PSI - Issue 44

Gaspar Auad et al. / Procedia Structural Integrity 44 (2023) 1474–1481 Gaspar Auad et al. / Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction Seismic isolation represents an effective way of protecting buildings and acceleration-sensitive equipment (Shenton and Lin (1993); Chimamphant and Kasai (2016)). Conventional seismic isolation is achieved by placing a laterally flexible and vertically rigid interface between the structure and the ground. In this way, the natural frequencies of the dynamic system are diminished, moving them away from the range of predominant frequencies in natural ground motions. This change in dynamic properties of the protected structure allows for a decrease in the magnitude of the seismic loads transmitted to the building and, consequently, reduces the deformation of structural elements and maximum acceleration developed in the superstructure. One alternative to achieve seismic isolation is to construct isolation systems employing Frictional Pendulum System (FPS) devices (Zayas et al. (1990)). This frictional isolator consists of an articulated slider and a spherical sliding surface. In base-isolated structures subjected to high-magnitude ground motions, internal lateral impacts between inner sliders and restraining rims of frictional devices can be observed. The impacts jeopardize the benefits of using a flexible interface to protect infrastructure. One suggested alternative is to develop adaptive systems that exhibit changes in the dynamics properties under increasing displacement demands. The FPS bearing is an attractive alternative to modifying and developing adaptive passive isolators. One of the design parameters of the FPS, the radius of curvature of the sliding surface, can be modified. Variable curvature frictional isolators are generated by using this approach. Some examples of variable curvature devices are the Polynomial Sliding Isolators with Variable Curvature (PSIVCs) (Lu et al. (2011)) and the Variable Frequency Pendulum Isolator (VFPI) (Pranesh and Sinha (2000)). In this study, a particular shape of the sliding curvature is studied. This shape is generated by revolving a portion of a plane ellipse around a vertical axis. This elliptical sliding surface provides a variable stiffness of the pendular force developed in frictional isolators. The stiffness of the isolator increases smoothly as the device is laterally deformed. This smooth-hardening behavior is examined as an alternative to mitigate the adverse effects of internal lateral impacts. This paper presents a physical model helpful in analyzing the dynamic response of structures equipped with variable curvature devices. The proposed model is validated using a Finite Element Model exposed to static and dynamic loads. While the static analysis validates the lateral behavior in terms of the pendular and frictional force transmitted by the bearing, the dynamic analysis supports the three-dimensional representation of the lateral impact behavior. Finally, a comparative example of a three-dimensional reinforced concrete structure equipped with classical spherical FPS devices and variable curvature frictional isolators is presented to illustrate the benefits of using passive adaptive isolation systems when internal lateral impacts are observed. 2. Physical model of variable curvature frictional isolator A physical model for dynamic analysis of structures equipped with Friction Pendulum System (FPS) bearings (Zayas et al. 1990) was proposed by Almazán and De La Llera (2003). This model represents the behavior of a classical frictional isolator composed of a spherical sliding surface and an articulated slider. The physical model accounts for important modeling aspects such as large deformation, P-∆ effects, sticking and sliding phases, horizontal interaction, and kinematic constraints, among other essential phenomena. This paper presents an extension of this numerical approach to consider variable curvature sliding surfaces and the lateral impact behavior. The shape of the sliding surface needs to be expressed as an implicit equation as follows: = ( , , ) = 0 (1) This study analyzes a specific variable curvature shape of the sliding surface. This surface is obtained by revolving a planar ellipse around a vertical axis. The planar ellipse with its geometric parameters (i.e., its height 2b and width 2a ) and the generated surface are presented in Fig. 1((a) and (b)), respectively. The implicit equation that describes this shape is the following: