energy in a variety of ways.Te sound energy is dissipated by the friction between the sound wave and the flm surface, the friction between the flms, and the cavity vibration, etc. Te complexity of sound energy transformation leads to broadband sound absorption characteristics.(4) In PB and FPB structures, the average sound absorption coefcient of FPB samples with a thickness of 30 mm can reach 0.84, and the starting sound absorption frequency is 544 Hz.Te average sound absorption coefcient of PB samples with a thickness of 30 mm can also reach 0.75, and the starting sound absorption frequency is 408 Hz.Te sound absorption performance of FPB structure is better than that of PB structure.(5) Te flm multicavity structure material has excellent broadband sound absorption performance, and has the advantages of ultralight weight, low cost, easy preparation, easy installation, convenient use, and the secondary utilization of discarded commercial flm bubble materials, which is benefcial to environmental protection.It is a new type of sound absorption material with a broad application prospect.