Experimental study on horizontal performance of multi-dimensional earthquake isolation and mitigation devices for long-span reticulated structures

Abstract

Earthquake excitation is a kind of complicated multi-dimensional ground motion. Therefore, anti-earthquake measuresfor complex and important engineering structures, such as long-span structures and high rise buildings under multi-dimensional earthquake excitations, have become an extremely important research topic. In this paper, a new multi-dimensional earthquake isolation and mitigation device (MEIMD) is proposed for protecting long-span reticulated structures due to strong earthquake motions. It consists of a viscoelastic bearing and several viscoelastic dampers. Property tests on the MEIMD under different excitation frequencies, excitation amplitudes and vertical pressure forces are carried out. Then, a mathematical simulation is carried out for the equivalent stiffness and the equivalent damping of the device, and the numerical results agree reasonably well with the experimental data. Experimental and numerical results show that the MEIMD has a fine energy dissipation capacity, and can be used for anti-earthquake purposes for long-span reticulated structures.

Keywords

Earthquake isolation earthquake mitigation multi-dimensional viscoelastic

1. Introduction

Conventional seismic design cannot usually ensure that some important structures are fully functional to avoid great economic losses and seismic casualties during a major earthquake (e.g., tall buildings, and long-span structures). Since 1972, when the vibration control theory was first proposed (Yao, 1972), the idea that reducing the seismic responses of structures by using vibration control devices has been widely accepted by structural engineers. The seismic isolation system is considered as the most effective method of decoupling seismic responses of structures. For example, at present, laminated rubber bearing has been extensively used in seismic isolation structures and it performs well (Ibrahim, 2008). However, conventional laminated rubber bearing can dissipate little earthquake energy during an earthquake (Narasimhan et al., 2006). Therefore new types of isolation systems with energy dissipation capacity were studied, such as laminated rubber bearing with a lead-core, frictional type sliding isolators and hybrid seismic isolation systems (Kasai et al., 1998; Roussis and Constantinou, 2006; Shrimali and Jangid, 2003). These isolation and mitigation devices are mostly designed to reduce only horizontal earthquake responses of structures. In fact, the earthquake excitations are complicated multi-dimensional ground motions, which include both horizontal and vertical components. Vertical earthquake-induced ground motion must be also be considered for important or complex structures, such as long-span reticulated structures and high-rise buildings. However, nowadays few devices have been studied and designed for reducing both horizontal and vertical earthquake responses of structures simultaneously. Laminated rubber bearings and viscous dampers were used to isolate the horizontal earthquake for a nuclear power station, while helical spring and viscous dampers were designed to control the vertical earthquake component (Huang et al., 2007). A new three-dimension isolation device composed of a rubber isolation device and sealed aircushion was proposed, and tests indicated that the device performed well in both horizontal and vertical directions (Suhara et al., 2002). On the basis of Suhara’s research results, a hydraulic cylinder and sealed aircushion were used to isolate a vertical earthquake while a rubber isolation device was used to reduce the horizontal response (Shimada et al., 2005). A device using a butterfly spring, rubber shock isolation blankets and MR damper was proposed to reduce the multi-dimensional earthquake responses (Qu, 2003).

Here, a new multi-dimensional earthquake isolation and mitigation device (MEIMD) which has not only earthquake isolation ability but also earthquake mitigation ability is proposed to reduce both horizontal and vertical earthquake responses of long-span reticulated structures simultaneously (Approved National Patent in China with granted number: ZL2006 1 0097219.3). The device makes full use of high energy absorption capacity of viscoelastic material. The excellent performance of passive control using a viscoelastic damper has been proved by both shaking table tests (Chang et al., 1995; Hayes et al., 1999; Xu, 2007) and real applications under strong earthquakes (Aiken et al., 1990; Crosby et al., 1994; Soong and Shen, 1995). The device consists of a viscoelastic bearing and several viscoelastic dampers, which can isolate and dissipate both horizontal and vertical vibration energy of structures. Property tests on the MEIMD under different excitation frequencies, excitation amplitudes and vertical pressure forces are carried out. Then, a mathematical simulation is carried out to simulate the equivalent stiffness and the equivalent damping of the device. The numerical results agree reasonably well with the experimental data. Experimental and numerical results show that the MEIMD has a fine energy dissipation capacity, and can be used for anti-earthquake purposes for long-span reticulated structures.

