Sage Journals: Discover world-class research

Abstract

An improved sound transmission loss (STL) experimental technique based on the sound pressure method (SPM) and acoustic box method is proposed to investigate the temperature influence on the STL of the ribbed carbon fiber reinforced plastics aircraft panel. SPM principle is given. The measurement procedure of the improved STL technique is presented and its reliability is verified. STL variable characteristics of the panel within −40°C–40°C were measured. Results showed that temperature had a significant effect on the panel’s STL. The overall STL varied nonlinearly with temperature, whereas STL exhibited a fluctuation or monotony trend at a single center frequency. Temperature variation caused changes of STL peak/dip frequencies and redistribution of stiffness-controlled, resonance-controlled, coincidence-controlled, and damping-controlled regions. The causes of the aforementioned are given. This study reveals the relationship between temperature, thermomechanical parameters and STL. The findings have applications in the design, measurement, analysis, and theoretical development of composite structure acoustics.

Keywords

Sound transmission loss composite structure experiment temperature effect aircraft

Introduction

Sound transmission loss (STL), which is usually determined via experiments, is an important design index for aerospace structures. However, due to the temperature dependence of composite structures’ STL and the widespread use of composite materials in aerospace structures,^1,2 STL experimental technologies developed at room temperature cannot fully meet measurement requirements under variable temperature environments. Meanwhile, this issue has not been addressed in the reported studies. In this paper, an improved STL experimental technique based on the sound pressure method (SPM) and acoustic box method (ABM) is proposed for demonstrating the vibroacoustic behavior sensitivity of a ribbed carbon fiber reinforced plastics (CFRP) aircraft panel at ambient temperature.

Aircrafts operate within a broad ambient temperature range, typically varying between −50°C and 50°C, for hours. Concerning spacecraft, ambient temperature is worse (typically −100°C to 200°C) within their mission. Studies have shown that composite structures’ properties (elastic modulus, damping loss factor, natural frequency, etc) strongly depend on temperature.^3–6 Given that the aforementioned properties are related to STL, the temperature should affect composite structures’ STL. Therefore, researchers conducted some investigations on the acoustic analysis of composite structures. However, the main concerns were sound transmission mechanism,^7–9 numerical simulation method,^10–13 and composite acoustic design.^14–16 The influence of thermomechanical behavior on composite structures’ STL is still a field of sporadic research.

Only a few papers have been reported. In 2013, the temperature-dependent STL was investigated based on statistical energy analysis.¹⁷ Following that, several theoretical models were proposed. Xin¹⁸ created a theoretical model of a simply supported plate and used numerical methods to determine its accuracy and feasibility. Li^19,20 studied sandwich panels’ STL in a thermal environment using the mode superposition method and presented an analytical method for sandwich panels in thermal environments. Then, Zhou²¹ investigated the sound radiation of porous functionally graded material (FGM) plates with a temperature gradient along with the thickness. Recently, Hu²² proposed a semi-analytical model to analyze FGMs’ STL. Meanwhile, an analytical strategy was proposed to determine the thermal load’s effect on STL via parametric studies.²³ In mentioned studies, attention is paid to theoretical derivation and simulation modeling, experimental methods are rarely adopted.

The reason is that the STL analysis of composite structures at varying temperatures is still preliminary. The experimental theory^24–27 is not perfect (thermal instability²⁸ problems), available techniques have not been proposed, and reliable measurement equipment for harsh environments (pull-in instability^29–32 influence) has been developed deficiently. Therefore, theoretical modeling³³ and numerical simulation^17,34 are the most viable options. Moreover, theoretical analyses and simulations are appropriate for studying various composite structures over a wide temperature range and are cost-effective compared to experimentation. Nowadays, in practice, the demand for STL measuring of composite structures has emerged and theoretical/simulation models should be modified via experiments. As a result, developing STL experimental technology under variable temperature environments is critical. Based on SPM and ABM, an improved STL experimental method is proposed in this study to reveal the relationship between temperature, thermomechanical parameters and STL.

The paper is organized as follows: In A Brief Statement of the Improved STL Experiment, Determination of Experimental Methods, Experiment principle, Measurement Objects and Experimental Devices, Measurement Process are introduced. Verification and Analysis of Experimental Results includes Reliability Analysis of Measurement Results, The Analysis of STL at Different Temperatures, Discussion of STL Variation. Finally, Conclusion discusses the concluding remarks and potential applications of the presented work.

A brief statement of the improved sound transmission loss experiment

Determination of experimental methods

As well known, the sound intensity method (SIM),²⁴ SPM,^25,27 and ABM²⁶ are commonly used for experimental measurement of STL in the aviation field.

In SIM, incident/transmitted sound power is measured using the sound intensity probe (Figure 1). To improve measurement efficiency, SPM (Figure 2) is being developed, where sound pressure level (SPL) is used to determine incident/transmitted sound power. However, the experiment cannot be standardized for some cases. Hence, ABM is being developed (Figure 3). Since each method has advantages and disadvantages, it’s difficult to determine which method should be used in this study. So, a comparison of the three methods in Table 1 is given.

Figure 1.

Experimental system of sound intensity method.

Figure 2.

Experimental system of sound pressure method.

Figure 3.

Experimental system of acoustic box method.

Table 1.

Methods comparison.

