Numerical prediction method for vibration characteristics of steel- framed ALC floor structure Haruki Mizunuma 1 , Takumi Asakura 1 , Yasuhiko Ishiwatari 2 , Takayuki Shiraishi 2 , Fumiaki Satoh 3 1 Tokyo University of Science 2641 Yamazaki, Noda-shi, Chiba, 278-0022, Japan 2 CEL corporation 3-7-1 Kyobashi, Chuo-ku, Tokyo, 104-0031, Japan 3 Chiba Institute of Technology 2-17-1 Tsudanuma, Narashino-shi, Chiba, 275-0016, Japan

ABSTRACT The prediction of floor vibration is of great importance from the viewpoint of accurate prediction of sound environment in the room. In this paper, applicability of the finite element analysis to the vibra- tion simulation of autoclaved lightweight aerated concrete (ALC) floor structure on a steel-framed structure was verified. The results of a numerical case study has confirmed that the numerical cou- pling scheme of the ALC floor panels and the steel-framed structure had a significant effect on the simulated vibration characteristics of the ALC floor panels. Then, validity of the proposed method was finally confirmed by comparison with the measurement results. 1. INTRODUCTION

In recent years, there has been growing interest in sonic environmental performance in building against a background of increased of staying time. Various studies have been reported on prediction methods for heavy weight floor impact sound insulation performance for reinforced concrete build- ings, but there are limited studies for steel-framed buildings. Examples of study on prediction meth- ods for heavy weight floor impact sound insulation performance of steel-framed buildings so far re- ported include the application of a finite element vibration analysis method for reinforced concrete buildings to steel-framed buildings [1], and the application of a coupled displacement in-plane and out-plane for deck plate slabs [2], but further studies are needed to improve the accuracy of the sim- ulation and expand the range of application.

In this paper, measurements were carried out on the vibration of ALC floor panels in a steel-framed building, and the modelling method of the finite element analysis was investigated for steel-framed building with ALC floor panels. Then, the proposed method was finally verified by comparison with the measurement results and the numerical results.

2. MEASUREMENT

For a span of the target building of measurement, ALC distribution setup showing measurement points and beam plan are shown in Figure 1. The target building of measurements is a three-story steel-framed building. The target floor of the measurements is a span of the second floor. The con- struction of the building was completed only frame when the measurements were carried. The floors consisted of ALC floor panels that have a thickness of 100 mm.

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(b)

(a)

E’ 5

1365 1365 455 455

1365 1820

E’ 0

D 5

D 0

Column

Pillar

Unit : mm

3185

2730 455

Unit : mm

Figure 1: (a) ALC distribution setup showing measurement points, and (b) Beam plan 3. CASE STUDIES

Preparatory to generate a numerical model for a comparison with measurement results, some case studies were carried out.

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3.1. Effect of the Cross-sectional Shape of Beams

In order to predict floor vibration in steel-framed buildings, the treatment of H-shaped beams, which are unique to steel construction, is an important point of the simulation. Therefore, the effect of beam cross-sectional shape was carried out by comparing the numerical results obtained from the two types of numerical models differing only in cross-sectional shape. The software used for simulations in this paper was SIMCENTER 3D from Siemense and direct frequency response analysis was carried out using FEM. The dimensions of the beams used in the case study are shown in Table 1.

Table 1: Beam dimensions

The numerical results are shown in Figure 2. The figure confirmed that the vibration characteristics of the ALC floor panels are significantly affected by the cross-sectional shape of the beams. Even when the second moment of area were equal, the vibration characteristics differed significantly when there were differences in the cross-sectional shape of beam. Therefore, it was confirmed that to sim- ulate the cross-sectional shape of the beam accurately is important in order to accurately predict the floor vibration of the steel-framed building.

1.E+01

Beam 1

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Beam 2

1.E+00

Accelerance (m/N s 2 )

1.E-01

1.E-02

1.E-03

1.E-04

10 100 1000

Frequency (Hz)

Figure 2: Effect of cross-sectional shape of beam

3.2. Effect of Constraint Conditions of ALC floor panels.

The target building of measurement was constructed by dry construction method and ALC floor panels were fixed to beams at two points by mounting parts as shown in figure 3 (b). In order to accurately predict the vibration characteristics of ALC floor panels, it is considered to be important to accurately simulate the restraint conditions of ALC floor panels. Therefore, the effect of the re- straint conditions of ALC floor panels on the vibration characteristics was carried out. A numerical model (a), the ALC floor panels were directly fixed to the beams. In contrast, the other numerical model (b), the ALC floor panels were fixed to the beams by mounting parts. The numerical model of joint parts between the ALC floor panels and beams are shown in Figure 3.

(a) (b)

General view of back side of the numerical model

Figure 3: The numerical model of joint parts between the ALC floor panels and beams (a), the ALC floor panels were directly fixed to the beams and, (b) the ALC floor panels were fixed to the beams by mounting part

The numerical results are shown in Figure 4. The figure confirms that the vibration characteristics of ALC floor panels are significantly affected by the constraint conditions of ALC floor panels. This figure shows that the results obtained from the two numerical models (a), and (b) are significantly different. Therefore, it was confirmed that to simulate the constraint conditions of the ALC floor panel accurately is important in order to predict the vibration characteristics of the ALC floor panel accurately.

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1.E+01

(a)

(b)

1.E+00

Accelerance (m/N s 2 )

1.E-01

1.E-02

1.E-03

1.E-04

10 100 1000

Frequency (Hz)

Figure 4: Effect of constraint conditions for ALC floor panels

3.3. Effect of Simulated range of columns and Beams

In this section, the effect of simulated range of columns and beams was carried out. Three numer- ical models with different simulated range of columns and beams were generated based on the target building of measurements. The numerical models are shown in Figure 5.