2. Test setup

2.1. Description of the multi-dimensional earthquake isolation and mitigationdevice (MEIMD)

The newly proposed MEIMD for reducing the dynamic responses of long-span reticulated structures is shown in Figure 1. The device consists of a viscoelastic core bearing and two viscoelastic dampers. For the horizontal earthquake excitation, the viscoelastic core bearing can isolate the transfer of vibration energy. At the same time, the viscoelastic core bearing, under vertical pressure due to the weight of the upper structure and two viscoelastic dampers, will dissipate vibration energy because of the high energy dissipation capacity of the viscoelastic material. For the vertical earthquake excitation, viscoelastic bearing and dampers also form a stiffness softening layer, i.e. isolation layer, which can isolate the transfer of vibration energy in a vertical direction.

Simultaneously, the viscoelastic dampers and bearing can dissipate vibration energy when the device produces a relative displacement. The energy dissipation is small under a minor earthquake due to a small relative vertical displacement of the device, while it is large under a strong earthquake which will lead to obvious vertical tension displacement of the device. If the MEIMD is tensioned, the upper steel plate will detach from the core bearing, therefore the viscoelastic dampers will dissipate most of the vibration energy, and the core bearing will be prevented from failure caused by tension. The tension failure is the important shortcoming of the traditional laminated rubber bearing. If the MEIMD is pressed, the pressure will be undertaken by the core bearing and the viscoelastic dampers. This is sufficient to carry the load of a superstructure just like the traditional laminated rubber bearing. It must be noted that the device cannot only permit a large deformation in a horizontal direction, but should also permit large tension deformation in a vertical direction. Above all, the viscoelastic damper and viscoelastic core bearing can work together to reduce the seismic responses effectively under both horizontal and vertical directions.

The core bearing in the device consists of viscoelastic layers and steel plates. There are four viscoelastic layers with a thickness of 8 mm in the middle and two viscoelastic layers with a thickness of 2.5 mm in the upper and bottom sides. Each layer is vulcanized alternatively with five layers of 2 mm steel plates. The diameter and the height of the core bearing are 187 mm and 47 mm, respectively. As shown in Figure 1, the core bearing and the bottom steel plate are connected by high-strength bolts, while the upper steel plate is placed on the bearing with no connection. Two dampers at two sides of the core bearing are made up of three layers of steel plates clamping two layers of viscoelastic material with a thickness of 10 mm. Two dampers are fixed by the high-strength bolts between the bottom and upper steel plates. The viscoelastic material in the device is a kind of polymer named VEMXZD-XIU1 developed by our group. The matrix of VEMZD-XIU1 is brominated butyl rubber, and more than ten kinds of additives including magraphite, stearic acid, modified resin, etc are added to improve the properties of viscoelastic material. The loss factor of the material is between 0.7 and 1.0, and the storage modulus is between 2 Mpa and 5 MPa.he optimal using frequency scope is from 0.1 Hz to 10 Hz and the optimal temperature scope is between −20 to 60°C for this material. Under excitations, part of the damper’s energy is stored as potential energy, and the other part of the energy is dissipated by transferring into heat. The main parameters of the MEIMD are listed in the Table 1. The advantage of the developed new device is that the device can isolate and mitigate both vertical and horizontal earthquakes. The shortcoming of the device is that its mechanical properties are influenced by temperature.

Table 1.

Detail design parameters of the MEIMD

Components	Area of viscoelastic layers (mm²)	Thickness of viscoelastic layers (mm)	Thickness of steel plate (mm)	Number of viscoelastic layers	Number of steel plate
Core bearing	27600	Upper and down 2.5; middle 8	2	6	5
Plate damper	15000	10	10	2	3

MEIMD: multi-dimensional earthquake isolation and mitigation device.

