A simulation study on the influence of aircraft panel thickness on the cabin sound quality Zhenjing Miao Institute of Vibration Shock and Noise, State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University 800 Dongchuan Road, Minhang District, Shanghai, China Yu Huang 1 Institute of Vibration Shock and Noise, State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University 800 Dongchuan Road, Minhang District, Shanghai, China

ABSTRACT Currently, noise control aims to optimise the psychoacoustic characteristics of aircraft interior noise to improve comfort and security during a flight. This study investigates the influence of trans- mission loss of aircraft panels on the sound quality of the cabin. We established an aircraft cabin acoustic model based on the statistical energy analysis method. The psychoacoustic metrics (i.e., loudness, sharpness, roughness, articulation index, and psychoacoustic annoyance) were simulated with the varying thickness of the aluminum alloy layer. Results showed that loudness and roughness significantly reduced, whereas sharpness increased with increasing thickness. The psychoacoustic annoyance also declined as the thickness increased. However, the articulation index appeared a sud- den drop when the thickness increased.

Keywords: Aircraft cabin noise, Transmission loss, Aircraft panel, Psychoacoustic parameters, Sound quality

1. INTRODUCTION

Aircraft cabin noise impacts passenger comfort and communication [1-2]. The source, transmis- sion path and control techniques of aircraft noise have been studied [3-7]. It shows that jet noise and the turbulent noise on the fuselage are two primary outside sources of aircraft cabin noise [4-7]. As the vibration of the turbofan engine is transmitted to the fuselage, the vibroacoustic radiation is gen- erated from the fuselage [4]. The pressure fluctuation on the turbulent boundary layer can also lead to the vibration of the fuselage outer skin and the vibroacoustic radiation [7]. Optimizing the aircraft panel structure effectively reduces the aircraft cabin noise originating from the vibroacoustic radiation [8-10]. Based on the SEA, Hu [9] confirmed that an acoustic treatment on the aircraft panel can lead to a 2 dB decrease in sound pressure level (SPL) of the cabin. Liu’s [10] result showed that SPL of the cabin can decrease by 27dB(A) with the use of damping material and acoustic packaging on air- craft panel compared to without acoustic treatment.

The evaluation indicator of most traditional measures for noise reduction is A-weighting SPL. Otherwise, people’s subjective sense of hearing is not only decided by the energy level of noise. Besides loudness, the strident high frequency component of noise and varying speed of noise energy

1 Corresponding email address: yu_huang@sjtu.edu.cn

in time domain and frequency domain also have an important effect on it [11-12]. For instance, Ber- glund demonstrated that people’s annoyance reaction to low-frequency noise is much stronger than that to high-frequency noise despite the same A-weighting SPL of the two kinds of noise [13]. Now- adays, although the energy of aircraft cabin noise can be reduced to a certain level, the annoyance caused by cabin noise still exist. Consequently, using A-weighting SPL as the evaluation indicator cannot satisfied the requirement of a comfortable aircraft cabin acoustic environment.

Evaluating sound quality in transport, vehicle, household appliance, and other fields is becoming widespread. Blauert defined sound quality as “the anthropic appropriateness of sounds under a spe- cific technical target or task” [14]. Its indicators include loudness, sharpness, roughness, fluctuation strength (FS), articulation index (AI) and other psychoacoustic metrics. The sound quality metrics (SQMs) describe the sensation of intensity, timbre and relatively quick changes produced by modu- lation frequencies [15] and the “effective proportion of the normal speech signal which is available to a listener for conveying speech intelligibility” [16]. The psychoacoustic annoyance (PA), describ- ing the psychoacoustic elements of annoying sound [15], is the subjective evaluation indicator com- monly used in psychoacoustic. There have been some studies on the SQMs and annoyance in aircraft cabin design. Quehl [1,17] investigated the effects of aircraft interior noise on passenger based on subjective comfort. Deng [18] analyzed the typical noise reduction measures in a helicopter cabin based on sound quality.

