## 1 Introduction  
Earthquakes are counted among the most severe and unpredictable threats to structures all around the world. Strong ground motions cause a lot of damage in a wide variety of ways, leaving sometimes thousands of casualties in their wake. The most frequently observed structural failures due to strong ground motions include soft-storey and weak-storey failures, brittle fracture and collapse of concrete and masonry structures, failures due to excessive plastic deformation in steel frame structures, bounding between adjacent buildings (see, for example, [1; 2; 3]), toppling of structures erected on soft and unstable soil, etc. During the last few years alone, the world has witnessed many major earthquakes, five of which have caused far-reaching consequences of a national scale for Haiti (January 2010), Chile (February 2010), New Zealand (February 2011), Japan (March 2011), and Turkey (October 2011). In spite of a number of available technical solutions to protect structures against seismic forces, earthquake peril remains the most sinister natural disaster for which many countries are still ill-prepared. Due to the randomness of occurrence, destructive potential, and insufficient early-warning systems, there is an incesant need for developing earthquake protection systems against seismic excitations and their devastating effects in order to enhance structural safety and reliability (see, for example, [4; 5; 6]). It has been recognized that structures can be effectively protected against strong ground motions by various methods of structural control (see, for example, [7; 8]). The general concept of this design strategy is to modify structural dynamic properties, such as the fundamental period of vibration and the damping ratio, so that structures can respond more favourably to dynamic excitations (see, for example, [9; 10; 11; 12]). The family of structural control methods has grown to include passive, active and hybrid (semi-active) systems (see, for example, [13]). Passive control (see, for example, [14; 15]) is considered to be the safest approach, because, in contrast to active and hybrid devices (see, for example, [16]), no external source of energy is required to activate the system. Among passive control methods, base isolation is one of the most commonly employed strategies for protecting structures against earthquake forces (see, for example, [17; 18; 19]). It works by separating the structure from the horizontal components of the earthquake ground motion by introducing a layer with low horizontal stiffness between the superstructure and its foundation (see, for example, [20; 21]). The main purpose of base isolation is to lengthen the fundamental period of vibration of the structure to reduce the base shear induced by the earthquake, while providing additional damping to the system (see, for example, [22]). Generally, base isolators can be grouped under laminated rubber bearings and sliding bearings. In the first approach, the isolation system introduces cylindrical or rectangular bearings with alternating layers of steel plates and hard rubber between the structure and its foundation (see, for example, [23]). In this approach, laminated rubber bearings are strong and stiff under vertical loads, and yet very flexible under lateral forces. One of the most popular devices of this type is the High Damping Rubber Bearing (HDRB). Because the natural damping of a standard rubber is relatively low, an additional damping can be introduced with the use of some sort of a mechanical damper (see, for example, [24; 25]). A typical example is the Lead Rubber Bearing (LRB), which combines the laminated rubber bearing with a central lead core to improve the energy dissipation properties of the device (see, for example, [26; 27; 28]). Another type of isolation system uses rollers or sliders between the foundation and the base of the structure (see, for example, [29; 30; 31; 32]). This approach assumes that a low level of friction reduces the transfer of shear across the isolation interface.