2.2. Test procedure

The most important mechanical characteristics of the MEIMD are force-displacement energy dissipation hysteresis loop, the equivalent stiffness, and the equivalent damping. In this study, the effects of excitation frequency, excitation amplitude and vertical pressure force on these characteristics of the MEIMD under horizontal direction are considered. The horizontal performance tests have been done in Key Laboratory of C&PC Structures of the Ministry of Education, People’s Republic of China. As shown in Figure 2, the MEIMD is mounted to a 30 ton MTS closed-loop feedback hydraulic testing machine which works through a displacement control mode. The test system can immediately return the actual output force, displacement, velocity and acceleration of the actuator and can show the force-displacement behavior simultaneously. The MEIMD is subjected to ten cycles of sinusoidal excitation with constant displacement amplitude, excitation frequency and vertical pressure load. The vertical load on the MEIMD is provided by a 50 ton oil jack. Outputs from the actuator load cell and displacement transducer are recorded by a high speed digital data acquisition system. The corresponding high speed digital data acquisition system is provided by MTS Systems Corporation in the USA, which includes a high speed computer server and some corresponding software. The system can immediately return actual output force, displacement, velocity and acceleration data, and can plot the force-displacement hysteresis curves simultaneously. Tests are conducted at displacements and frequencies selected to be appropriate for seismic applications. Tests are carried out under the ambient temperature 22°C.

There are 64 test conditions in the performance tests, as listed in Table 2. In the tests, the vertical pressure loads include 0 ton, 10 ton, 20 ton and 30 ton. For each vertical load, excitation with the amplitudes of 2 mm, 4 mm, 6 mm and 8 mm are performed. The excitation frequencies of 0.1 Hz, 0.2 Hz, 0.5 Hz and 1 Hz are adopted for each vertical pressure load and displacement amplitude. After a working condition is completed in the test, whether bolts and the ground anchors are fixed tightly and whether the test device is fractured are checked to make sure the correct experimental data is obtained.

Table 2.

Horizontal property test conditions of the MEIMD

Vertical load (T)	Frequency f (Hz)	Displacement amplitude d (mm)	Cycle number
0	0.1	2, 4, 6, 8	10
	0.2	2, 4, 6, 8	10
	0.5	2, 4, 6, 8	10
	1.0	2, 4, 6, 8	10
10	0.1	2, 4, 6, 8	10
	0.2	2, 4, 6, 8	10
	0.5	2, 4, 6, 8	10
	1.0	2, 4, 6, 8	10
20	0.1	2, 4, 6, 8	10
	0.2	2, 4, 6, 8	10
	0.5	2, 4, 6, 8	10
	1.0	2, 4, 6, 8	10
30	0.1	2, 4, 6, 8	10
	0.2	2, 4, 6, 8	10
	0.5	2, 4, 6, 8	10
	1.0	2, 4, 6, 8	10

MEIMD: multi-dimensional earthquake isolation and mitigation device.

3. Tests results and analysis

During the entire process of the tests, the MEIMD isnot damaged. When the vertical load is 0 ton, theviscoelastic core bearing does not deform at all, andonly the dampers cause shear deformation and dissipate energy. While the vertical load is applied onthe MEIMD, the shear deformation of the core bearing can be found because the horizontal shear force can be transmitted to the bearing by the friction force between the upper steel plate and the core bearing.