Method	Advantage	Disadvantage
SIM	Standardized High precision Mature technology	Limited spectral information Time-consuming Potential hearing damage
SPM	Standardized Mature technology Engineering application friendly Spectrum information completeness	Precision lower than SIM Measurement correction
ABM	Actual application status Mature technology Engineering application friendly	Relatively low precision Not standardized

SIM: sound intensity method; SPM: sound pressure method; ABM: acoustic box method.

Considering the aforementioned comparison, the principle of SPM should be adopted. Based on existing experimental conditions, the design idea of ABM is applied.

Experiment principle

To introduce SPM’s principle, whose model has been shown in Figure 2, this section is given. It was assumed that the specimen was the only source-to-receiving sound transmission path. A diffusion sound field was created in the source room, then sound waves were randomly incident on the specimen, forcing the specimen to radiate sound. Sound energy density $D_{1}$ in the source room is

D_{1} = \frac{4 W}{c r_{1}}

(1)

where

W

is source sound power,

c

is the sound velocity in air, and

r_{1}

is the room constant of the reverberation chamber. Incident sound power is given as

W_{1} = \frac{1}{4} D_{1} c S_{1}

(2)

S₁ is specimen area; thus, the transmission coefficient

τ

τ = \frac{W_{1}}{W_{2}}

(3)

Transmitted sound power $W_{2}$ is

W_{2} = τ W_{1} = \frac{1}{4} τ D_{1} c S_{1}

(4)

Then

S T L = 10 \log_{10} (\frac{1}{τ})

(5)

Sound energy density $D_{2}$ in the receiving room is.

D_{2} = \frac{W_{2}}{c} (\frac{1}{S_{1}} + \frac{4}{r_{2}})

(6)

r₂ is the room constant of the receiving room. Considering the relationship between sound energy density

D

and effective sound pressure

p_{e}

in equation (7), we would find the SPL.

D = \frac{p_{e}^{2}}{ρ c^{2}}

(7)

L = 20 \log_{10} \frac{p_{e}}{p_{r e f}}

(8)

L is SPL,

p_{r e f}

is the reference sound pressure, and

p_{r e f} = 2 \times 10^{- 5} Pa

By substituting equations (3), (4), (6)–(8) into equation (5), the STL is calculated as

S T L = L_{r} - L_{t} + 10 \log_{10} (\frac{1}{4} + \frac{S_{1}}{r_{2}})

(9)

L_r is the effective sound pressure in the source room and

L_{t}

is the effective sound pressure on the specimen surface in the receiving room.

r_{2}

is the room constant of the receiving room.

r_{2} = \frac{S_{2} α_{2}}{1 - α_{2}}

(10)

S₂,

α_{2}

are the indoor surface area and absorption coefficient of the receiving room, respectively.

In equation (9), $L_{r}$ and $L_{t}$ can be measured directly. Next to solve equation (10). In anechoic chambers, $α_{2} < 1$ , $S_{1} ≪ S_{2}$ . So, $S_{1} / r_{2} \approx 0$ , then $10 \log_{10} (1 / 4 + S_{1} / r_{2}) \approx - 6$ . Thus equation (9) is simplified to

S T L = L_{r} - L_{t} - 6

(11)

In semi-anechoic chambers, $α_{2} < 1$ , which should be measured. In practice, to get accurate results, the standard specimen method is often used to modify $10 \log_{10} (1 / 4 + S_{1} / r_{2})$ (as shown in Step 1, Measurement Process). $L_{t} - 10 \log_{10} (1 / 4 + S_{1} / r_{2})$ is represented by the corrected average effective SPL $\bar{L_{t}^{'}}$ ; $L_{r}$ is represented by the average effective SPL $\bar{L_{r}}$ . Then equation (9) is simplified as

S T L = {\bar{L}}_{r} - {\bar{L}}_{t}^{'}

(12)

In equation (12), the near field is ignored and assuming that the correction parameter does not vary with temperature. During measuring, microphones were arranged at $k$ selected positions in the source room; Microphone Array 1 was placed at the optimal measurement distance $d_{o p}$ in the receiving room. $\bar{L_{r}}$ and $\bar{L_{t}'}$ are calculated by equation (13).

\bar{L} = 10 \log_{10} \frac{1}{k} \sum_{i = 1}^{k} 10^{0.1 L_{p i}}

(13)

L_pi is SPL at the i-th measurement position.

Measurement objects and experimental devices

In order to investigate the temperature effect on composite structures’ STL via experiments, the experimental system shown in Figure 4 was proposed based on SPM and ABM. A ribbed reinforced CFRP aircraft panel (Figure 5) and an environmental simulator device (Figure 6) were designed and then manufactured. Table 2 shows the properties of monolayer CFRP.

Figure 4.

Scheme of the experimental system.

Figure 5.

Model of the panel (Oxyz: global coordinate; O’123: local coordinate; Panel size: 2240 mm × 1560 mm × 4 mm; Skin layer: [45/0/−45/90]_4s). (a)Front (b) Back and (c) Relationship between local and global coordinate of monolayer carbon fiber reinforced plastics in the skin.

Figure 6.

