2982 日本機械学会論文集 (C 編 ) 77 巻 780 号 (2011-8) 原著論文 No.2011-JCR-0378 TMD *1 *2 *3 *4 *5 *6 Research and Development of Tuned Mass Damper Using Impact Force for Environment Vibration and Earthquakes Keisuke MINAGAWA *1, Satoshi FUJITA, Toshio OMI, Katsuya SHINNO, Keiji YAMAGATA and Hiroshi MIYANO *1 Saitama Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering 1690 Fusaiji, Fukaya, Saitama 369-0293, Japan Uncomfortable vertical vibration, which is caused by walking and traffic vibration occurs in long spans on lightweight floors and pedestrian decks. In order to suppress such vibrations, Tuned Mass Damper (TMD) is most commonly used. Usually strokes of TMD are limited by rigid stoppers in order to avoid collisions with control targets. In case of large earthquakes, the stroke of TMD increases, so that TMD collides with the stoppers. Therefore it does not exhibit enough vibration control performance. In order to solve this problem, this paper proposes a TMD with buffers. This TMD has buffers, which suppress the stroke of TMD. The buffers are installed beside the TMD, and gaps between buffers and the TMD are a few millimeters. Thus, in case of environment vibration, collisions with buffers do not occur, and the TMD retains as good vibration control performance as conventional one. In case of large earthquakes, the TMD collides with buffers, so that strokes of the TMD are suppressed and the vibration response of target structures is mitigated. In this paper, the selection of parameters of the TMD with buffers such as gaps and specification of buffers was conducted by simulation analysis. In addition, an experimental model of the TMD with buffers was made. Then vibration control performance is investigated by vibration experiment. As a result, it was confirmed that the TMD has a good performance of vibration control and stroke suppression. Key Words : Vibration Control, Vibration Control Device, Damper, Dynamic Absorber, Shock, Impact Force, Seismic Vibration, Environment Vibration 1. * *1 *2 *3 *4 *5 *6 原稿受付 2011 年 5 月 6 日正員, 埼玉工業大学工学部 ( 369-0293 埼玉県深谷市普済寺 1690) 正員, フェロー, 東京電機大学工学部正員, 東京電機大学工学部東京電機大学大学院特許機器 ( 株 ) 正員, 特許機器 ( 株 ) E-mail: mina@sit.ac.jp 30
2983 TMDTuned Mass Damper TMD TMD TMD TMD TMD TMD TMD TMD TMD (1)(8) TMD (9) (11) 21 2. TMD TMD gap TMD TMD TMD TMD TMD TMD 1 2 TMD TMD gap Fig. 1 General drawing of TMD with buffer Fig. 2 Example of application of TMD with buffer 31
2984 Fig. 3 Analytical model for selection of buffer parameter TMD TMD TMD TMD TMD TMD TMD f D! D TMD 12 f S µ TMD f D = f S 1+ µ 1 " D = 3µ ( ) 3 2 8 1+ µ TMD TMD gap 22 TMD gap 3 TMD TMD x A gap 36 x D < gap m S x S + c S x S " c D ( x D " x S ) + k S x S " k D (x D ) = "m S z V 3 m D x D + c D ( x D " x S ) + k D (x D ) = "m D z V 4 32