The force-displacement hysteresis curves are plotted to understand thoroughly the energy dissipation capacity and the horizontal seismic performance of the proposed MEIMD under different excitation frequencies and excitation amplitudes without the vertical pressure force, as shown in Figures 3 and 4. Figure 3 shows force-displacement hysteresis curves under different displacement amplitudes at the excitation frequencies of 0.1 Hz, 0.2 Hz, 0.5 Hz and 1.0 Hz. The hysteresis loops shown in Figure 3 are smooth and plump ellipses, and this means that the MEIMD has fine energy dissipation ability. With the increase of the excitation amplitude, the damping force amplitude and the area of the hysteresis curve both increase, while the obliquity of the center inclined line decreases, and this decrease of the obliquity means a decrease of the equivalent stiffness of the MEIMD. These characteristic of hysteresis curves are the same under the frequencies of 0.1 Hz, 0.2 Hz, 0.5 Hz and 1 Hz. It is also found that the real displacement amplitude of the MEIMD cannot reach the required values under the frequency of 1 Hz, which is due to the limitation of the output power of servo-hydraulic test machine (MTS) under high frequency. Figure 4 shows force-displacement hysteresis curves under different excitation frequencies at the excitation amplitudes of 2 mm, 4 mm, 6 mm and 8 mm. It can be seen that the obliquity of the center inclined line increases with the increase of excitation frequency, which means that there is an increase in equivalent stiffness of the MEIMD when the excitation frequency increases. In order to acquire the effect of the vertical pressure on properties of the MEIMD, the force-displacement hysteresis curves under different pressure loads at the excitation amplitudes of 2 mm, 4 mm, 6 mm and 8 mm and the excitation frequency of 0.1 Hz are plotted as Figure 5. As seen, vertical pressure loads have no obvious effect on properties of theMEIMD when the excitation amplitudes are 2 mm, 4 mm, 6 mm, and the inclination of the hysteresis curves increases slightly with the increasing vertical pressure loads at the excitation amplitude of 8 mm.

As mentioned above, the equivalent stiffness K_e and the equivalent damping C_e are the most important factors that reflect the horizontal characteristics of the MEIMD. The two factors can be obtained from the tested hysteresis curves. Under the sinusoidal excitation of $u_{d} = u_{0} \sin ω t$ (u₀ and ω are the amplitude and the circular frequency of excitations), the relationship between the damping force and the displacement of the MEIMD can be expressed as follows:

(1)

where F_d and u_d are the damping force and the displacement of the MEIMD, u₀ is the maximum horizontal displacement of the MEIMD, F is the maximum damping force of the MEIMD, F₁ is damping force at displacement u₀, F₂ is the damping force at 0 displacement, K_d1 is the storage stiffness,

K_{d 1} = F_{1 / u_{0}}

, F₁ is the damping force at the maximum displacement, as shown in Figure 6. The equivalent stiffness K_e, equivalent C_e can be obtained by the following equations (Xu,2007)

(2)

(3)

where F₂ is the damping force corresponding to zero displacement,

F_{2} = η K_{d 1} u_{0}

nn is the number of viscoelastic layers of the device, ω is circular frequency of excitation load, t is time variable. Damping ratio ξ can be obtained by the following equation,

ξ = W_{c} / (2 π K_{e} u_{0}^{2})

, where W_c is area of single hysteretic curve. The size parameters of the multi-dimensional earthquake isolation and mitigation device are known and F₁,F₂ canbe determined from the test hysteresis curves. Therefore, the equivalent stiffness K_e and the equivalent damping C_e of the device can be calculated by equations (2) and (3). In order to reveal the effects of excitation frequency and amplitude, a single steady-state cycle is selected from ten cycles for each case. The equivalent stiffness and the equivalent damping of the device without vertical pressure loads can be calculated as listed inTable 3.

Table 3.

The equivalent stiffness and damping of the MEIMD without vertical loads

f (Hz)	r (mm)	Force at maximum disp.	Force at zero disp.	Equivalent stiffness	Equivalent damping
f (Hz)	r (mm)	F1 (N)	F2 (N)	Ke (kN/m)	Ce (kN·s/m)
0.1	2	21524	5346	10554	4172
	4	37810	9235	9386	3649
	6	50184	12104	8352	3206
	8	50290	12040	6288	2396
0.2	2	22010	5647	11075	2261
	4	39210	10005	9911	2012
	6	50336	12440	8504	1672
	8	49471	12210	6267	1231
0.5	2	21045	6205	12795	1201
	4	38264	11200	11116	1035
	6	50146	14197	9604	865
	8	49710	13890	7027	625
1.0	2	15448	4904	14313	723
	4	30063	9462	12785	640
	6	40280	11540	11092	506
	8	41126	11752	7968	362

MEIMD: multi-dimensional earthquake isolation and mitigation device.

