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A Study on the Vibroacoustic Analysis of Aluminum Extrusion Structures Kwanju Kim1, Junheon Lee2 and Daeyong Kim3 1

Hongik University, [email protected] 2 Hongik University, [email protected] 3 Hongik University, [email protected] ABSTRACT

Recently, frame structures of high speed train and airplane fuselage have been manufactured with extruded aluminum panels. Sound transmission loss (STL) of the extruded aluminum panel is less satisfactory than flat panels with the same surface density. This study proposes a prediction method of the STL of the aluminum extruded panel using finite element analysis. In order to verify the validity of the predicted value, STL is measured on the aluminum specimen by following the ASTM E2249-02. The proposed analysis method will be utilized to predict the sound insulation performance of the panels in the early design stage, or suggest improvements. Keywords: sound transmission loss (STL), extruded panel, vibro-acoustic analysis. DOI: 10.3722/cadaps.2012.PACE.1-8 1

INTRODUCTION

Weight reduction is essential to increase the speed of trains and airplanes. Aluminum extruded panels are substituted for conventional stainless steel corrugated-shaped frame in order to reduce the weight, and it has reduced maximum 21 % of its weight. However, sound insulation characteristics of the aluminum extruded panel are less satisfactory than flat panels with the same surface density. Kim [1] has predicted sound STL of the extruded panel by assuming the equivalent isotropic panel. Heckl [2] proposed a STL model with 2 critical frequencies for infinite panels. Xie [3,4] has calculated the average radiation efficiency of stripped square plates with high aspect ratio for simple support boundary conditions. In this study, STL of the extruded aluminum panel has been calculated by using finite element method. In order to get the most accurate value, the joint area of the core structure was modeled in detail to identity the vibrational behavior. STL of the panels is calculated by subtracting the transmitted sound power from the incident sound power. The way how boundary conditions of the structure and the damping loss factor influence STL was investigated. The results from FEM analysis were compared with those from sound intensity experiments based on ASTM E2249-02. Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

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2

TRANSMISSION LOSS EXPERIMENT OF THE ALUMINIUM EXTRUDED PANELS

STL of the aluminum panel was measured by calculating the transmitted intensity through the specimen, which is located between a reverberant source room and an anechoic receiving room, according to the ASTM E2249-02 as shown in Fig. 1. Table 1 is the specifications of the reverberant room used in our experiments.

Fig. 1 Experimental set up for TL measurement. Room Volume

240.75 m3

Cut off frequency

100 Hz

Background noise

25.7 dB(A)

Opening size

840mm × 840 mm

Tab. 1: Specifications of the reverberant room. Transmitted intensity was calculated as follows: The sound pressure level in the source room( ) was measured by rotating microphone and was averaged in space and time. Averaged sound intensity in receiving room was calculated by using the following procedure. Intensity was measured in M subdivision areas according to ASTM E2249-02 scanning method; average intensity level( ̅ ) was calculated by using the following equation (1). size

I

=

Lo Sm

M

å éë S mk *10

0.1 LIk

K =1

éW ù * sgn( I k ) ù ê 2 ú û ëm û

(1)

In the above equation, I0 stands for the reference intensity(1 pW/m2), Sm, total measuring area(m2), Smk, kth measuring area(m2), LIk, intensity of kth measuring area. æ ç

LI = sgn ( I k )10log ç

I ö÷

÷ dB ç I0 ÷ è ø

(2)

Equation (2) was used to obtain LI , signed normal sound intensity level. LI will be used to calculate STL using equation (3).

TL = éê L1 - 6 + 10log ( S s ) ùú - éê LI + 10log ( Sm )ùú ë

û

ë

û

(3)

Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

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3

SPECIFICATIONS OF THE EXTRUDED ALUMINUM PANEL SPECIMEN

Specimen of aluminum panel, used in this study, is selected from the floor frame of rapid train. Floor panels’ size is 0.84 m by 0.84 m, and it is composed of square plates with aspect ratio of 6:1~20:1. The cross section of the aluminum specimen is asymmetric as shown in Fig. 2 and the specifications of it are listed in Table 2.