The environmental simulator device. Indicators: External size: 4520 mm × 2950 mm × 2700 mm; Internal size: 3000 mm × 2500 mm × 1800 mm; Controllable temperature range: −55°C–90°C; Fluctuation: ±0.5°C; Accuracy: ±0.1°C; Uniformity: ±2°C; 25°C –−50°C time loss: ≤70 min; 25°C–85°C time loss: ≤30 min; Controllable humidity range: 30%–98%; Walls’ sound insulation: ≥40 dB.

Table 2.

Properties of monolayer carbon fiber reinforced plastics material (25°C).

E₁ (GPa)	E₂ (GPa)	E₃ (GPa)	G₁₂ (GPa)	G₁₃ (GPa)	G₂₃ (GPa)	ν₁₂	ν₁₃	ν₂₃
122	8.91	8.91	4.16	4.16	3	0.31	0.31	0.45

Note. E₁−Longitudinal modulus; E₂, E₃−Transverse modulus; G₁₂, G₁₃, G₂₃−Shear modulus; ν₁₂, ν₁₃, ν₂₃−Poisson’s ratio.

One of the inner walls of the device was designed with a window to install the specimen, and the others were designed with cylindrical reflectors to ensure the diffusion sound field could be generated. The device performed temperature control and humidity adjustment to meet STL experimental requirements under variable temperatures.

Before measurements, the system shown in Figure 4 was constructed. The device was placed in a semi-anechoic chamber. The panel was installed in the window, and the boundaries were clamped and sealed. The device’s reverberation chamber functioned as a source room, where white noise generated by a loudspeaker was used to excite the diffusion sound field. Figures 7 and 8 show experimental status in the source and receiving rooms. The measurement process is given in Measurement Process.

Figure 7.

Internal measuring points arrangement and speaker position.

Figure 8.

Position of external measuring points and installation status of measuring parts.

Measurement process

According to Determination of Experimental Methods, Experiment Principle and Measurement Objects and Experimental Devices, the measurement process shown in Figure 9 was designed. During experiments, it was assumed that all equipment operate stably. To avoid pull-in instability,^29–32 electronic instruments were protected and maintained regularly.

Figure 9.

Measurement process.

Step 1: Determination of optimal measurement distance d_op

First, at room temperature, STL ( $S T L_{0}$ ) was measured via SIM and calculated using equations (13) and (14).

S T L_{0} = \bar{L_{r}} - L_{t I} - 6

(14)

L_tI is the transmitted sound intensity level.

Then, in the receiving room, the measurement distance $d$ between Microphone Array 1 and the panel was set as $d_{1}$ (usually d₁ = 10 cm), STL ( $S T L_{1}$ ) was measured via SPM and calculated by equations (12) and (13).

Next, setting $d$ to $d_{2}$ ( $d_{2} = d_{1} + Δ d$ , $Δ d = 5 cm$ ), STL ( $S T L_{2}$ ) was measured again using SPM. This measurement was repeated until $d = d_{n} = 1 m$ ( $d_{n} = d_{n - 1} + Δ d$ ), corresponding result was marked as $S T L_{n}$ .

Finally, all results were plotted in one graph to find out the STL curve which was consistent with STL₀’s, the calculation method is given as equations (15) and (16).

χ_{n}^{2} = \frac{1}{N} \sum_{r = 1}^{N} {[S T L_{0} (f_{r}) - S T L_{n} (f_{r})]}^{2}

(15)

χ_{n}^{2}

is the mean square deviation,

f_{r}

is the center frequency, and

N

indicates center frequency number.

χ_{o p}^{2} = M i n {χ_{1}^{2}, χ_{2}^{2}, χ_{3}^{2}, \dots, χ_{n}^{2}}

(16)

d_op was determined by

χ_{o p}^{2}

Step 2: Control of target temperature

Before controlling the temperature, the panel and source room were sealed with adiabatic devices. Then, the temperature control-monitoring system was turned on to heat or cool the reverberation field until the target temperature $T$ was achieved. To mitigate the effects of temperature shock³⁵ and instability,³⁶ temperature sensors were arranged on both surfaces of the panel. After temperatures (T_i, T₀) on both surfaces were consistent with $T$ ( $T_{i} \approx T$ , $T_{o} \approx T$ ), keep the temperature for a while (>0.5 h) to meet the experiment state. The judgment criterion was $Δ T_{i} \leq 0.5 ° C$ , $Δ T_{o} \leq 0.5 ° C$ .

Step 3: The measurement of sound pressure level

In the source room, the loudspeaker was turned on to excite the diffusion sound field, which was monitored via Microphone Array 2 (comprising $k$ microphones, the position sequence is $s_{0}, s_{1}, \dots, s_{k - 1}, s_{k}$ ). To determine whether the sound pressure was stable, the stability analysis was performed, which is similar to step 1.

For each microphone, mark the time series as $t_{0}, t_{1}, \dots, t_{m - 1}, t_{m} (t_{m - 1} < t_{m})$ , the SPL measured at $t_{m}$ was denoted as $S P L_{m}$ . Judgment criterion was

Δ χ_{m}^{2} = χ_{m}^{2} - χ_{m - 1}^{2}, χ_{m}^{2} = \frac{1}{N} \sum_{r = 1}^{N} {[S P L_{m - 1} (f_{r}) - S P L_{m} (f_{r})]}^{2}

(17)

χ_{m}^{2}

is the mean square deviation between

S P L_{m}

and

S P L_{m - 1}

. Once

Δ χ_{m}^{2} \approx 0

, the sound field is considered to be stable.