This study aims to set up the simulation method to analyze the influence of the acoustic design parameters on sound quality and PA in the aircraft cabin. We selected the aircraft panel thickness, an essential factor of sound transmission loss of aircraft panels, as the acoustic design parameters to accomplish the analysis. Firstly, we established an aircraft cabin acoustic model based on the SEA and the application programming interface (API) of VA one. Secondly, we calculated the psychoa- coustic metrics (i.e., loudness, sharpness, roughness, FS, AI, and PA) with the varying thickness of the aluminium alloy layer. Finally, we analyzed the influence of the thickness of the aluminium alloy layer on the psychoacoustic metrics.

2. METHOD

Based on the SEA, we used VA One to establish the acoustic model of a civil aircraft cabin. The excitation we used is the outer fuselage panel noise measured in an experiment. We employ MATLAB to extend the function of VA One by taking advantage of API. The extended functionality can simulate the psychoacoustic metrics with varying thickness of the aluminium alloy layer.

2.1. Aircraft cabin SEA acoustic model

SEA is a calculation method to predict the high-frequency energy flow between subsystems of a complex and coupled system [19]. The advantages of SEA are its fast calculation speed and accurate results. As for the system with plenty of medium-frequency and high-frequency resonant modals, both finite element analysis (FEA) and boundary element method (BEM) will be limited by the cal- culation speed and capacity when used to attain the response of the system. Therefore, SEA is a more suitable method to obtain the results of aircraft cabin noise, the excitation of which is high-frequency, broadband and random.

Equation 1 is the power flow equilibrium matrix of an acoustic-structure coupled system of N subsystems [19].

 − −      

  

...

E

1 1 21 1 1

a N

       − −       =      

   

...

E

2 12 2 2 2

a N c

1 , ( )

... ... ... ... ...

      − −         

  

...

E

1 2

N N Na N N

where 𝜔 𝑐 is the centre frequency of a frequency band, Π 𝑖 is the average power flow of the ith subsys- tem, 𝐸 ത 𝑖 is the average stored energy of the ith subsystem, 𝜂 𝑖𝑗 ( 1 < 𝑖, 𝑗< 𝑁 , and 𝑖≠𝑗 ) is the coupling loss factor between the ith subsystem and jth subsystem and 𝜂 𝑖𝑎 is the total loss factor of the i th subsystem.

𝜂 𝑖𝑎 is defined in Equation 2:

N

+  2 , ( )

  

1 =

ia i ij j j i

= 

where 𝜂 𝑖 is the damping loss factor of the ith subsystem.

VA One is the simulation software integrating SEA, FEA and BEM. The two crucial problems in using SEA to stimulate the acoustic model are the principles of dividing a system and the value of coupling loss factor and damping loss factor of each subsystem. The subsystem is an energy element which has similar vibration modal in frequency domain. To reduce the error caused by the average statistical treatment, the modal density under the target frequency band of each subsystem should be high enough. VA One will give out the damping loss factor according to the geometric parameters and material we set in each subsystem [20]. The coupling loss factor will be calculated according to the junction between subsystems in VA One, which requires us to divide the system and set junctions reasonably.

Figure 1: The Exploded view of aircraft cabin SEA acoustic model

Based on the SEA subsystem division principle [19], the aircraft cabin was divided into 119 SEA subsystems in Figure 1. There are 110 structural subsystems and nine cavity subsystems. The amount, material, geometric type, physical property and noise control treatment (NCT)of each subsystem are listed in Table 1.

Table 1: The information about the subsystems of aircraft cabin SEA acoustic model