3.1. Excitation frequency effect

In order to reveal the effect of the excitation frequency on the equivalent stiffness and the equivalent damping of the device, the calculated data listed in Table 3 are plotted in Figure 7. It can be seen from Figure 7(a) that the equivalent stiffness K_e increases slowly with increasing frequency. The equivalent stiffness K_e mainly comes from the stiffness of two viscoelastic plate dampers when the pressure load is 0 ton. Take a 4 mm excitation displacement amplitude condition for example, when the frequency increases from 0.1 Hz to 0.2 Hz, 0.2 Hz to 0.5 Hz, 0.5 Hz to1 Hz, and by every 0.1 Hz increasing frequency, the corresponding equivalent stiffness K_eis increased by 7.3%, 4.1%, 3%, respectively, and the detailed data can be seen in Table 3. Adopting thesame data disposal measures, under the excitation displacement amplitude of 4 mm and the vertical pressure load of 30 ton, and by every 0.1 Hz of increasing frequency, the corresponding increase percentages of the equivalent stiffness K_e are 6.4%, 5.8% and 3.2%. The equivalent stiffness is increased with more frequency which is due to the storage modulus of viscoelastic materials increasing with more frequency. The storage modulus and loss factor are the main indices of properties for viscoelastic materials, and they mean the stored energy representing the elastic portion and the energy dissipated as heat representing the viscous portion, respectively.

Variation of the equivalent damping C_ewith excitation frequency can be seen in Figure 7(b). It can be found that the equivalent damping C_e decreases sharply when the frequency changes from 0.1 Hz to 0.2 Hz, and it decreases slowly when the frequency changes from 0.2 Hz to 1 Hz. Take 4 mm excitation displacement amplitude condition for example, when the frequency is increased from 0.1 Hz to 0.2 Hz, 0.2 Hz to 0.5 Hz, 0.5 Hz to 1 Hz, and by every 0.1 Hz increasing frequency, the corresponding equivalent damping C_e is decreased by 44.9%, 16.2%, 12.7%, respectively. In the same way, the equivalent damping under the excitation displacement amplitude of 4 mm and the vertical pressure load of 30 ton, and by every 0.1 Hz increasing frequency, the corresponding decrease percentages of the equivalent damping C_e are 42.5%, 16.7%, 8.6%. Decrease of the damping coefficient C_e with increasing frequency is primarily caused for two reasons, one is the energy dissipation per cycle will decrease slightly in higher frequency because of the power limitation of MTS, and the other is that the loss factor of viscoelasticmaterials decreases with increasing frequency. Inaddition, as shown in Figure 7(b), the excitation frequency has a more significant effect on the equivalent damping than high frequency, because the equivalent damping C_e and the frequency ω are inversely proportional according to equation (3), so the equivalent damping is more sensitive at low frequency.

3.2. Excitation displacement amplitude effect

For the purpose of showing the excitation displacement amplitude effect on the equivalent stiffness and damping of the device, the data listed in Table 3, obtained from the tests, are plotted in Figure 8. It can be seen in Figure 8(a) that the equivalent stiffness K_e decreases slowly with increasing displacement amplitude. Take 1.0 Hz excitation frequency as an example, when the displacement amplitude increases from 2 mm to 4 mm, 4 mm to 6 mm, 6 mm to 8 mm, the corresponding equivalent stiffness K_e decreases by 10.6%, 13.2%, and 28.2%, respectively. When the excitation frequency is 1.0 Hz and the vertical load is 30 ton, the corresponding decreasing percentages of the equivalent stiffness K_e are 10.3%, 11.7% and 9.4%. This phenomenon of the decreasing equivalent stiffness is due to the fact that the energy dissipation per cycle increases with increasing displacement amplitude. This dissipation energy transfers into the heat energy of the viscoelastic material, which leads to a temperature rise. This rise of temperature will in turn cause a decrease in the storage modulus of the viscoelastic material, and the decrease in storage leads to the decrease in equivalent stiffness K_e. Variation of the equivalent damping C_e with excitation amplitude can be seen in Figure 8(b). It can be found that the equivalent damping coefficient C_e decreases slowly with an increasing displacement amplitude.