Then, the incident SPL was measured, and the radiated SPL was tested at $d_{o p}$ .

Step 4: Analysis of measurement data

Above all, uniformity analysis and repeatability analysis were performed to ensure the reliability of the measured data. The uniformity analysis was used to determine whether the sound field was uniform and it was performed after the sound field was stabilized. The procedure was the same as for the stability analysis. Just convert the time series, $S P L_{m - 1}$ and $m$ to the position series, $S P L_{0}$ (SPL measured at $s_{0}$ ) and $k$ . The repeatability analysis determined whether the experimental results were valid. The procedure was the same as for the stability analysis. Set the sequences of multiple independent STL measurement results as $a_{0}, a_{1}, \dots, a_{p - 1}, a_{p}$ , and mark the a_p-th measurement result as $S T L_{p}$ . Next, repeatability analysis could be done by equation (17). In practice, measured results are usually drawn in one figure and compared directly.

Then, the error analysis was performed to verify the effectiveness of the improved STL experimental method. First, STL was calculated by equation (12). Second, the overall STL $L_{T}$ was obtained by equation (18). Third, equation (19) was employed to solve the STL range $R a n g e (f_{r})$ at $f_{r}$ (See Reliability Analysis of Measurement Results for detailed examples).

L_{T} = 10 \log_{10} \sum_{r = 1}^{N} 10^{0.1 L_{p r}}

(18)

L_pr is STL at r-th 1/3 octave band.

R a n g e (f_{r}) = M a x {S T L (f_{r})} - M i n {S T L (f_{r})}

(19)

M a x {S T L (f_{r})}

M i n {S T L (f_{r})}

represent the maximum and minimum STL at

f_{r}

Verification and analysis of experimental results

After the preparations were all completed, STL measurements of the panel under variable temperatures were performed according to Measurement Process. Considering the potential ambient temperature of the panel being in −25°C–30°C and the temperature simulation capacity of the device, the temperature range of measurement was determined as −40°C–40°C. The temperature interval was set to 5°C, the sampling frequency band was 50 Hz–10,000 Hz, and the recording time was 30 s. The maximum background SPL was 44.6 dB.

Reliability analysis of measurement results

The reliability of the improved STL experimental technique is discussed first. Figure 10 depicts the results of the uniformity analysis; Figures 11 and 12 show the results of the repeatability analysis, while Figure 13 illustrates the difference between the proposed and standard laboratory methods.

Figure 10.

Reverberation chamber sound pressure level at six uniformly distributed spatial measuring points (25°C).

Figure 11.

Repeated experiments at −40°C on June 10, 12, and 13, 2018.

Figure 12.

Repeated experiments at 40°C on June 11, 12, and 13, 2018.

Figure 13.

STL comparison between the standard and improved STL experiments. STL: sound transmission loss.

Figure 10 shows that all SPL spectra were consistent with each other, indicating that the diffusion sound field was uniform. SPL ≥ 60 dB within 50 Hz–100 Hz and SPL ≥ 90 dB within 100 Hz–10,000 Hz, proving that the SPL met the measurement standard.^24,25,27 The principle can be used to guide the functional identification and modification of equipment.

As shown in Figures 11 and 12, STL results were similar, indicating the good repeatability of experiments at −40°C and 40°C. The same conclusion could be obtained at other temperatures within −40°C–40°C, meaning that the repeatability of the experiment was good. The method can also be used to validate the assumption in Measurement Process. When there is a significant deviation in data, devices must be overhauled.

Figure 13 shows that the error between the standard and improved STL experiments was within 50 Hz–100 Hz, which was caused by the environmental simulator device. The reverberation chamber of the device was too small to reach the ideal state in low frequency. The results should be corrected before use. The deviation was small in 125 Hz–10,000 Hz, demonstrating that the results measured via the improved STL technique were accurate and reliable within these bands. To obtain accurate results, equation (20) was given.

ε = S T L_{standard} - S T L_{present}

(20)

ε

is corrected value,

S T L_{present}

is STL measured via the improved method, and

S T L_{standard}

is STL obtained by the standard laboratory measurement. Introducing equation (20) into equation (12), accurate STL expression equation (21) was obtained.

S T L = \bar{L_{r}} - \bar{L_{t}^{'}} + ε

(21)

The mentioned methods can be used in the development of acoustic experiments.

The analysis of STL at different temperatures

After making sure the measurements are reliable and accurate, the existence of temperature influence on the panel’s STL is confirmed. The range of STL at each center frequency was solved by equation (19) and listed in Table 3.

Table 3.

Measurement results of sound transmission loss.

1/3 octave (Hz)	STL interval (dB)	Range (dB)	1/3 octave (Hz)	STL interval (dB)	Range (dB)
50	[1.636, 13.867]	12.23	800	[25.436, 27.586]	2.15
63	[13.617, 22.184]	8.57	1000	[27.666, 29.810]	2.14
80	[13.418, 20.215]	6.80	1250	[28.758, 30.001]	1.24
100	[16.562, 20.977]	4.41	1600	[28.890, 30.407]	1.52
125	[20.716, 23.343]	2.63	2000	[29.827, 31.542]	1.72
160	[19.013, 20.801]	1.79	2500	[29.456, 32.283]	2.83
200	[17.847, 24.576]	6.73	3150	[29.114, 32.517]	3.40
250	[23.408, 26.172]	2.76	4000	[29.701, 32.251]	2.55
315	[20.356, 25.642]	5.29	5000	[29.631, 30.819]	1.19
400	[14.381, 19.918]	5.54	6300	[30.144, 32.446]	2.30
500	[18.804, 20.217]	1.41	8000	[32.776, 35.953]	3.18
630	[23.110, 24.038]	0.93	10,000	[34.913, 38.139]	3.23

STL: sound transmission loss.