(a) (b) (c)

Figure 5: (a) Basic numerical model, and (b) vertically expanded numerical model, and (c) Horizon-

tally expanded numerical model

The numerical results are shown in Figure 6. The figure shows that the results obtained from the numerical models (a), (b) and (c) all have similar tendencies. Therefore, it's just enough to simulate a span of the target building as shown in Figure 5 (a) in order to predict the vibration characteristics of ALC floor panels.

1.E+01

(a)

(b)

1.E+00

(c)

Accelerance (m/N s 2 )

1.E-01

1.E-02

1.E-03

1.E-04

10 100 1000

Frequency (Hz)

Figure 6: Effect of simulated range of columns and beams 4. COMPARISON OF MEASUREMENT AND SIMULATION

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In this section, in order to verify the numerical results, the measurement results and the numerical results were compared. Based on the results of the case studies, the numerical model accurately sim- ulated the cross-sectional shape of the beam and the constraints of the ALC floor panel based on the building of measurement target. The numerical model was generated by simulating only a span of the target building of measurement. The numerical parameters used in the simulation are shown in Table 2.

Table 2: Numerical parameters used in the simulation

Comparisons between measurement and simulation at the two measurement points are shown in Figure 7. The measurement points are as shown in Figure 1. Although differences in peak and dip frequencies were observed between the measurement and the simulation, and further improvement of the simulation accuracy would be desirable, both numerical results at the two points shown a similar tendency to the vibration characteristics of the ALC floor panel confirmed in the measurements. Therefore, validity of the modelling method was confirmed.

Simulation (a) (b)

1.E+01

1.E+01

Measurement

Measurement

Simulation

1.E+00

1.E+00

Accelerance (m/N s 2 )

Accelerance (m/N s 2 )

1.E-01

1.E-01

1.E-02

1.E-02

1.E-03

1.E-03

1.E-04

1.E-04

10 100 1000

10 100 1000

Frequency (Hz)

Frequency (Hz)

Figure 7: Comparison of measurement and simulation at (a) D 50 , and (b) E’ 50 , respectively. 5. EFFECT OF SOUND INSULATION IN THE SIMULATION

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A previously measured results by Kimura et al. [3] have shown that heavy floor impact noise re- duction measures for steel-framed building with ALC floor panels include increasing the number of beams and integrating the ALC floor panels with each other. Therefore, in order to confirm the effect of this sound insulation in the simulation, the following simulation was carried out.

5.1. Effect of Beam Structure

Two numerical models with different beam structure were generated and the changes in vibration characteristics with increasing number of beams were compared with previously measured result [3]. The numerical models are shown in Figure 8.

(a) (b)

Figure 8: (a) Beam structure 1, and (b) Beam structure 2

The effects of the countermeasure in the simulation and measurement are shown in Figure 9. These figures confirm that similar countermeasure effects, such as a reduction in peak frequency and overall mobility were decreased with an increase in the number of beams, both in the simulation and in the measurement.

Beam structure 2 (a) (b)

1.E-02

1.E-02

Beam structure 1

Beam structure 1

1.E-03

1.E-03

Beam structure 2

Mobility (m/N s )

Mobility (m/N s )

1.E-04

1.E-04

1.E-05

1.E-05

1.E-06

1.E-06

1.E-07

1.E-07

10 100 1000

10 100 1000

Frequency (Hz)

Frequency (Hz)

Figure 9: (a) Numerical result, and (b) Measurement result

5.2. Effect of bonding adjacent panels

A numerical calculation was carried out for a numerical model with and without bond between adjacent ALC floor panels. The changes in vibration characteristics due to the bonding of adjacent ALC floor panels were compared with previously measured data [3]. The effects of the countermeasure in the simulation and measurements are shown in Figure 10. These figures confirm that similar countermeasure effects, such as reduced mobility, were achieved by bonding adjacent ALC floor panels, both in the simulation and in the measurements.

combined panels (a) (b)

1.E-02

1.E-02

uncombined panels

uncombined panels

combined panels

1.E-03

1.E-03

Mobility (m/N s )

Mobility (m/N s )

1.E-04

1.E-04

1.E-05

1.E-05

1.E-06

1.E-06

10 100 1000

10 100 1000

Frequency (Hz)

Frequency (Hz)

Figure 10: (a) Numerical result, and (b) Measurement result

6. CONCLUSIONS

Concerning the simulation of floor vibrations in steel-framed buildings with ALC floor panels, the following findings were obtained:

(a) The accuracy of the constraint conditions of the ALC floor panels in the numerical model is

important for the accurate prediction of the vibrations of the ALC floor panels. (b) The accuracy of the Cross-sectional shape of steel beams in the numerical model is important for

the accurate prediction of the vibrations of the ALC floor panels. (c) The numerical results obtained from the numerical model with sound insulation are also tended

to reduce vibrations as well as the previous measurements [3], confirming validity of the numer- ical results. 7. REFERENCES

1. Hikari, T., Kiyoshi, M. Floor impact sounds by heavy impact source in steel structure buildings

― vibrational properties of floor slabs and prediction using FEM ― . Noise Control (in Japanese), 36(6) , 425–434 (2012). 2. Yu, A., Norihisa, H. Study on natural vibration analysis of deck plate slabs and their conversion

to flat plate. AIJ J. Technol. Des, 21(47) , 171–176 (2015). 3. Sho, K., Katsuo, I., Mitsuo, O. Method for improving the performance of floor impact sound

insulation for heavy impact source in steel frame ALC-type dwellings. J. Archit. Plann. Environ. Eng., AIJ, (496) , 15–21(1997)

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