Subsystem Amount Material Geometric Type Physical Property NCT

Double curved

General laminate with

Cockpit plate 4 Al7075

shell or singly

a damping layer None

curved shell

Passenger cabin plate 4 Al7075 Singly curved shell General laminate with

a damping layer None

Fuselage plate 6 Al7075 Singly curved shell General laminate with

a damping layer None

Double curved

Sound absorp-

Luggage com-

partment 6 Polycarbonate

shell or singly

Uniform

tion of glass

curved shell

wool Outer window

28 Glass Singly curved shell Uniform Sound absorp-

of passenger

tion of glass

cabin

Inner window

28 Glass Singly curved shell Uniform Sound absorp-

of passenger

tion of glass

cabin

Window of

cockpit 1 Glass Double curved

shell Uniform Sound absorp-

tion of glass

Sound absorp-

Trim panel 3 Polycarbonate Singly curved shell Uniform

tion of glass

wool

Sound absorp-

Luggage com- partment plate 16 Polycarbonate Plate Uniform

tion of glass

wool

Cabin floor 4 Al7075 Plate Uniform None

Bulkhead 10 Al7075 Plate Uniform None

Air cavity 9 Air Cavity None None The aircraft panel consisting of fuselage plates, trim panel and the air layer is the main structure for sound insulation. General laminate with a damping layer, the typical structure in aeronautics and astronautics, is used as the fuselage plate. The top and bottom layers are aluminium alloy, and the middle layer is viscoelastic damping material. The middle surface of the damping layer coincides with the middle surface of the laminated plate. The design parameter set in the model is the thickness of the aluminium alloy layer. The total thickness of fuselage plates is invariant.

Table 2: Boundary condition of SEA cavity under different configurations in VA One [20]

SEA Cavity Configuration Boundary Condition

No connection or treatment Rigid, fully-reflective boundaries

NCT on a face Impedance boundary, partial reflection

Connection to an acoustic subsystem Open, non-reflection boundary

Connection to a structural subsystem Flexible boundary

The line junctions between structural subsystems are rigid, which means their boundary is a series of rigid joints to convey vibration and energy. The cavity subsystems and the structure subsystems are connected with area junctions. VA One can judge the acoustic boundary condition according to the junction type between subsystems. The judgements of VA One is shown in Table 2.

The measured outer fuselage panel noise in an experiment is located in the middle section of the cabin and near the wings. Since we use it as the excitation of the aircraft SEA acoustic model, the excitation should be set at the corresponding position. There are two diffuse acoustic fields on the left side and the right side of the panel surface near the 13th row of seats in Figure 2. The frequency spectrum of cabin noise can be obtained in the solution of the model.

The connection area of diffuse acoustic field

Figure 2: the diffuse acoustic field on the aircraft panel surface

2.2. Extended functionality of VA One

The core of VA ONE consists of a database and a computational engine[21]. The database stores all the data necessary to represent the model, and the computational engine is responsible for the mathematical operations performed during software operation[21]. The API provides access to the core of VA One.

MATLAB was used in the extended functionality of VA One to calculate psychoacoustic metrics with varying thickness of the aluminium alloy layer. The processing shown in Figure 3 is following: (1) establish the connection between MATLAB and VA One by opening the client connection; (2) initialize the API; (3) obtain the pointer associated with a new database to access the database of the aircraft cabin SEA acoustic model; (4) find the design parameter in the model and assign its value. (5) invoke the computational engine to solve the model; (6) read the simulated result of the target cavity subsystem; (7) calculate the psychoacoustic metrics according to the spectrum. The above procedures were realized by running the MATLAB scripts consisting of API functions. The API functions used in this study are listed in Table A of the appendix.

Start

Open client connection

Initialize the API

Access the database of the aircraft

cabin SEA acoustic model

Set value of the design parameter

Solve

Read results

Calculate the psychoacoustic metrics

End

Figure 3: the processing of VA One extended functionality

2.3. Calculation of psychoacoustic metrics

Loudness describes the sensation of sound intensity. The loudness of the simulated aircraft cabin noise was calculated based on the Zwicker loudness model standardized in ISO532B. The main cal- culation procedures are following: (1) pressure spectrum transfers from the one-third octave to critical bands; (2) SPLs are corrected according to the transmission characteristics of the ear; (3) specific loudness of each critical band is calculated according to specific loudness figures; (4) total loudness is obtained from the integration of specific loudness.

Sharpness describes the proportion of the high-frequency components. It reflects the subjective sensation of high-frequency sound. At present, the calculation model of sharpness has not been stand- ardized. Aures sharpness model was used in this study. This model is described in Equation 3:

24Bark '

N  , 3 ( )

0 ( ) =0.11 acum N g z zdz S

where 𝑆 is the sharpness, 𝑁 is the loudness, 𝑁 ′ is the specific loudness of each critical band and 𝑔(𝑧) is the weighting factor of each critical band.