Three conclusions can be drawn from Table 3: I) Temperature significantly affected the STL of the panel. Once the panel was immersed in different temperature environments, the STL changed. II) STL temperature sensitivity was different at each center frequency. The range at 50 Hz, 63 Hz, 80 Hz, 100 Hz, 200 Hz, 315 Hz, 400 Hz, 3150 Hz, 8000 Hz, and 10,000 Hz was >3 dB, and it was 1–2 dB at others. III) Overall, the panel’s STL was most affected by temperature at low/high frequencies and less in middle frequency. Conclusions I)–III) show that STL measurement at room temperature is insufficient for composite structures and it is necessary to study STL at various temperatures. The proposed STL experimental technique is a good choice.

Since Table 3 cannot visually reveal the variation of the panel’s STL with temperature, Figures 14–17 and Appendix A are given. These figures exhibit that temperature had a severe impact on the STL variation trend of the panel, mainly including monotonicity and fluctuation. The monotonically increasing trend appeared at 2500 Hz (Figure 16), 3150 Hz (Figure 27), and 4000 Hz (Figure 28); the monotonically decreasing trend appeared at 6300 Hz (Figure 17), 8000 Hz (Figure 31), and 10,000 Hz (Figure 32); fluctuation trend appeared at other center frequencies. These trends suggest that the acoustic design of CFRP structures at room temperature may fail. A solution is: I) Finding out the temperature $T_{\min}$ where the minimum STL is; II) Noise reduction scheme design at $T_{\min}$ .

Figure 14.

The relationship between sound transmission loss and temperature at 125 Hz.

Figure 15.

The relationship between sound transmission loss and temperature at 315 Hz.

Figure 16.

The relationship between sound transmission loss and temperature at 2500 Hz.

Figure 17.

The relationship between sound transmission loss and temperature at 6300 Hz.

Due to STL variation trends being different at different center frequencies, the overall STL ( $L_{T}$ ) was applied to describe the temperature effect on the panel’s STL (Figure 18).

Figure 18.

L_T with temperature.

Figure 18 shows that $L_{T}$ fluctuated with temperature, temperatures of −15°C and 15°C were the extreme points of change. $L_{T}$ increased within −40°C−15°C and 15°C–40°C and decreased within −15°C–15°C. The smallest $L_{T}$ appeared at −40°C and 15°C. The results have application in the noise reduction design of composite structures. Noise reduction schemes, for example, should be designed at −40°C, 15°C and redesigned when the temperature rises above 40°C or falls below −40°C. Given the laboratory’s limited temperature simulation capability (−55°C–90°C), theoretical modeling or simulation analysis should be used if the temperature simulation capability is insufficient.

Discussion of sound transmission loss variation

STL variation in The Analysis of STL at Different Temperatures was essentially caused by the change of damping loss factor and elastic modulus, with temperature. To illustrate the mechanism, measurement results at 40°C, 0°C, and −40°C were employed, as shown in Figure 19 and Table 4.

Figure 19.

Sound transmission loss measured at −40°C, 40°C, and 0°C.

Table 4.

Distribution of the controlled regions.

Temperature (°C)	Region (Hz)
Temperature (°C)	Stiffness-controlled	Resonance-controlled	Mass-law	Coincidence-controlled	Damping-controlled
40	—	50–400	400–800	800–6300	6,300–10,000
−40	—	50–500	500–800	800–5000	5,000–10,000

Figure 19 and Table 4 show that temperature change led to the redistribution of controlled regions. When the temperature dropped from 40°C to −40°C, the resonance-controlled region expanded to the high frequency, while the coincidence-controlled and damping-controlled regions had an opposite change. The phenomenon was directly caused by the change of STL peak/dip frequencies with temperature. The basic reason is discussed later.

Figure 19 exhibits, in the resonance-controlled region, the maximum STL dip frequency decreased with temperature. Therefore, when the temperature dropped, the resonance-controlled region expanded to a high frequency. The problem was caused by the change in composite stiffness. In Refs. 20,21 and 37, it has been proved that the increased temperature results in decreased composite stiffness, the decreased stiffness produces reduced resonance frequencies, and the reduced resonance frequencies induce the decreasing of STL peak/dip frequencies. Hereby, the reason is verified via experiments shown in Figure 20.

Figure 20.

Measurement of elastic modulus. (a)−55°C (b) 23°C and (c) 71°C.

Considering that elastic modulus is the microscopic reflection of stiffness, the problem is to verify that the elastic modulus of composites would change with temperature. Thus, the mechanical properties of the panel’s skin used in this study were measured at −55°C, 23°C, and 71°C. Results are plotted in Figures 21 and 22. Obviously, the elastic modulus decreased with temperature, indicating the correctness of the above analysis. Changes in elastic modulus are detrimental to composite acoustic design and may fail noise reduction schemes. An adiabatic design of composite structures should be developed to overcome the failure, bionics³⁵ is a potential option.