Fig. 2: The cross section shape of the extruded aluminum panel. Young’s modulus (E) Mass density (ρ)

71.5 x 109 N/m2 2800 kg/m3

Poisson’s ratio (υ)

0.33

Panel height (h) Plate thickness (Tp) Core thickness (Tc) Panel dimensions (Lx, Ly)

70 mm 2.8 mm 2.6 mm 0.84 m, 0.84 m

Tab. 2: Specifications of the extruded aluminum panel. 4

TRANSMISSION LOSS ANALYSIS OF THE ALUMINIUM EXTRUDED PANELS

4.1 Finite Element Analysis Model Insulation performance of the extruded panels has been calculated by using the commercial vibroacoustic program MSC ACTRAN. In order to find the modal behavior of the strips composing the floor accurately, joint sections of the strips are modeled in detail as shown in Figure 3. 3 dimensional 20-node solid-shell element has been employed.

Fig. 3: Description of the fine FE meshes in the vicinity of joint region. The source room was modeled with 1,078 quad 4 elements. The diffuse sound field in the source room was postulated by using the average of 10 random incidents. Receiving room was made of fine meshes near the specimen but was made of coarse meshes afterwards. The dimension of the receiving room is 1.6 m by 1.6 m by 0.8 m. The boundaries of the receiving room were Sommerfeld boundaries where sound can propagate without any hindrance. The receiving room was composed of 11,393 20node acoustic elements. The specimen was modeled by 4,004 solid-shell elements. Figure 4 shows the FE model, and Table 3 illustrates the data about the model. STL of the panels is calculated by subtracting the transmitted sound power from the incident sound power by using MSC ACTRAN. Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

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Fig. 4 FEM model of the extruded aluminum panel located between semi anechoic acoustic chamber above and reverberant field below.

component

Number of elements

Elements topologies

Type of elements

Air cavity

11,393

Hexahedron20

Acoustic fluid

Aluminum extruded panel

4,004

Hexahedron20

Solid shell

Tab. 3: Elements properties of FEM model for the specimen. 4.2 Boundary Conditions In order to obtain the most accurate analysis results, the boundary conditions of finite element model should be closer to the real situation. The specimen in the experiment was placed in the test section by 12 clamps and the boundary was sealed with clay to prevent leakage of sound as shown in Figure 5. In the finite element analysis, 4 boundary condition cases are plausible. Clamped-clamped case (CL-CL) is constraining all 4 boundaries, clamped-free case(CL-FR) is fixing only two boundaries perpendicular to the extruded direction, free-clamped case(FR-CL) is constraining two boundaries parallel to the extruded direction, and finally free-free case (FR-FR) is freeing all boundaries. These cases are illustrated in Figure 6.

Fig. 5: Installation of the specimen between the source room and the receiving room.

Fig. 6: Proposed boundary conditions of the extruded aluminum panel. (upper left: clamped-clamped, upper right: free–clamped , lower left: clamped-free, lower right: free-free) Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

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80 60

TL(dB)

40 20 0 80

100

125

160

CL-CL

200

250

315

400

500

630

800 1000 1250 1600 2000 2500

1/3 octave band frequency (Hz) FR-CL

CL-FR

Fig. 7: STL results from finite element analysis and by an experiment. STL values from finite element analysis, experiment and mass law are depicted in figure 7. Analysis results of CL-CL and FR-CL cases are higher than the result from the experiment in the low frequency band where the stiffness is dominant. It is because CL-CL and FR- CL cases constraint the boundaries too much. In the low frequency band, results from experiment are located between FR-FR and CL-FR cases. The specimen of the CL-CL and FR-CL case first resonate at approximately 630 Hz. At this frequency, the STL curve becomes a trough. On the other hand, the CL-FR case has the first resonant frequency near 250 Hz, lower than resonant frequency of the CL-CL and FR-CL. The peaks and troughs of the STL graph greater than 630 Hz are caused by local vibration modes of the panel. STL values, which are calculated by the analysis, are lower than STL value of the mass law and the experiment. In order to reduce the differences between the analysis and the experiment, the damping loss factor will be discussed in the next section. 4.3 Damping Loss Factor After selecting CL-FR case which shows closest result with experiment, relation between STL and damping loss factor are examined. According to Kim [2], STL shows two distinct behavior. First one is the global resonance modes affected by the size of the specimen and boundary conditions and other is local resonance modes by strips. In figure 8, analysis result of 10% damping loss factor for aluminum material shows closest STL values to those of experiment in 200 ~ 250 Hz band, whereas 5 % damping loss factor is similar to that of the 315 ~ 1000 Hz region; In fact, it is natural for the damping value to decrease as the frequency increases. Considering the indoor noise of the rapid railway, below 1000 Hz is the most important. The result illustrates that in order to make the insulation capability of the extruded aluminum panel efficient, it is essential to increase the damping loss factor of the panel. For example, the damping loss factor can be increased by placing some foam rubber inside the core area or by attaching visco-elastic layers below or on the panel. 60