The value of the weighting factor can be determined by Equation 4:

0.171 ( ) 0.078

z e N g z N =

4 , ( )

+

lg( 1) 20

Both roughness and FS describe the subjective sensation of changes in sound pressure amplitude produced by modulation frequency. FS is used to evaluate the frequency-modulated sound with mod- ulation frequency below 20Hz. Zwicker FS model [15] used in this study is described in Equation 5:

24Bark

+  5 , ( )

 =

( ) / (dB/Bark) 0.008 vacil 4Hz 4Hz

E L z dz F f

0

mod

f

mod

Roughness is used to evaluate the frequency-modulated sound with modulation frequency within 20Hz to 300Hz. Zwicker roughness model [15] used in this study is described in Equation 6:

24Bark

mod 0 0.0003 ( ) / (dB/Bark) asper E R f L z dz =   6 . ( )

where 𝑓 𝑚𝑜𝑑 is the modulation frequency and ∆𝐿 𝐸 (𝑧) is the temporal masking depth of each critical band. Under the limitation of no access to obtain temporal sound pressure of the aircraft cabin SEA acoustic model, we use the amplitude change of SPL as the temporal masking depth.

PA is a combination of hearing sensations. It describes the psychological elements of annoying sounds. Zwicker and Fastl [15] took into account the effect of loudness, roughness, sharpness, and FS to established the PA model:

2 2 5 = 1+ s FR PA N w w + （ ） 7 , ( )

2 described in Equation 8 and Equa- tion 9 are the factors of sharpness and roughness/FS.

2 and 𝑤 𝐹𝑅

where 𝑁 5 is the 5th percentile of the loudness metric, 𝑤 𝑆

N S S    −  +     

， 8 , ( )

5 = 1.75 0.25lg( 10) 1.75acum acum sone s

where 𝑆 is described in Equation 3.

N    +    

2.18 = 0.4 0.6 vacil asper /sone FR

F R

9 , ( )

( )

0.4

5

where 𝐹 is described in Equation 5, and 𝑅 is described in Equation 6.

AI describes the effective proportion of the normal speech signal which is available to a listener for conveying speech intelligibility [16]. It is concerned with the frequency characteristics of back- ground noise. The value can be obtained by looking up the table listing the AI of each frequency band with different SPLs.

3. RESULT and DISCUSSION

The thickness of the aluminium alloy layer is the design parameter of the aircraft cabin SEA acous- tic model. The variation range is 0.45mm to 0.55mm. It varies every 0.01mm, and the total thickness of the fuselage panel is maintained at 1.2mm. Psychoacoustic metrics were stimulated in the SEA model with varying thickness of the aluminium alloy layer. The results are listed in Table 3. The sensations described by roughness and FS are the same. Since the stimulated results of FS were much less than roughness, we selected roughness to analyze the influence of sensation of modulated sound. The trends of psychoacoustic metrics are shown in Figure 4.

Table 3: The stimulated results of psychoacoustic metrics with varying thickness of the aluminium alloy layer

𝒉 𝟏 (mm) Loudness

Sharpness

FS (vacil)

Roughness

(asper) PA AI%

(sone)

(acum)

0.45 24.59 1.323 0.1941 1.019 34.85 79.67 0.46 24.52 1.333 0.1933 1.015 34.72 79.74 0.47 24.45 1.342 0.1933 1.015 34.63 79.79 0.48 24.38 1.350 0.1906 1.001 34.40 79.87 0.49 24.32 1.362 0.1902 0.998 34.31 79.93 0.50 24.25 1.371 0.1877 0.986 34.09 80.01

Table 3 (continue)

𝒉 𝟏 (mm) Loudness

Sharpness

FS (vacil)

Roughness

(asper) PA AI%

(sone)

(acum)

0.51 24.17 1.375 0.1865 0.979 33.93 80.07 0.52 24.15 1.388 0.1856 0.974 33.86 78.19 0.53 24.12 1.394 0.1853 0.973 33.80 78.22 0.54 24.03 1.405 0.1839 0.965 33.62 78.25 0.55 24.25 1.408 0.1842 0.967 33.91 78.27 Maximum relative

