Seismic Isolation of Building-Equipment System Using Modified Variable Friction Pendulum System

In this study, building-equipment system with Modified Variable Friction Pendulum System (MVFPS) is investigated under different earthquake ground excitations. Earthquake response of buildingequipment system isolated with MVFPS is compared with Variable Friction Pendulum System (VFPS) and Friction Pendulum System (FPS) in order to find efficiency of MVFPS. Newmark’s linear acceleration method is used for solving governing equation of motion for building-equipment system. In this investigation, different storey buildings are considered. It is observed that MVFPS is more efficient in reducing the recoverable energy than FPS, but less efficient than VFPS. From the comparative study, it is found that FPS shows robust performance in comparison to MVFPS and VFPS in reducing equipment acceleration and displacement. Darshak Patel1, V. R. Panchal2, Maulik Patel3 1,2Chandubhai S. Patel Institute of Technology, Charotar University of Science and Technology, Changa, Gujarat, India. 3Knowledge Institute of Technology and Engineering, Bakrol, Gujarat, India. 1Email: darshak254@gmail.com


Introduction
In last few decades, base isolation technique has gained vast adoption because it protects different types of structures, like water tanks, multistoreyed buildings, bridges etc. against adverse effects of earthquake. The main concept of base isolation technique is that it reduces damages in building by shifting the fundamental time period of building from dominant periods of earthquake. After implementation of base isolation system in building, energy dissipation capability and fundamental time period of building increases. Buildings without base isolation attract more earthquake forces where as buildings which have base isolation attract less amount of earthquake force and protect building against earthquake.
Among different types of base isolation systems, sliding isolators are mostly used for actual implementation as they are insensitive to the frequency content of ground motions. Number of sliding isolators, i.e., Friction pendulum system (FPS), Variable Frequency Pendulum Isolator (VFPI), Variable Curvature Friction Pendulum System (VCFPS), and Triple Friction Pendulum System (TFPS) were examined during last few decades. Mrunal and Sinha [1] supervised study on multi-storey building along with equipment with VFPI, PF and FPS; they concluded that VFPI is more effective as compared to FPS and PF system. Lu et al. [2] considered sliding bearings with variable curvatures for near fault ground motions. They showed that CFPI and VFPI is more effective compared to FPS. Joshi et al. [3] studied performance of CFPI and VFPI in multi-storey building with building equipment and concluded that VFPI is more effective than CFPI. Bhayani and Panchal [4] carried out numerical study on multi-storey building with equipment isolated with PFPI and VFPI and demonstrated that VFPI is more effective than PFPI.
In this research work, MVFPS isolated multi-storey building with equal mass at all floor are considered. Here Equipment mass is taken 1% of total mass of building. Different near fault ground excitations are used to determine response of equipment displacement, equipment accelerations and recoverable energy of MVFPS isolated building with view to examine the performance of MVFPS with building equipment. Comparison of MVFPS, VFPS and FPS has been made.

Concept of MVFPS
As variation of coefficient of friction is not easy to be attain in case of VFPS, Ali and Abbas [5] suggested MVFPS, which is more advantageous in real practice. The MVFPS system is the variation of VFPS system. The basic difference among FPS, VFPS and MVFPS lies in the variation of friction coefficient with respect to isolator displacement, which is demonstrated in Fig.  1. Variation of friction coefficient in case of MVFPS is similar to that of FPS throughout isolator except in displacement range from 0.5d to 1.5d (d is the value of isolator displacement with respect to extreme value of friction coefficient of VFPS). In this range, maximum value of friction coefficient of VFPS is considered.

Governing equation of motion
The governing equation of motion for building equipment system is given by Eq. (1). (1) Here where F x denotes frictional force in MVFPS, k = W / R represents stiffness of MVFPS; R indicates radius of concave interface of MVFPS.
The MVFPS can be subjected (before sliding) to the limiting frictional force, Q, which is given by Eq.
where µ and W indicate coefficient friction of MVFPS and weight of structure. Stiffness k , of MVFPS is designed in such a way that certain value of isolation period, T b , is obtained; which is given by Eq. (4).

(4)
In above equation M indicate total mass of the MVFPS-isolated building with equipment. The MVFPS has nonlinear force deformation behaviour. So, it becomes very tough to solve the equations of governing motion of the building equipment system by classical modal superposition technique. Therefore, the Newmark's linear acceleration method is used to obtain solution of this equation over small time step.

