# Study of Lead Rubber Bearings for Vibration Reduction in High-Tech Factories
## 4 Parametric Study Using LRBs in High-Tech Factories
### Micro-Vibration Simulation Under Wind Loads  
In addition to vibration generated by moving cranes, wind-induced floor vibration in high-tech buildings is another major source of environmental loads affecting production operations. Therefore, we followed the reference [23] to study the wind induced vibration, and the LRB effect was investigated in this paper, where the analysis only included dead and wind loads and the seismic load was not used in this section. Since wind forces applied to the factory are space- and time-dependent, we used the wind speed simulation software TurbSim [27] to generate the space- and time-dependent wind speed field in the \(Y\) direction on the whole \(X\)-direction outer plane to compare the floor vibration of the factory with and without LRBs. Since the building is much longer in the \(X\) direction than that in the \(Y\) and \(Z\) directions, the \(Y\)-direction wind-induced vibration should be the largest, and we will thus only focus on this direction vibration. The normal turbulence model is used in the analysis with the average wind speed at the height of 30 m (\(V_{30m}\)) during 10 min, while \(V_{30m}\) is set to 5, 10, 15, 20, and 25 m/s for the five cases, and the turbulence standard deviation is set according to IEC-61400-1 in 2019 [28], as follows:  
\[\sigma_{1}(m/s)=0.16(0.75V_{30m}+5.6) \tag{6}\]  
In the setting of this program, an area of 500 m wide by 60 m high was arranged with 41 by 41 girders to find the turbulent wind speeds. The average wind speed in the vertical direction is according to the normal wind profile as below:  
\[VZ=V_{30m}\Big{(}\frac{Z}{30}\Big{)}^{\alpha} \tag{7}\]  
where \(Z\) (m) is the vertical height above the ground, and \(\alpha\) equal to 0.14 is the power law exponent. Figure 11 shows the turbulent wind velocity at the height of 30 m on the building center, and it is noted that the wind velocity is time- and location-dependent. The wind pressure is determined as below:  
\[P(X,Y,Z,t)=C_{P}\rho V(X,Y,Z,t)^{2}/2 \tag{8}\]  
where \(P(X,Y,Z,t)\) is the time- and space-dependent wind pressure, \(V(X,Y,Z,t)\) is the time-and space-dependent wind speed from the TurbSim result, \(C_{p}\) (0.8) is the shape coefficient, and \(\rho\) (0.00128 t/m\({}^{3}\)) is the air density. Finally, the time-history finite element analysis is performed to find the wind-induced vibrations on the three floors, which are shown in Figure 12 for the case of the average wind speed \(V_{30m}\) equal to 15 m/s. These figures indicate that the high-tech factory with LRBs will have much larger wind-induced vibration than that without LRBs, especially for the RC level that is located at the first level. The increased velocity vibration dBs for the RC level, the first steel level, and the second steel level are about 19, 6, and 4 dB, respectively. Therefore, this situation will bring great disadvantage to the use of LRB in high-tech factories. The reason for largely increasing the floor vibration induced by wind loads is that the initial stiffness of the LRB is considerably soft, so that the rigid body motion of the factory superstructure cannot be avoided due to the wind load. Even for a small wind load, which is still much larger than the load of moving cranes, the wind induced rigid body motion still causes problems for the factory with LRBs. We further analyzed the factory under different average wind speeds (\(V_{30m}\)) and then only selected the maximum dB from all the frequencies, as shown in Figure 13. This figure indicates a very similar conclusion as that of the average wind speed equal to 15 m/s not only for the steel levels but also for the RC level, while the average wind speed was set to a board range from 5 to 25 m/s. An interpolation scheme was used to find the requirement of micro vibration according to the guidelines for high-tech factories, and the result is shown in Table 3. The table can be used to estimate the wind-induced vibration for a high-tech factory approximately, although the result is dependent on the structure dimensions and member sizes.