After nearly a decade of application and investigation,a motion amplifi cation device with viscous dampers for energy dissipation has been recognized as an effective solution to mitigate wind or seismic excitation,especially for stiff structural systems.As a result of compensation of amplifi ed motion,it has been proved that the effi ciency of viscous damper largely depends on the motion amplifi cation device confi guration,particularly for device stiffness.In this paper,a "scissor-jack" type of motion amplification device,called a "toggle brace damper" system,is studied.It is demonstrated that the effi ciency of such a device reflected by its amplifi cation factor is not merely a function of its geometric confi guration,but is highly dependent on the support elements' stiffness as well,similar to the mechanism of a leverage arm.Accordingly,a mathematical model in terms of complex modulus of the viscous damper with consideration of the support brace's stiffness is established.The results indicate that the effi ciency of the motion amplif ication device with viscous dampers signif icantly depends on the stiffness of the support elements.Other parameters,such as toggle brace confi guration and damping values of the viscous damper,are studied and compared.As an application example,numerical analyses are conducted to study the dynamic performance of a 39-story offi ce tower installed with toggle brace dampers constructed on soft soil in a reclaimed area,under a combined effect of the vortex shedding of an adjacent existing 52-story building and earthquakes.The results show that viscous dampers with a motion amplifi cation system using a properly designed toggle brace device proved to be an effective solution to alleviate the external excitations.
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