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High Static Low Dynamic Stiffness (HSLDS) is a kind of nonlinear visco-elastic device with features of passive control systems. This device presents the main advantages of working without a need for external energy and a maintenance of low cost. Thus, the paper deals with effects of HSLDS-outriggers at a predefined location on a high rise building subjected under earthquake excitation. The partial derivative equations based on the Timoshenko theory are used to model the tall building as an elastic-continuum beam. The nonstationary random approach is used to illustrate the dynamics of earthquake excitation of repeated sequences. Known as the powerful analytical tool and currently applicable to a variety of stochastic and deterministic problems, the stochastic averaging generalized by harmonic function is developed to linearize the modal equation of the structural system. It is showed that the direct simulation is good agreement with equivalent linearization technique. In doing so, it appears that this approximate analytical technique is very convenient to quantify the threshold values of parameters of the HSLDS control device. The obtained results come out that the control device significantly improved the seismic performance of the structural system at an acceptable level.

High static low dynamic stiffness outriggers effects on vibration control on cantilever Timoshenko Beam under earthquake excitation