23rd ABCM International Congress of Mechanical Engineering December 6-11, 2015, Rio de Janeiro, RJ, Brazil THE USE OF A VIRTUAL PENDULUM AS PASSIVE ENERGY DISSIPATION SYSTEM FOR SEISMIC PROTECTION OF BUILDINGS Eliot Pezo Zegarra Paulo Batista Gonçalves Departament of Civil Engeneering, Pontifical Catholic University, PUC-Rio,Rio de Janeiro, RJ, Brazil. eliotpz@hotmail.com, paulo@ Abstract. The passive control of structures using a pendulum absorber has been extensively studied in the technical literature and used in tall buildings such as the Taipei 101 in Taiwan. As the frequency of the pendulum depends only on its length and the acceleration of gravity, to tune the frequency of the pendulum with that of the structure, the pendulum length is the only design variable. However, in many cases, the required length and the space required for its installation are not compatible with the project. In these cases one can replace the classical pendulum by a virtual pendulum which consists of a mass moving over a curved surface, allowing thus for a greater flexibility in the absorber design, since the length of the pendulum becomes irrelevant and the shape of the curved surface can be optimized. Several designs are possible and the device can be used as a tuned mass damper or a base isolation system. The aim of this work is to develop a mathematical model for a building with a virtual pendulum and to study the influence of this device on the nonlinear oscillations and stability of the main system under a base excitation. Through simulations under harmonic and recorded ground motions of increasing intensity, the performance of the virtual pendulum used as a tuned mass damper or base isolation is evaluated on an SDOF structure in order to illustrate their respective advantages as well as the drawbacks inherent to their non-linear behavior. Several values of the relevant parameters are assumed in the analyses. Keywords: Seismic protection, virtual pendulum, tuned mass damper, base isolation, nonlinear vibrations. 1. INTRODUCTION As structures become lighter and more slender, the fundamental frequency of the structure decreases and approaches the values of the excitation frequency associated with environmental loads, such as wind, waves or earthquakes. With this the structures may have undesirable levels of vibration, causing discomfort to users, damage to structural elements and, in extreme cases, the ruin of the structure. This is quite common in high seismicity regions. The seismic energy and its frequency content are very dangerous for buildings regardless of their height. Passive vibration control systems have been studied analytically and experimentally by different researchers and used in various kinds of structures in order to minimize the effects of excitation on the structure. In the case of earthquakes, the passive vibration control can be obtained using attenuators generating control forces on the structure which oppose excitation, or by base isolation mechanisms (Soong, et.al.1997). One mechanism that can be used both as a tuned mass damper and base isolation is the so called virtual pendulum, which consists of a mass that moves over a curved surface, causing forces opposed to movement, in the case of the tuned mass damper, or allows the displacement of the structure as a whole, in the case base isolation, reducing stresses and displacements within the structure. Several researches are found in the literature on the use of pendulum absorbers. Gonçalves and Orlando (2013) studied a hybrid control system to mitigate the vibrations of tall towers. The hybrid control is based on the simultaneous use of a pendulum absorber with an external force applied at the tower-pendulum connection. Oliveira (2012) studied the efficiency of a tuned pendulum on the vibrations of a ten-story building modeled as a shear frame. As the frequency of the pendulum depends only on its length and the acceleration of gravity, to tune the frequency of the pendulum with that of the structure, the pendulum length is the only design variable. However, in many cases, the required length and the space required for its installation are not compatible with the project. In these cases one can replace the classical pendulum by a virtual pendulum which consists of a mass moving over a curved surface, allowing thus for a greater