variation 2.28% 6.06% 5.31% 5.31% 2.70% 2.35%

ℎ 1 is the thickness of the aluminium alloy layer

24.8

1.42

1.40

Sharpness/acum

24.6

Loudness/sone

1.38

24.4

1.36

1.34

24.2

1.32

0.45 0.50 0.55 24.0

0.45 0.50 0.55 1.30

h1/mm

h1/mm

（ a ）

（ b ）

1.04

80.5

80.0

Roughness/asper

1.02

79.5

AI/%

1.00

79.0

0.98

78.5

0.45 0.50 0.55 78.0

0.45 0.50 0.55 0.96

h1/mm

h1/mm

（ d ）

（ c ）

35.0

34.5

PA

34.0

0.45 0.50 0.55 33.5

h1/mm

（ e ）

Figure 4: The trend of loudness (a), sharpness (b), roughness (c), AI (d) and PA (e) with varying

thickness of the aluminium alloy layer

The loudness and roughness significantly reduced with the increasing thickness of the aluminium alloy layer, whereas the sharpness increased with increasing thickness. The psychoacoustic annoy- ance also declined as the thickness increased. Within the variation range, loudness, roughness, and PA have the minimum value when the thickness was 0.54mm. The minimum loudness value was 24.03sone, the roughness was 0.965asper, and the PA was 33.62. AI increased with the thickness increasing from 0.45mm to 0.51mm. However, the articulation index dropped from 80.01% to 78.19% when the thickness increased from 0.51mm to 0.52mm. After the sudden drop, AI increased gradually in a small step when the thickness of aluminium alloy increased from 0.52mm to 0.55mm. The maximum relative change is 6.03% for sharpness and 5.31% for roughness, as shown in Table 3, demonstrating the significant influence of the thickness of aluminum alloy layer on sharpness and roughness.

The sound transmission loss spectrum of the aircraft panel is concerned with aluminium alloy thickness. With the thickness increasing, the total sound transmission loss increases. In Figure 5, it’s significant that the low-frequency and medium-frequency bands of the simulated cabin noise SPL decreases with the increasing thickness. However, the variation of high-frequency bands is almost zero, leading to the stable increasing sharpness that reflects the proportion of the high-frequency components with increasing thickness. Since the sharpness was less than 1.75acum, the PA is domi- nated by loudness, roughness and FS, with much greater values of the loudness than roughness and FS. Therefore, PA and loudness of the aircraft cabin SEA acoustic model appeared to be the same trend.

Figure 5: The frequency spectrum of the aircraft cabin noise with different thicknesses of the alu-

minium alloy layer There were developed PA models for mechanical sounds in general and aircraft noise by taking the tonality factor into consideration [12, 23]. Torija et al. [24] also developed a new PA model for rotor noise by introducing the impulsiveness factor. There is a good agreement among the reported values of annoyance estimated by the above PA models [25], so we have adopted the original PA model for the aircraft cabin noise.

4. CONCLUSION

This study provides a simulation approach to analyze the influence of the main acoustic design parameters on the aircraft cabin sound quality and PA. Psychoacoustic metrics (i.e., loudness, sharp- ness, roughness, AI and PA) were simulated with varying thickness based on an SEA acoustic model. The loudness and roughness decreased, whereas the sharpness increased with the increasing thick- ness. The PA was dominated by the loudness and roughness and reduced with the increasing thick- ness. However, the articulation index appeared a sudden drop when the thickness increased. It is deserved to emphasize that acoustic design parameters and its variation range should be further de- termined in a practical application.

5. ACKNOWLEDGE

We gratefully acknowledge National Natural Science Foundation of China: 52072242. 6. REFERENCE

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Appendix

Table A: API functions of VA One used in this study [22]

API function name Function

pi_ClientOpenConnection Establish the connection between MATLAB and VA One

pi_fInit Initialize the API

pi_fNeoDatabaseCreate Create a new database and call the pointer associated with it

pi_fNeoDatabaseFileSpec Use the pointer to associate the database of loaded file

pi_fNeoDatabaseOpenReadWrite Open the database

pi_fNeoDatabaseFindByName Find the class ID by the inputted string

pi_fGeneralLaminateGetClassID Read the class ID of general laminate

pi_fGeneralLaminateGetLayer Select the layer of the laminate

pi_fIsoLayerSetThickness Set the isotropic layer thickness

pi_fDatabaseSolve Solve the model

pi_fResultsAtFreq Read the results in frequency domain

pi_fNeoDatabaseClose Close the database