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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

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Front. Struct. Civ. Eng.    2023, Vol. 17 Issue (3) : 350-367    https://doi.org/10.1007/s11709-022-0923-0
RESEARCH ARTICLE
Development of rocking constraint device with vertical damping capacity for three-dimensional base-isolated frame structures
Yundong SHI1,2,3, Qi WANG3(), Wenqing DONG3, Bo ZHAO3
1. Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
2. Key Laboratory of Earthquake Disaster Mitigation, (Ministry of Emergency Management), Harbin 150080, China
3. School of Civil Engineering, Tianjin University, Tianjin 300072, China
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Abstract

A new rocking constraint device (RCD) is developed for three-dimensional (3D) base-isolated frame structures by connecting a custom-designed cylinder pair to provide vertical damping with replaceable damping components installed outside the cylinders when the superstructure undergoes translational motion, and rocking constraint capacity when the superstructure is susceptible to rocking. Theoretical formulas for calculating the damping and rocking constraint stiffness of the RCD are proposed. Two series of sinusoidal loading tests are conducted at different loading frequencies and amplitudes to verify the damping and rocking constraint performance of the RCD. The test results show that the cylinder without orifices on its piston can provide the desired damping with a replaceable damping component, and that the RCD can effectively suppress rocking. Although the vertical stiffness of an individual cylinder is affected by the location of the replaceable damping component and loading frequency, the average vertical stiffness of the two cylinders, which determines the rocking constraint stiffness of the RCD, is independent of the two factors. Comparisons of the test and theoretical results indicate that the errors of the proposed formulas for calculating the damping and rocking constraint stiffness of the RCD do not exceed 12.9% and 11.0%, respectively.
Keywords three-dimensional isolation      rocking behavior      rocking constraint device      replaceable damping component      sinusoidal test     
Corresponding Author(s): Qi WANG   
Just Accepted Date: 04 January 2023   Online First Date: 19 April 2023    Issue Date: 24 May 2023
 Cite this article:   
Yundong SHI,Qi WANG,Wenqing DONG, et al. Development of rocking constraint device with vertical damping capacity for three-dimensional base-isolated frame structures[J]. Front. Struct. Civ. Eng., 2023, 17(3): 350-367.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0923-0
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I3/350
Fig.1  Rocking constraint device.
Fig.2  Arrangement of the RCD: (a) longitudinal and transverse directions; (b) diagonal directions.
Fig.3  Operating states of RCD: (a) vertical translational movement; (b) rocking movement.
Fig.4  Dimensional parameters of the RCD.
Fig.5  Fluid flow in the chambers and pipe: (a) without replaceable damping component; (b) with replaceable damping component.
dimensional properties value (mm)
height of the upper chamber, luc 225
height of the lower chamber, llc 225
diameter of the piston, dpt 100
diameter of the piston rod, dpr 50
length of the pipe, lp 2000
diameter of the pipe, dp 51
length of damping component, lo 90
diameter of the orifices, do 8
Tab.1  Dimensional properties of the RCD
Fig.6  Schematic illustration of damping performance test setup.
loading no. frequency, f (Hz) displacement amplitude, A (mm) velocity amplitude, v (mm/s)
D1-0.05 Hz-10 mm 0.05 10 3.1
D2-0.05 Hz-20 mm 20 6.3
D3-0.05 Hz-40 mm 40 12.6
D4-0.05 Hz-60 mm 60 18.9
D5-0.05 Hz-80 mm 80 25.1
D6-0.1 Hz-10 mm 0.1 10 6.3
D7-0.1 Hz-20 mm 20 12.6
D8-0.1 Hz-40 mm 40 25.1
D9-0.1 Hz-60 mm 60 37.7
D10-0.1 Hz-80 mm 80 50.3
D11-0.2 Hz-10 mm 0.2 10 12.6
D12-0.2 Hz-20 mm 20 25.1
D13-0.2 Hz-40 mm 40 50.3
D14-0.2 Hz-60 mm 60 75.4
D15-0.2 Hz-80 mm 80 100.5
D16-0.5 Hz-10 mm 0.5 10 31.4
D17-0.5 Hz-20 mm 20 62.8
D18-0.5 Hz-40 mm 40 125.7
D19-0.5 Hz-60 mm 60 188.5
D20-0.5 Hz-80 mm 80 251.3
D21-0.75 Hz-10 mm 0.75 10 47.1
D22-0. 75 Hz-20 mm 20 94.2
D23-0. 75 Hz-40 mm 40 188.5
D24-0. 75 Hz-60 mm 60 282.7
D25-0. 75 Hz-80 mm 80 377.0
D26-1 Hz-10 mm 1 10 62.8
D27-1 Hz-20 mm 20 125.7
D28-1 Hz-40 mm 40 251.3
D29-1 Hz-10 mm 1.5 10 94.2
D30-1 Hz-20 mm 20 188.5
D31-2 Hz-10 mm 2 10 125.7
D32-2 Hz-20 mm 20 251.3
D33-2.5 Hz-10 mm 2.5 10 157.1
D34-2.5 Hz-20 mm 20 314.2
D35-3 Hz-10 mm 3 10 188.5
D36-3 Hz-20 mm 20 377.0
Tab.2  Loading program for testing damping performance
Fig.7  Test setup and specimen for damping test.