Figure 21.

Elastic modulus E₁.

Figure 22.

Elastic modulus E₂ (E₂ = E₃).

But it seems different from the conclusions obtained in Refs. 18,19 and 22 that peak/dip frequencies of the panel’s STL did not present a simple decline with temperature. As shown in Figure 19 and Table 5, there were two peak frequencies and two dip frequencies within 100 Hz–630 Hz. The first peak frequency appeared at 125 Hz, which did not change with temperature; the first dip frequency was 200 Hz at 40°C, 0°C, and became 160 Hz at −40°C. These phenomena appear to be distinct from those described in Refs. 18,19 and 22. The data processing method is to blame for these phenomena. Measured data is difficult to analyze because the STL spectra of the panel are not smooth curves. To make the analysis easier, data is filtered by 1/3 octave. Thus, the results in Figure 19 and Table 5 represent the STL within each 1/3 octave band rather than the STL at each frequency point. As a result, the illusion is formed. According to the findings, structural-acoustic design should be done for the frequency band rather than the frequency points, thereby improving the noise reduction effect.

Table 5.

The sound transmission loss peak/dip frequencies in the resonance region.

Temperature (°C)	Peak frequency (Hz)		Dip frequency (Hz)
Temperature (°C)	1st	2nd	1st	2nd
40	125	315	200	400
0	125	250	200	400
−40	125	200	160	500

It can also be found that, when STL peak/dip frequencies did not change with temperature, temperature increase caused a decrease in STL peak value and an increase in STL dip value, in Figure 19 and Table 5. To clearly describe this phenomenon, Figure 23 was given. At 125 Hz (a peak frequency), STL value declined with temperature; conversely, STL value rose at 160 Hz (a dip frequency). The phenomenon was caused by $η$ , the damping loss factor.

Figure 23.

Change in the peak/dip value of sound transmission loss.

The panel was made from CFRP, so its glass transition temperature $T g$ was ≤90°C, which was documented in Ref. 37 (Figure 24). And $η$ increased with temperature when the temperature is below $T g$ , which had been verified (Figure 25).^4,17 Meanwhile, considering that $η$ increase made STL peak values decrease and STL dip values rise(Figure 26)²⁶, the phenomenon in Figure 23 appeared. Further, it explains why the STL of the panel decreased with temperature (Figure 14) within −40°C–−15°C.

Figure 24.

The aging curve of carbon fiber reinforced plastics glass transition temperature.

Figure 25.

The relationship among η, temperature, T_g.

Figure 26.

Sound transmission loss variation with η (η1 < η2 < η3).

In Figure 14, when the temperature continued to increase, the stiffness reduced, then STL peak/dip frequency changed. While $η$ increased with temperature. As a result of the common change of both $η$ and STL peak/dip frequency, STL fluctuation was produced. Changes in Appendix A can also be explained. The fluctuation indicates that the best noise reduction measures should be designed at the temperature where the STL is the lowest.

With further measurements in the coincidence-controlled region, Figures 27 and 28 were plotted. They show that the panel’s STL increased with temperature at 3150 Hz, 4000 Hz, which was caused by $η$ too. Because STL increased with $η$ ²⁶ in the coincidence-controlled region and the panel’s $η$ increased with temperature³⁷. The finding suggests that in the coincidence region, the STL of CFRP panels could be improved by increasing the temperature.

Figure 27.

Relationship between sound transmission loss and temperature at 3150 Hz.

Figure 28.

Relationship between sound transmission loss and temperature at 4000 Hz.

After that, adding data in Figure 19 formed Figure 29. It can be seen that critical frequency $f_{c}$ increased with temperature, which was caused by elastic modulus reduction as the temperature rose (Figures 21 and 22). $f_{c}$ is exhibited in equation (22).

f_{c} = \frac{c^{2}}{2 π h} \sqrt{12 ρ_{m} (1 - ν^{2}) / E}

(22)

where

h

represents the thickness,

ρ_{m}

describes the surface density, and

E

is elastic modulus.

Figure 29.

Critical frequency variation with temperature.

Considering $ν$ was less affected by the temperature (Figure 30), $ρ_{m}$ is constant, $h$ is constant when the effect of thermal expansion and contraction is ignored, and f_c would be proportional to $c^{2} \sqrt{1 / E}$ . As $c$ and $\sqrt{1 / E}$ increase with temperature, so does f_c. Due to f_c increases, the whole damping-controlled region of the panel moves towards the high-frequency band, resulting in decreased STL at each center frequency in the damping-controlled region (Figures 31 and 32). This indicates that temperature rise in the damping-controlled region is detrimental to the acoustic performance of CFRP structures and should be avoided.

Figure 30.

Poisson’s ratio variation with temperature.

Figure 31.

Relationship between sound transmission loss and temperature at 8000 Hz.

Figure 32.

Relationship between sound transmission loss and temperature at 10,000 Hz.

So far, the STL variation mechanism of CFRP structures with temperature has been explained.