Take 0.2 Hz excitation frequency condition as an example, when the displacement amplitude is increased from 2 mm to 4 mm, 4 mm to 6 mm, 6 mm to 8 mm, the corresponding decrease percentages of the equivalent damping C_eare 10.5%, 14.2% and 26.3%, respectively. In the same way, considering the equivalent damping under the excitation frequency of 0.2 Hz and the vertical load of 30 ton, the corresponding decrease percentages of the equivalent damping C_e are 11.4%, 9.2% and 7.4%. Decrease of the damping with increasing amplitude is also caused by the temperature rise of viscoelastic material under large amplitudes. The transferred heat during vibration under large amplitudes in viscoelastic material is difficult to be radiated into the air space very quickly, which will lead to a rise in the temperature of viscoelastic material and cause the loss factor of viscoelastic materials decreases with increasing frequency.

3.3. Vertical pressure load effect

In order to reveal the vertical pressure load effect on the equivalent stiffness and damping of the device, the data obtained from tests are plotted in Figure 9. It can be seen from Figure 9(a) that the influence of vertical load on K_e is not as obvious as the excitation frequency anddisplacement amplitude. The equivalent stiffnessK_e increases slowly, and the increasing percentage decreases with an increasing vertical load. Take 0.2 Hz excitation frequency and 6 mm displacement amplitude for example, when the vertical load increases from 0 ton to 10 ton, 10 ton to 20 ton and 20 ton to 30 ton, the corresponding equivalent stiffness is increased by 2.26% and 0.08% and 1.8%. In the same way, when the equivalent stiffness under the excitation frequency of 1 Hz and the excitation amplitude of 6 mm, the corresponding increase percentages of the equivalent stiffness are 5.4%, 1.1% and -0.4%, respectively. The equivalent stiffness under the excitation frequency of 0.5 Hz and the excitation amplitude of 8 mm are 7027, 8664, 8975, 9225 kN/m. When the vertical load increases from 0 ton to 10 ton, 10 ton to 20 ton and 20 ton to 30 ton, the corresponding equivalent stiffness is increased by 23.3%, 3.6% and 2.8% respectively. The law of variation of the equivalent damping C_ewith the vertical load is plotted in Figure 9(b). It can be found that the effect of vertical load on C_e is also not as obvious as the effects of the excitation frequency and displacement amplitude. The equivalent damping coefficient C_e increases slowly and the increasing percentage decreases with an increasing vertical load. Take 0.2 Hz excitation frequency and 6 mm displacement amplitude condition for example, when the vertical load increases from 0 t to 10 t, 10 t to 20 t and 20 t to 30 t, the corresponding equivalent damping coefficient is increased by 20.1%, 3.6%, 2.98%. The equivalent damping under the excitation frequency of 0.5 Hz and the excitation amplitude of 8 mm are 625, 869, 916, 916 kN…s/m. When the vertical load increases from 0 ton to 10 ton, 10 ton to 20 ton and 20 ton to 30 ton, the corresponding equivalent stiffness is increased by 39.0%, 5.4% and 0%, respectively.

4. Numerical analysis

4.1. Mathematical simulation

As mentioned before, the MEIMD consists of a viscoelastic core bearing and several viscoelastic dampers, which makes the device a newly complex and nonlinear system.

It is necessary to develop mathematical equations to simulate the characteristics of the MEIMD. The horizontal characteristic parameters of the MEIMD include the equivalent stiffness K_e and equivalent damping C_e. As known from the above tests, the excitation frequency and displacement amplitude have influence on K_e and C_e, while the vertical load has a slight influence. Therefore, when developing mathematical equations only the excitation frequency and excitation displacement amplitude are considered. It can be seen from experimental data that the equivalent stiffness increases with increasing excitation frequency or decreasing displacement amplitude, and the equivalent damping decreases with increasing excitation frequency or displacement amplitude. The equivalent stiffness K_e andthe equivalent damping C_e can be expressed as follows

(4)

(5)

where α(f) is the polynomial function relative to frequency

f, β (r)

is the exponent function relative to displacement amplituder. For the new device, 32 pairs of experimental data are used to determine the parameters of the equivalent stiffness and the equivalent damping, then

(6)

(7)

where f is excitation frequency, ris excitation displacement amplitude. Equations (6) and (7) form the formulas of the mathematical model of MEIMD.

