Mathematical Formulation for Determining Lateral Displacement of Tubular Frame and Outriggers Equipped with Viscous Dampers

Abstract

Viscous Dampers are mainly used to mitigate and control vibration, acceleration and lateral displacement in buildings. A hybrid system comprised of framed tube, shear core and outriggers equipped with passive linear viscous dampers is investigated, and the mathematical formulation is developed to analyze the hybrid system as a beam-like structure. A mathematical model, based on Euler-Bernoulli flexural beam theory, is developed to build a simple, yet accurate model for calculating the lateral displacement profile of the hybrid system, under lateral load patterns varying against time. The properties of the hybrid system may vary in arbitrary segments, and any number of outrigger systems may be considered through the height of the structure in the proposed method. Kinetic and potential energies and non-conservative works due to the velocity dependent viscous dampers force and the lateral load exerted on the hybrid system are obtained. Next, Hamilton’s principle is implemented, and the governing equation of motion and boundary conditions are derived. As the aforementioned partial differential equations are dependent on both time and space, the central finite difference method is chosen as a numerical method to find the answer to the equation of motion.