Unfortunately, STL variable characteristics of the panel with temperature in the stiffness-controlled region were not observed. This was caused by the panel’s first-order frequency. To validate the reason, an assumption was made, that the first-order frequency was less than 50 Hz, exceeding the lower frequency bound of STL measurements. Then, a modal test was performed. Figure 33 and Table 6 show the current status of the test and result. The result supports the assumption. We can infer that the panel’s STL in the stiffness-controlled region was decreased with temperature. Because in the stiffness-controlled region, STL increased with stiffness²⁶ and the panel’s stiffness decreased with temperature according to Figures 21 and 22.

Figure 33.

Modal test.

Table 6.

Natural frequencies of the panel (20°C).

Mode	1	2	3	4	5
Nature frequency (Hz)	47.94	62.68	76.79	93.96	105.20
Mode	6	7	8	9	10
Nature frequency (Hz)	116.96	150.11	163.93	173.28	193.88

Considering the discussion above, the thermal characteristics of $E$ and $η$ in the acoustic design of composite structures should be focused upon. The relationship between temperature, thermomechanical parameters ( $E$ , $η$ ), and STL can be used in composite structures’ noise control. By temperature control to change $E$ to redistribute controlled regions, the structural sound insulation capacity can be enhanced in some local frequency bands. By temperature control to change $η$ to improve structural STL in resonance, coincidence, and damping-controlled regions. The relationship can also be used for acoustic metamaterial design.

Conclusion

Herein, a novel STL experimental technique was demonstrated. The effect of temperature on the vibroacoustic performance of composite structures was revealed, and the relationship between temperature, thermomechanical parameters, and STL was elucidated. Accordingly, the following conclusions were obtained:

1. The improved STL experimental technique provided a new way for composite structures’ acoustic analysis and was complementary to theoretical modeling and simulation analysis.

2. Temperature had a significant impact on composite structures’ acoustic behavior. The influence was realized by changing temperature-dependent parameters ( $E$ , $η$ ). It can be inferred that this phenomenon is common in composite structures.

3. Findings in this paper can be used to guide the acoustic design of composite structures in vehicle manufacturing, shipping industry, environmental protection, etc.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data availability

The data used to support the findings of this study are included in the article.

ORCID iD

Tao Peng

Appendix

STL variations of the panel with the temperature at the other center frequencies are presented as follows:

(a) Relationship between STL and temperature at 50 Hz. (b) Relationship between STL and temperature at 63 Hz. (c) Relationship between STL and temperature at 80 Hz. (d) Relationship between STL and temperature at 100 Hz. (e) Relationship between STL and temperature at 160 Hz. (f) Relationship between STL and temperature at 200 Hz. (g) Relationship between STL and temperature at 250 Hz. (h) Relationship between STL and temperature at 400 Hz. (i) Relationship between STL and temperature at 500 Hz. (j) Relationship between STL and temperature at 630 Hz. (k) Relationship between STL and temperature at 800 Hz. (l) Relationship between STL and temperature at 1000 Hz. (m) Relationship between STL and temperature at 1250 Hz. (n) Relationship between STL and temperature at 1600 Hz (o) Relationship between STL and temperature at 2000 Hz. (p) Relationship between STL and temperature at 5000 Hz.

References

Ilcewicz

Smith

Horton

. Advanced composite fuselage technology. Report 4733. Washington, DC: NASA, 1993.

Mcmanus

HLN

Springer

. High temperature thermomechanical behavior of carbon-phenolic and carbon-carbon composites, II. Results. J Compos Mater 1992; 26: 230–255.

Rozenberg

Grishchak

Il’man

. Effect of temperature on the mechanical characteristics of carbon plastics reinforced with metal mesh. Mech Compos Mater 1971; 7: 320–322.

Barker

Vangerko

. Temperature dependent dynamic shear properties of CFRP. Composites 1983; 14: 141–144.

Dimitrienko

. Thermomechanical behaviour of composite materials and structures under high temperatures: 1. Materials. Compos A Appl Sci Manuf 1997; 28: 453–461.

Dimitrienko

. Thermomechanical behaviour of composite materials and structures under high temperatures: 2. structures. Compos Part A Appl Sci Manuf 1997; 28: 463–471.

Talebitooti

Daneshjou

Kornokar

. Three dimensional sound transmission through poroelastic cylindrical shells in the presence of subsonic flow. J Sound Vib 2016; 363: 380–406.

Talebitooti

Zarastvand

. The effect of nature of porous material on diffuse field acoustic transmission of the sandwich aerospace composite doubly curved shell. Aerosp Sci Technol 2018; 78: 157–170.

Wan

Liu

, et al. Transmission characteristics and mechanism study of hydrodynamic and acoustic pressure through a side window of driver model based on modal analytical approach. J Sound Vib 2021; 501: 116058.

10.

Liu

Daudin

. Analytical modelling of sound transmission through finite clamped double-wall sandwich panels lined with poroelastic materials. Compos Struct 2017; 172: 359–373.

11.

Proena

Sousa

Garrido

, et al. Acoustic performance of composite sandwich panels for building floors: experimental tests and numerical-analytical simulation. J Build Eng 2020; 32: 101751.

12.

Sui

Cong

, et al. Preparation and sound transmission loss analysis of carbon fiber composite sandwich panel. Nanotechnol Environ Eng 2021; 6: 52.

13.

Magliacano

Petrone

Franco

, et al. Numerical investigations about the sound transmission loss of a fuselage panel section with embedded periodic foams. Appl Acoust 2021; 182: 108265.