4.2. Comparison analysis

In order to show the availability and accuracy of the mathematical equations, the equivalent stiffness K_e and the equivalent damping C_e under different excitation frequencies and displacement amplitudes are calculated in accordance with equations (6) and (7). The numerical results of K_e and C_e are compared with the experimental data, which are listed in Table 4.

Table 4.

Comparison of experimental and numerical values

r(mm)	f (Hz)	Experiment value		Numerical value
r(mm)	f (Hz)	Ke (kN/m)	Ce (kN.s/m)	Ke(KN/m)	Ce(kN.s/m)
2	0.1	10554	4172	10919	2859
	0.2	11075	2261	11347	2309
	0.5	12795	1201	12632	1215
	1.0	14313	723	14773	418
4	0.1	9386	3649	9496	2435
	0.2	9911	2012	9869	1966
	0.5	11116	1035	10986	1035
	1.0	12785	640	12848	356
6	0.1	8352	3206	8259	2010
	0.2	8504	1672	8583	1623
	0.5	9604	865	9555	855
	1.0	11092	506	11174	294
8	0.1	6288	2396	7183	1585
	0.2	6267	1231	7464	1280
	0.5	7027	625	8309	674
	1.0	7968	362	9718	232

MEIMD: multi-dimensional earthquake isolation and mitigation device.

Figure 10 shows the experimental and numerical results comparison of the MEIMD under different frequencies with the fixed displacement amplitude of6 mm.

This group of experimental data is not included in those fitting data for obtaining equations (6) and (7). The experimental data for the equivalent stiffness K_e are 8352, 8504, 9604, 11092 kN/m under frequencies of 0.1, 0.2, 0.5, 1.0 Hz excitations, and the corresponding numerical data are 8259, 8593, 9555, 11174 kN/m, respectively. The experimental equivalent damping C_e are 3206, 1672, 865, 506 kN·s/m and the corresponding numerical results are 2010, 1623, 855, 294. As shown in Figure 10(a), there is little difference between the numerical and experimental results, and the maximum error is 1.1%. As shown in Figure 10(b), when loading frequency is between 0.2 Hz and 0.5 Hz, the numerical results agreewell with experimental values, and the maximum error is 2.9%; however, when the loading frequency is at 0.1 Hz or 1.0 Hz, there are some differences between experimental and numerical results.

Figure 11 shows the comparison results between experimental and numerical results of the MEIMD under different displacement amplitudes with a fixed frequency of 0.5 Hz. The experimental data for the equivalent stiffness are 12795, 11116, 9604 and 7027 kN/m under 2 mm, 4 mm, 6 mm and 8 mm displacement amplitudes, and the corresponding numerical data are 12632, 10986, 9555 and 8309 kN/m, respectively.

The experimental equivalent dampings are 1201, 1035, 865 and 625 kN…s/m, and the corresponding numerical data are 1215, 1035, 855 and 674 kN…s/m. It is shown from Figure 11(a) that the numerical results agree well with experiment results for the equivalent stiffness when the excitation displacement amplitude is between 2 mm and 6 mm, and the maximum error is 1.2%, while the maximum error is 18.26% under 8 mm displacement amplitude working condition. As shown in Figure 11(b), when the displacement amplitude is between 2 mm and 6 mm, the numerical results agree well with the experimental results, and the maximum error of the equivalent damping is 1.2%, and the maximum error is 7.8% under 8 mm working condition. It can be found from the analysis that the mathematical equations can describe the equivalent stiffness and damping of the MEIMD under different excitation frequency and displacement amplitudes.

5. Conclusions

In this paper, a new MEIMD has been developed and horizontal property tests are carried out. In accordance with the experimental data, the numerical simulation on the equivalent stiffness and the equivalent damping of the device is carried out. The following conclusions can be obtained from the experimental and numerical analysis.

