22.1 Introduction

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Conventionally, structural designers are concerned about the safety of buildings, bridges, and other civil

engineering structures that are subjected to earthquakes. The recent history of earthquakes reveals that

strong earthquakes, such as the 1994 Northridge earthquake (U.S.A.), 1995 Kobe earthquake (Japan),

and 1999 Chi-Chi earthquake (Taiwan), can cause some badly designed structures or buildings to fail or

collapse, and also cause some well-designed structures to malfunction due to the damage or failure of the

equipment housed in the structure or building. Both the failures of structures and equipment, also

known as structural and nonstructural failures, respectively, can cause serious harm to the residents or

personnel working in a building. For the case where the equipment is part of a key service system, such as

in hospitals, power stations, telecommunication centers, high-precision factories, and the like, the lives

and economic losses resulting from the malfunctioning of the equipment can be tremendous. Thus, the

maintenance of the safety of structures and attached equipment during a strong earthquake is a subject of

high interest in earthquake engineering (also see Chapter 29 to Chapter 31). In this regard, base isolation

has been proved to be an effective means for protecting the structures and attached equipment, which is

made possible through reduction of the seismic forces transmitted from the ground to the superstructure

(Yang et al., 2002).

For light secondary systems mounted on heavier primary systems, it was concluded that the response

of the light secondary system, that is, the equipment, is affected by four major dynamic characteristics in

earthquakes (Igusa and Der Kiureghian, 1985a, 1985b, 1985c; Yang and Huang, 1993). The first issue is

tuning, which means that the natural frequency of the equipment is coincident with that of the structure.

Such an effect may amplify the response of the equipment due to the fact that the light secondary system

behaves as if it were a vibration absorber of the heavier primary system. The second issue is interaction,

which is related to the feedback effect between the motions of the primary and secondary systems.

Ignoring the feedback effect of interaction may result in an overestimation of the true response of the

combined system. The third issue is non-classical damping, which may occur when the damping

properties of the two systems are drastically different, such that the natural frequencies and mode shapes

of the combined system can only be expressed in terms of complex numbers. Under such a circumstance,

the conventional response spectrum analysis, based on modal superposition, becomes inapplicable. The

last issue is spatial coupling, which relates to the effect of multiple support motions when the secondary

system of interest is mounted at multiple locations. By considering the inelastic effect, Igusa (1990)

proposed an equivalent linearization technique for investigating the response characteristics of an

inelastic primary – secondary system with two degrees of freedom (DoF) under random vibrations. His

results indicated that the existence of small nonlinearity is helpful for reducing the coupling system

responses. With the concept of equivalent linearization, Huang et al. (1994) explored the response and

reliability of a linear secondary system mounted on a yielding primary structure under white-noise

excitations. It was concluded that the response of the secondary system could be reduced by increasing

the equipment damping or by locating equipment at higher levels of the primary structure.

Owing to the fact that the mass and stiffness of a secondary system are much smaller than those of the

primary structure, the interaction effect of the combined system, as well as the ill-conditioning in system

matrices, may take place when one performs the dynamic analysis. To deal with this problem, some

researchers chose to evaluate the response of the secondary systems from the floor motions. To avoid

solving large eigenvalue problems and to account for the interaction between the building and

equipment components, Villaverde (1986) applied the response spectrum technique to the analysis of a

combined building – equipment system, by which the maximum response of light equipment mounted

on the building under the earthquake is expressed in terms of the natural frequencies and mode shapes of

22-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

the building and equipment. To take into account the equipment – structure interactions, Suarez and

Singh (1989) proposed an analytical scheme for computing the dynamic characteristics of the combined

system, using the modal properties to compute the floor spectra. Lai and Soong (1990) presented a

statistical energy analysis technique for evaluating the response of coupling primary – secondary

structural systems, based on the concept of power-balance equation, that is, the power input to the

primary system is equal to the dissipated energy of the primary system plus the transferred energy to the

secondary system. Using a mean-square condensation procedure, Chen and Soong (1994) considered

the effect of interaction by calculating the multi-DoF response of a primary – secondary system under

random excitations. Later on, Chen and Soong (1996) derived an exact solution for the mean-square

response of a structure – equipment system under dynamic loads, indicating that there exists an optimal

damping ratio for reducing the vibration of equipment attached to the primary structure. Gupta and

coworkers investigated the response of a secondary system with multiple supports on a primary structure

subjected to earthquakes, taking into account the interaction effect between the equipment and structure

(Dey and Gupta, 1998, 1999; Chaudhuri and Gupta, 2002). Their results indicated that when the soil –

structure interaction (SSI) is taken into account, the response of the equipment – structure system will be

affected by the SSI, unless a very stiff soil condition is considered.

