Analysis of Behavioral Damped Outrigger in Tall Structures by Fourier Method in Hilbert Space

Achieving efficient methods to protect the structure against forces such as wind and earthquake is one of the first steps in the design of structures and has led to the provision of structural control systems. Structural control systems include three systems, active control, passive control and semi-active control. (Spencer Jr et al. 2003), (Mulligan et al. 2007). The outrigger system with the viscous damper, was proposed by, (Gamaliel, 2008) and its effect on tall structures was investigated, (O'Neill, 2006) showed that the use of damper and increasing damping in the outrigger system in proportion to increasing the stiffness and dimensions of the structure. (Farzad et al. 2019) has also used ultrasonic algorithms to determine the optimal position of outrigger system in tall steel frames. Experimental and analytical researches also show that the use of outrigger system is effective in reducing the lateral displacement of tall structures. (Tan et al. 2012), (Deng et al. 2014).(Jovanovich, 2011) Used the Fourier series method in Hilbert space to investigate the transverse vibrations of the beam with boundary conditions of linear viscosity.In this paper, the vibrations of the structure and the effect of central core system with the damped arm brace using axial load (due to the mass of the central mass) in the control of lateral displacement due to harmonic loading are investigated. Previous studies have not considered the effect of perimeter columns stiffness and the effect of axial force on frequencies and lateral displacement of the structure, and for solving the partial differential equation governing the problem, the Fourier series method is used to define the differential operator in Hilbert space.