The force-displacement hysteretic loops of the MEIMD are full smooth ellipse, which means that the device has a good performance of energy dissipation.

The properties of the MEIMD are affected by the excitation frequency, the excitation amplitude, and the vertical pressure load. Excitation frequency has obvious influence on the equivalent stiffness and damping, excitation amplitude has a smaller influence, and vertical pressure load has a slight influence.

The mathematical equations can describe the equivalent stiffness and damping of the MEIMD under different excitation frequency and displacement amplitudes.

Footnotes

Acknowledgements

The authors are grateful for the support of their funding bodies.

Funding

This work was supported by the National Natural Science Foundation of China (grant number 90915004), Jiangsu Province Natural Science Foundation (grant number BK2011282), Doctoral Fund of Ministry of Education of China (grant number 20090092110012) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

References

Aiken

Kelly

Mahmoodi

(1990) The application of viscoelastic dampers to seismically resistant structures. In Proceedings of the 4th US National Conference on Earthquake Engineering, Palm Springs, CA, May 20–23, vol.3, pp. 499–506.

Chang

Soong

Lai

(1995) Seismic behavior of steel frame with added viscoelastic dampers. Journal of Structural Engineering, ASCE 121(10): 1418–1426.

Crosby

Kelly

Singh

(1994) Utilizing viscoelastic dampers in the seismic retrofit of a thirteen story steel framed building. In Proceedings of ASCE Structures Congress XII, Atlanta, GA, April 24–28, vol. 2, pp. 1268–1291.

Hayes

JJR

Foutch

Wood

(1999) Influence of viscoelastic dampers on the seismic response of a lightly reinforced concrete flat slab structure. Earthquake Spectra 15(4): 681–710.

Huang

Whittaker

Constantinou

Malhushte

(2007) Seismic demands on secondary systems in base-isolated nuclear power plants. Earthquake Engineering and Structural Dynamics 36(10): 1741–1761.

Ibrahim

(2008) Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration 314(3–5): 371–452.

Kasai

Watanabe

(1998) Passive control systems for seismic damage mitigation. Journal of Structural Engineering, ASCE 124(5): 501–512.

Narasimhan

Nagarajaiah

Johnson

Gavin

(2006) Smart base-isolated benchmark building, Part I: roblem definition. Structural Control and Health Monitoring 13(2–3): 573–588.

(2003) Torsional-vertical seismic response control ofmulti-story structure with intelligent compound base-isolation system. Earthquake Engineering and Engineering Vibration 23(2): 187–195 (in Chinese).

10.

Roussis

Constantinou

(2006) Experimental and analytical studies of structures seismically isolated with an uplift-restraining friction pendulum system. Earthquake Engineering and Structural Dynamics 35(5): 595–611.

11.

Shimada

Suhara

Inoue

(2005) Three dimensional seismic isolation system for next-generation nuclear power plant with rolling seal type air spring and hydraulic rocking suppression system. In Proceedings of ASME 2005 Pressure Vessels and Piping Conference, Denver, CO, July 17–21, vol.8, pp.183–190.

12.

Shrimali

Jangid

(2003) The seismic response of elevated liquid storage tanks isolated by lead-rubber bearings. Bulletin of the New Zealand Society for Earthquake Engineering 36(3): 141–164.

13.

Soong

Shen

(1995) Seismic upgrade of reinforced concrete structures using viscoelastic dampers. In Proceedings of the 3rd National Concrete & Masonry Engineering Conference, San Francisco, CA, June 14–17, pp. 583–594.

14.

Suhara

Tamura

Okada

Umeki

(2002) Development of three dimensional seismic isolation device with laminated rubber bearing and rolling seal type air spring In Proceedings of ASME 2002 Pressure Vessels and Piping Conference, Vancouver, Canada, August 5–9, vol. 2, pp. 43–48.

15.

(2007) Earthquake mitigation study on viscoelastic dampers for reinforced concrete structures. Journal of Vibration and Control 13(1): 29–45.

16.

Yao

JTP

(1972) Concept of structural control. Journal of Structure Division 98(7): 1567–1574.