On the other hand, a number of research works have been conducted by implementing isolation

systems at the base of the equipment – structure system, aiming to reduce the earthquake forces

transmitted from the ground. Based on a theoretical and experimental investigation, Kelly and Tsai

(1985) showed that seismic protection can be achieved effectively for lightweight equipment mounted on

an isolated structure installed with elastic bearings at the base. A hybrid isolation system with baseisolated

floors was proposed by Inaudi and Kelly (1993), for the protection of highly sensitive devices

mounted on a structure subjected to support motions. Considering the effects of torsion and translation,

Yang and Huang (1998) studied the seismic response of light equipment items mounted on torsional

buildings supported by elastic bearings. Their results indicated that the response of an equipment –

structure system can be effectively reduced through installation of base isolators, and that there exists an

optimal location for mounting the equipment. Juhn et al. (1992) presented a series of experimental

results for the secondary systems mounted on a sliding base-isolated structure. They concluded that the

acceleration response of the secondary system may be amplified when the input motions are composed of

low-frequency vibrations. In this case, the sliding bearings are not considered to be an effective isolation

device, which implies that the base-isolated structure is not suitable for a construction site with soft soil.

Concerning the use of sliding bearings (supports) as base isolators, Lu and Yang (1997) investigated the

response of an equipment item attached to a sliding primary structure under earthquake excitations.

Their results showed that the response of the equipment can be effectively reduced through the

installation of a sliding support at the structural base, in comparison with that of a structure with fixed

base. To overcome the discontinuous nature of the sliding and nonsliding phases of a structural system

with sliding base, a fictitious spring model was proposed by Yang and coworkers for simulating the

mechanism of sliding and nonsliding (Yang et al., 1990, 2000; Yang and Chen, 1999). Such a model will be

described in a later section of this chapter. Agrawal (2000) adopted the same fictitious spring model in

studying the response of an equipment item mounted on a torsionally coupled structure with sliding

support. His results indicated that sliding supports could effectively reduce the equipment response,

compared to that of a fixed-base structure. However, in the tuning region, where the natural frequency of

the equipment coincides with the fundamental frequency of the structure, the equipment response may

be adversely amplified due to the increase in eccentricity of the torsionally coupled structure.

The problem of building isolation has recently received more attention than ever from researchers

and engineers, due to the construction of high-precision factories worldwide. More and more

stringent requirements have been employed in this regard for removing the ambient or man-made

vibrations (Rivin, 1995; Steinberg, 2000). To allow sensitive electronic equipment to operate in a harsh

environment, Veprik and Babitsky (2000) proposed an optimization procedure for the design

of vibration isolators aimed at minimizing the response of the internal components of

electronic equipment. As for the protection of high-tech equipment from micro- or ambient

Structure and Equipment Isolation 22-3

© 2005 by Taylor & Francis Group, LLC

vibrations, Yang and Agrawal (2000) showed that passive hybrid floor isolation systems are more

effective in mitigating the equipment response than passive or hybrid base isolation systems. Xu and

coworkers studied the response of a batch of high-tech equipment mounted on a hybrid platform,

which in turn is mounted on a building floor (Xu et al., 2003; Yang et al., 2003). Both their theoretical

and experimental studies showed that the hybrid platform, which is composed of leaf springs, oil

dampers, and an electron-magnetic actuator with velocity feedback control, is more effective in

mitigating the velocity response of the high-tech equipment than the passive platform.

The objective of this chapter is to give an overview on the seismic behavior of various base isolators.

The organization of this chapter can be summarized as follows. In Section 22.2, the mechanisms of

various seismic isolators that are currently in use are introduced and explained. In Section 22.3, a

structure – equipment system isolated by bearings of the elastomeric type is modeled by a three-DoF

system composed of a spring and dashpot unit, for which a closed-form solution is obtained for the

dynamic response of the isolated system subjected to harmonic earthquakes; remarks on the dynamic

response of the system components are also made. In Section 22.4 and Section 22.5, the seismic behaviors

of a structure – equipment system isolated by a sliding support, with and without resilient capability, will

be investigated. Also presented are numerical methods based on the incremental-integration procedure

for the analysis of structural systems with sliding-type isolators. Further information on seismic behavior

and isolation of structures and equipment is found in Chapter 29 to Chapter 31.

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