Energy balance
Base isolators work as a combination of reducing the energy transferred to the structure and dissipating energy by applicable mechanism. Most of the time it becomes difficult to select convenient trade off among isolator displacements and structural deformations in order to obtain best isolator properties. With the help of energy quantities, it becomes easier to evaluate the isolator performance as it involves all the responsible quantities. Hence, it represents overall response of structure. The equation of energy balance stated by Uang and Bertero [6] for base isolated shown in Eq. (5).
In above equation, terms V K , V r , V s and Vi stand for to the kinetic energy, potential energy, strain energy and absolute input energy respectively. and indicate the non conservative energies because of structural damping and sliding friction.
The energy balance equation of a equipment resting on the MVFPS isolated building at any instant of time is given by Eq. (7).

Numerical study
In this study, MVFPS isolated one and five storey buildings with equal mass are considered. Also, light equipment with 1% of total floor mass of building is considered at top. In this study, the response of building equipment system is carried out under six different near-fault ground excitations. Fig. 2       In Fig 5 (a) Northridge, 1994 (Newhall) in this earthquake ground excitations equipment acceleration and equipment displacement found less compared to MVFPS and VFPS and MVFPS is better compared to VFPS and FPS in reducing recoverable energy and Fig 5 (b) Landers 1992 (Lucerne Valley) shows that FPS show better in reducing equipment acceleration and equipment displacement and in MVFPS recoverable energy is less compared to VFPS and FPS.

Results and discussion
In Fig 6 (a) Northridge 1994 (Rinaldi) in this earthquake ground excitations equipment acceleration and equipment displacement is less in FPS compared to MVFPS and VFPS and recoverable energy is less in VFPS and Fig 6  (b) shows that in Northridge 1994 (Sylmar) earthquake ground excitations FPS shows robust performance compared to MVFPS and VFPS and also it founds that recoverable energy is very less in VFPS.
All the results value of Fig 4 to 6 shows in Table 3.  Fig. 8 (a) Imperial valley (El Centro Array#5) earthquake ground excitations shows that for five storey building-equipment system equipment acceleration and equipment displacement is less in FPS compared to MVFPS and VFPS and also recoverable energy result less in MVFPS and in Fig 8. (b) Imperial valley (El Centro Array#7) in this earthquake ground excitations FPS is good compared to MVFPS and VFPS. and recoverable energy found less in VFPS, Both Fig. 9 (a) Northridge 1994 (Newhall) (b) Landers 1992 (Lucerne Valley) shows that equipment acceleration, displacement and recoverable energy is less in FPS compared to MVFPS and VFPS. Fig. 10 (a) Northridge 1994 (Rinaldi) in this earthquake excitations equipment acceleration, displacement and recoverable energy is less in FPS compared to MVFPS and VFPS and 10 (b) shows that in Northridge 1994 (Sylmar) earthquake excitations equipment acceleration placement is high in VFPS but recoverable energy value is less in VFPS compared to MVFPS and FPS.
Result values of Fig. 8 to 10 Which depict Time vs equipment acceleration, displacement and recoverable energy of five storey building-equipment isolated with MVFPS,VFPS and FPS under different earthquake ground excitations shows in Table 3. (e) (f) Figure 11: (a to f) shows Hysteresis loop of MVFPS, VFPS and FPS for five storey building with equipment under different earthquake ground excitations  The above Table 3 shows result of  Table 3 it is clearly shows that increasing number of storey equipment acceleration, displacement and recoverable energy also increased. Table 4 shows result of Fig. 7 and 11 for different earthquake ground excitations. This table depict result of isolator displacement and base shear for one storey and five storey building.

Conclusions
The Base isolated multi-storied building with light weight equipment at top is analyzed to determine its response under nearfault ground excitations with the help of Newmark's linear acceleration method. One and five storey buildings with equipment system isolated with MVFPS are compared with that of FPS and VFPS. The different response quantities examined are equipment displacement, equipment acceleration and recoverable energy. Following conclusions are derived from this comparative study: From the above study, it is evident that equipment acceleration and equipment displacement increases when studied for five storey building-equipment system as compare to that of a single storey building-equipment system isolated using MVFPS,VFPS and FPS, where there is little increase observed in recoverable energy for five storey building as compared to that of a single storey building. FPS is performing better in reducing equipment acceleration pp. 60 and equipment displacement as compared to VFPS and MVFP. It is found that in MVFPS, base shear and isolator displacement are less as compared to that of VFPS and FPS. The amount of energy dissipation is higher in case of MVFPS than that of FPS and VFPS. From this study it show that MVFPS is more efficient in reducing recoverable energy than FPS, but less efficient than VFPS.