2985 x D # gap m S x S + c S x S " c D ( x D " x S )" c B ( x D " x S )+ k S x S " k D (x D )" k B ( x D " gap)sgn(x D ) = "m S z V 5 m D x D + c D ( x D " x S )+ c B ( x D " x S )+ k D (x D )+ k B ( x D " gap)sgn(x D ) = "m D 3. gap z V 6 31 TMDTMD TMD gap 32 1 25m m S 50 000kg 6.0Hz 2.0% (12) TMD m D µ 0.02 TMD f D! D 1 2 TMD TMD 34 TMD 6.0Hz 6.0Hz 29.010-3 m/s 2 70% (13) 29.010-3 m/s 2 1.1610-3 m/s 2 El Centro UD Taft UD Hachinohe UD JMA Kobe UD 33 4 4 TMD 0.0334mm TMD gap 0.0334mm TMD TMD TMD 5 TMD (14) 1/2 5 TMD 3 0.040.125m/s 2 1.0mm 4 0.1250.40m/s 2 1.03.0mm 1 0.125m/s 5.0mm gap 1.0mm 3 Table 1 Parameters of analytical model Floor TMD Mass [kg] 50 000 1 000 Natural Frequency [Hz] 6.00 5.88 Damping Ratio [%] 2.00 8.41 33
2986 TMD Floor without Device with Device Floor Max. Response Acc. 0.029 0.00853 Floor Max. Response Disp. 0.0204 0.00606 0 0.01 0.02 0.03 0 0.01 0.02 0.03 Max. Acc. [m/s 2 ] Max. Disp. [mm] TMD Max. Response Acc. 0.0459 TMD Max. Response Disp. 0.0334 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 Max. Acc. [m/s 2 ] Max. Disp. [mm] Fig. 4 Analytical results (Sinusoidal wave) Fig. 5 Analytical results (earthquake) 41 4. TMD TMD TMD 42 2 1 gap 1.0mm TMD 0.01100 TMD TMD k D 1 1.37!10 6 N/m c B 7! B 1040% c B = 2" B m D k B 7 34
2987 Fig.6 Relationship between buffer parameter and maximum response (JMA Kobe UD 0.125m/s) JMA Kobe UD 1 0.125m/s 3 JMA Kobe UD 310Hz TMD JMA Kobe UD 43 6 TMD 6 TMD 1.0 TMD 0.60.7 0.60.7 6 TMD 0.016.0 TMD 6.0 TMD 0.11.0 0.11.0 40% JMA Kobe UD TMD 5. 51 TMD 3 TMD 35
2988 52 7 2 TMD TMD TMD TMD TMD Table 2 Parameters of experimental model Floor TMD Mass [kg] 484 34 Natural frequency [Hz] 6.30 5.50 Damping ratio [%] 3.46 14.7 Stiffness [N/m] 75810 3 40.610 3 Damping coefficient [Ns/m] 1325.8 347.8 Table3 Parameters of buffer Diameter [mm]!20!30 Length [mm] 51 51 Stiffness [N/m] 12.210 3 35.210 3 Fig. 7 Experimental model Fig. 8 Buffer 36
2989 TMD 484kg34kg 7.02% 6.30Hz3.46%TMD 5.50Hz14.7%TMD 12 5.89Hz14.7% 2030mm 2 2 3 1 8 TMD 1 gap 1.0mm 53 1.010.0Hz 1.0Hz 5.07.0Hz 0.1Hz 0.50m/s 2 (15) 60kg 3 50 000kg 0.0216m/s 2 0.5m/s 2 JMA Kobe UD 0.125m/s 1 54 9 9 TMD TMD TMD TMD TMD TMD TMD TMD TMD 10 10 TMD 30mm TMD TMD 10 TMD 60% TMD JMA Kobe UD 0.125m/s 1.05m/s 2 Fig. 9 Resonant curve of experimental model 37
2990 Floor without Device Floor Max. Response Acc. 1.05 0.58 TMD with Buffer Floor Max. Response Disp. 0.70 0.39 TMD 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Max. Acc. [m/s 2 ] TMD Max. Response Acc. 1.27 0 0.4 0.8 1.2 1.6 Max. Acc. [m/s 2 ] 0 0.2 0.4 0.6 0.8 1 Max. Disp. [mm] TMD Max. Response Disp. 0.85 0 0.2 0.4 0.6 0.8 1 1.2 Max. Disp. [mm] Fig. 10 Experimental results (walking vibration) Floor TMD without TMD TMD with buffer,!=20[mm] Ideal TMD TMD with buffer,!=30[mm] Floor Max. Response Acc. Floor Max. Response Disp. 0 0.5 1 1.5 2 2.5 3 3.5 Max. Accerelation [m/s 2 ] 5.81 2.96 2.57 2.57 2.59 TMD Max. Response Acc. 8.00 8.66 2.03 1.88 1.93 2.05 0 0.5 1 1.5 2 2.5 Max. Displacement [mm] TMD Max. Response Disp. Gap 2.50 3.88 4.55 0 2 4 6 8 10 Max. Accerelation [m/s 2 ] 0 1 2 3 4 5 6 Max. Displacement [mm] Fig. 11 Experimental results (JMA Kobe UD 0.125m/s) 11 11 TMD TMD TMD TMD TMD TMD TMD TMD TMD 12 JMA Kobe UD 0.125m/s TMD 30mm 3 4 23 875.2Ns/m 40 12 TMD gap TMD 38
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