Fig.8  Hysteresis curve with the following loading frequencies: (a) 0.05 Hz; (b) 0.1 Hz; (c) 0.2 Hz; (d) 0.5 Hz; (e) 0.75 Hz; (f) 1 Hz; (g) 1.5 Hz; (h) 2 Hz; (i) 2.5 Hz; (j) 3 Hz.
case number of orifices, N flow index, m consistency coefficient, k damping coefficient, c (N?s/m)
test Eq. (3) error (%)
A 2 1 0.98 15261 15261 0
B 1 1 34664 30426 –12.9
Tab.3  Damping parameters
Fig.9  Damping force and velocity relationship for specimen with (a) two orifices and (b) one orifice.
Fig.10  Schematic showing RCD loading.
Fig.11  Setup for evaluating RCD: (a) longitudinal direction view; (b) transverse direction view.
loading no. frequency, f (Hz) displacement amplitude, A (mm) loading no. frequency, f (Hz) displacement amplitude, A (mm)
S1-0.05 Hz-10 mm 0.05 10 S20-0.5 Hz-20 mm 0.5 20
S2-0.05 Hz-20 mm 20 S21-0.5 Hz-40 mm 40
S3-0.05 Hz-40mm 40 S22-0.5 Hz-60 mm 60
S4-0.05 Hz-60 mm 60 S23-0.5 Hz-80 mm 80
S5-0.05 Hz-80 mm 80 S24-0.75 Hz-10 mm 0.75 10
S6-0.05 Hz-100 mm 100 S25-0.75 Hz-20 mm 20
S7-0.1 Hz-10 mm 0.1 10 S26-0.75 Hz-40 mm 40
S8-0.1 Hz-20 mm 20 S27-0.75 Hz-60 mm 60
S9-0.1 Hz-40 mm 40 S28-1 Hz-10 mm 1 10
S10-0.1 Hz-60 mm 60 S29-1 Hz-20 mm 20
S11-0.1 Hz-80 mm 80 S30-1 Hz-40 mm 40
S12-0.1 Hz-100 mm 100 S31-1 Hz-10 mm 1.5 10
S13-0.2 Hz-10 mm 0.2 10 S32-1 Hz-20 mm 20
S14-0.2 Hz-20 mm 20 S33-2 Hz-10 mm 2 10
S15-0.2 Hz-40 mm 40 S34-2 Hz-20 mm 20
S16-0.2 Hz-60 mm 60 S35-2.5 Hz-10 mm 2.5 10
S17-0.2 Hz-80 mm 80 S36-2.5 Hz-20 mm 20
S18-0.2 Hz-100 mm 100 S37-3 Hz-10 mm 3 10
S19-0.5 Hz-10 mm 0.5 10 S38-3 Hz-20 mm 20
Tab.4  Loading program for evaluating rocking constraint stiffness
Fig.12  Displacement and force time histories of specimen with damping component for the following loadings: (a) S6-0.05 Hz-100 mm; (b) S11-0.1 Hz-80 mm; (c) S22-0.5 Hz-60 mm; (d) S34-2 Hz-20 mm; (e) S37-3 Hz-10 mm.
Fig.13  Comparison of force–displacement relationship: (a) Cylinders 1 and 2 with replaceable damping component; (b) Cylinder 1 with replaceable damping component and without replaceable damping component. NRDC denotes specimen without replaceable damping component; RDC denotes specimen with replaceable damping component.
Fig.14  Force–displacement relationship under loadings of different frequencies and the same displacement amplitude: (a) Cylinder 1 with damping component; (b) average values of Cylinders 1 and 2 with damping component; (c) Cylinder 1 without damping component.
case damping bulk modulus, E (MPa) average vertical stiffness rocking constraint stiffness
test (kN/m) Eq. (14) (kN/m) test (kN·m·rad−1) Eq. (16) (kN·m·rad−1) error (%)
A NRDCa) 390.5 3793 3793 11852 11852 0
B RDCb) 3321 3689 10378 11527 11.0
Tab.5  Stiffness parameters
Fig.15  Maximum force–displacement relationship: (a) Cylinder 1 with replaceable damping component; (b) Cylinder 2 with replaceable damping component; (c) average values for case with replaceable damping component; (d) average values for case without replaceable damping component.
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