Keywords: output frequency response function, nonlinearity, multi-storey building, displacement vibration isolation.

Multi-storey building structures are one of the most common engineering structural systems and the displacement vibration isolation is an issue with considerable practical significance. The tragic consequences of the recent earthquakes in China (2008), Haiti (2010) and Chile (2010) have shown the tremendous importance of the vibration isolation for buildings, bridges and other infrastructure.

In recent years, a variety of control devices have been proposed to increase the structural safety and reliability against strong earthquakes and wind [1]. As one of the passive energy dissipation devices, nonlinear viscous damping devices were first proposed by Soong and Constantinou [2] in 1994. Up to now, different nonlinear viscous damping devices have been studied, manufactured, and used in engineering structures such as civil buildings, towers and bridges, demonstrating good performance in seismic protection, vibration isolation, noise control and other fields [2,3].

In this paper, in order to study the nonlinear systems in the frequency domain, the output frequency response function (OFRF), a new concept recently proposed by the authors is applied to evaluate the effect of a nonlinear viscous damping device on the displacement vibration isolation of multi-storey building structures. The OFRF concept shows an explicit analytical relationship between the output frequency response of nonlinear systems and the system nonlinear characteristic parameters. The finite element (FE) analysis is used to evaluate the structural displacement transmissibility in different cases, and the results are compared with their OFRF estimates.

The results indicate an excellent agreement between the displacement vibration transmissibility obtained by the FE simulation and the result evaluated using an OFRF estimation. These demonstrate the effectiveness of the use of the OFRF to evaluate the displacement vibration transmissibility and imply that the OFRF concept can be used to significantly facilitate the design of nonlinear viscous damping devices and find suitable values of the nonlinear parameters to achieve an appropriate optimal design for the vibration isolation of multi-storey building structures.

1

S.J. Dyke, B.F. Spencer Jr, M.K. Sain, J.D. Carlson, "Modeling and control of magnetorheological dampers for seismic response reduction", Smart Materials and Structures, 5(5), 565-575, 1996. doi:10.1088/0964-1726/5/5/006

2

T.T. Soong, M.C. Costantinou, "Passive and Active Structural Vibration Control in Civil Engineering", Springer, 1994.

3

R.A Ibrahim, "Recent Advances in Nonlinear Passive Vibration Isolators", Journal of Sound and Vibration, 314, 371-452, 2008. doi:10.1016/j.jsv.2008.01.014

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