TL(dB)

50 40 30 20 10 0 80

100

125

160

200

250

315

400

500

630

800 1000 1250 1600 2000 2500

1/3 octave band frequency (Hz) 0% 1%

5%

Fig. 8: STL of the extruded aluminum panel with clamped-free boundary condition depending on the damping loss factor of the panel. Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

6 4.4 The Relationship between the Vibration and the Sound Radiation of the Extruded Aluminum Panel with the Clamped-free Case In order to observe the properties of the acoustic radiation according to the vibration of the panel, modal density and mode shapes were calculated by the program ACTRAN. The number of modes depending on the octave band is presented in figure 9. The number of modes drastically increases above the 600 Hz area where local resonance modes occur. Thus, acoustic radiation is generated, and sound insulation of the aluminum panel is less satisfactory than flat panels with the same surface density. 50

Numbers of modes

40

30

20

10

0 100

125

160

200

250

315

400

500

630

800

1000

1250

1600

2000

2500

1/3 Octave band frquency (Hz)

Fig. 9: Modal density of the extruded aluminum panel of CL-FR case depending on frequency band. In figure 10, STL in the 100 ~ 1000 Hz area was calculated and expressed in the narrow band instead of the 1/3 octave band to find the accurate resonance frequency. In the resonance frequency range, the sound transmitted easily. In other words, STL loss decreased in that range. 230 Hz, 390 Hz, and 590 Hz, where resonance mode occur, were selected to investigate the vibration mode of the panel and the sound field. 60 50

TL(dB)

40 30 20 10 0 100

1000

Frequency (Hz)

200

0%

1%

5%

500

10%

experiment

Damping loss factor :

Fig. 10: STL calculation of the extruded aluminum panel with clamped-free boundary condition with respect to damping loss factor of the panel represented in frequency. Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

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At 230 Hz, where the first mode occurs, the panel vibrates globally. As shown in figure 11, the triangle truss structure is deformed tremendously. Sound is radiated loudly in the center similar to the vibration deformation as shown in figure 12.

Fig. 11: Structural mode shape at 230Hz.

Fig. 12: Sound radiation field at 230Hz.

At 390 Hz, the strip in the left side is deformed the most. Similarly, the sound propagates obliquely from the left to right.

Fig. 13: Structural mode shape at 390Hz.

Fig. 14: Sound radiation field at 390Hz.

At 590 Hz, local resonance modes take place on the right side of the strip. Hence, most of the sound is radiated from the most deformed strip.

Fig. 15: Structural mode shape at 590Hz.

Fig. 16: Sound radiation field at 590Hz.

In the low frequency band, the panel vibrates globally, whereas as the frequency increases, the panel starts to vibrate locally. In these local resonances, the modal density is higher, so more sound energy passes through the panel. In other words, STL of the panel decreases drastically. This way of predicting STL will guide finding the resonance mode and improving the insulation capability by reforming the structure. 5

CONCLUSIONS

To improve the insulation capability of the extruded aluminum panel broadly used in frames of the rapid railway and airplane fuselages, the vibration and acoustic characteristics of the panels were analyzed by using finite element method, and the finite element results were verified by STL experiments. The insulation characteristics could be precisely predicted if accurate cross-sectional Computer-Aided Design & Applications, PACE (2), 2012, 1-8 © 2012 CAD Solutions, LLC, http://www.cadanda.com

8 shape and the material properties were provided. Because fabricating extruding panels costs much, proposed “vibration and sound analyzing method” will be useful when predicting the insulation performance. ACKNOLEDGEMENTS This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (2011-0025751) and 2010 Hongik University Research Fund.

REFERENCES [1] [2] [3] [4]

Seo, S. L.; Kim, J. Sl.; Cho, S. H.: A study on the economic feasibility of hybrid body shell made of sandwich composite plate, Journal of the Korean Society for Railway, 15(2), 2012, 97-103. Heckl, M.: Untersuchungen an orthotropen platten, ACUSTICA, 10, 1960, 109-115 Xie, G.; Thompson, D. J.; Jones, C. J. C.: The radiation efficiency of baffled plates and strips, Journal of Sound and Vibration, 280, 2005, 181-209 http://dx.doi.org/10.1016/j.jsv.2003.12.025 Xie, G.; Thompson, D. J.; Jones, C. J. C.: A modeling approach for the vibroacoustic behavior of aluminium extrusions used in railway vehicles, Journal of Sound and Vibration, 293, 2006, 921932 http://dx.doi.org/10.1016/j.jsv.2005.12.015

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