14.

Yuan

Z-X

Xiao

. Sound transmission loss of double-layered structure plates and pasted damping. J Braz Soc Mech Sci Eng 2021; 43: 1–12.

15.

Liu

. Analytical modelling of acoustic transmission across double-wall sandwich shells: effect of an air gap flow. Compos Struct 2016; 136: 149–161.

16.

Dragonetti

Napolitano

Boccarusso

, et al. A study on the sound transmission loss of a new lightweight hemp/bio-epoxy sandwich structure. Appl Acoust 2020; 167: 107379.

17.

Chronopoulos

Ichchou

Troclet

, et al. Thermal effects on the sound transmission through aerospace composite structures. Aerosp Sci Technol 2013; 30: 192–199.

18.

Xin

F-X

Gong

J-Q

Ren

S-W

, et al. Thermoacoustic response of a simply supported isotropic rectangular plate in graded thermal environments. Appl Math Model 2017; 44: 456–469.

19.

Zhao

, et al. Sound transmission loss of composite and sandwich panels in thermal environment. Compos B Eng 2018; 133: 1–14.

20.

Zhao

. Vibro-acoustic response of a clamped rectangular sandwich panel in thermal environment. Appl Acoust 2018; 132: 82–96.

21.

Zhou

Lin

Huang

, et al. Vibration and sound radiation analysis of temperature-dependent porous functionally graded material plates with general boundary conditions. Appl Acoust 2019; 154: 236–250.

22.

Zhou

Huang

, et al. Sound transmission analysis of functionally graded material plates with general boundary conditions in thermal environments. Appl Acoust 2020; 174: 107795.

23.

Rahmatnezhad

Zarastvand

Talebitooti

. Mechanism study and power transmission feature of acoustically stimulated and thermally loaded composite shell structures with double curvature. Compos Struct 2021; 276: 114557.

24.

ISO 9614-2:1996 . Acoustics-Determination of sound power levels of noise sources using sound intensity-Part 2: measurement by scanning.

25.

ISO 3741:2010 . Acoustics-Determination of sound power levels and sound energy levels of noise sources using sound pressure-Precision methods for reverberation test rooms.

26.

Yao

Q-H

. Aircraft noise engineering. 1st ed. Xi’an, China: Northwestern Polytechnical University Press, 1998, pp. 50–86. (in Chinese).

27.

ISO 3745:2012 . Acoustics-Determination of sound power levels and sound energy levels of noise sources using sound pressure-Precision methods for anechoic rooms and hemi-anechoic rooms.

28.

J-H

Moatimid

Sayed

. Nonlinear EHD instability of two-superposed walters’ B fluids moving through porous media. Axioms 2021; 10: 258.

29.

Tian

Ain

Anjum

. Fractal N/MEMS: from pull-in instability to pull-in stability. Fractals 2020; 9: 2150030.

30.

Anjum

J-H

Ain

QT.

, et al. Li-He’s modified homotopy perturbation method for doubly-clamped electrically actuated microbeams-based microelectromechanical system. Facta Univ Ser Mech Eng 2021; 19: 601. DOI: 10.22190/FUME210112025A.

31.

Tian

C-H

J-H

. Fractal pull-in stability theory for microelectromechanical systems. Front Phys 2021; 9: 606011.

32.

Anjum

J-H

. Nonlinear dynamic analysis of vibratory behavior of a graphene nano/microelectromechanical system. Math Methods Appl Sci 2020. Epub ahead of print. DOI: 10.1002/mma.6699.

33.

Abouelregal

Sedighi

Faghidian

, et al. Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load. Facta Univ Ser Mech Eng 2021; 19: 633–656.

34.

Pacheco-Chérrez

Cárdenas

Probst

. Measuring crack-type damage features in thin-walled composite beams using de-noising and a 2d continuous wavelet transform of mode shapes. J Appl Comput Mech 2021; 7: 355–371.

35.

Liu

Zhang

C-H

, et al. Thermal oscillation arising in a heat shock of a porous hierarchy and its application. Facta Univ Ser Mech Eng 2021. Epub ahead of print. DOI: 10.22190/FUME210317054L.

36.

J-H

Abd-Elazem

. Insights into partial slips and temperature jumps of a nanofluid flow over a stretched or shrinking surface. Energies 2021; 14: 6691.

37.

Huang

Y-Q

Zhang

K-Z

Wang

X-J

. Resist to thermal and wetting aging research on T700 carbon fiber composite. Hi-Tech Fiber & Appl 2006; 31: 19–21 (in Chinese).

Analysis of sound transmission loss characteristics of aircraft composite panel under variable temperature environment

Abstract

Keywords

Introduction

A brief statement of the improved sound transmission loss experiment

Determination of experimental methods

Experiment principle

Measurement objects and experimental devices

Measurement process

Step 1: Determination of optimal measurement distance d op

Step 2: Control of target temperature

Step 3: The measurement of sound pressure level

Step 4: Analysis of measurement data

Verification and analysis of experimental results

Reliability analysis of measurement results

The analysis of STL at different temperatures

Discussion of sound transmission loss variation

Conclusion

Footnotes

Declaration of conflicting interests

Funding

Data availability

ORCID iD

Appendix

References

Step 1: Determination of optimal measurement distance d_op