Frequency Domain Optimization of Dry Friction Dampers on Buildings Under Harmonic Excitation

Abstract

Friction mechanism has an extensive usage in many different fields for energy dissipation. It is also used at buildings to reduce the displacement that is caused by ground acceleration during an earthquake. Despite friction damper is a simple device to use on structures, due to its nonlinear characteristic, analysis and design of a structure equipped with a friction damper is difficult. In this paper, Harmonic Balance Method (HBM) is employed to represent the frictional contact as a nonlinear complex stiffness in order to find the steady state displacement of each story of a multi-story building under harmonic ground acceleration. Application of HBM results in a set of nonlinear algebraic equations in frequency domain which can be solved by an iterative method. As a result of this, the solution method presented reduces the computational effort compared to time integration methods; therefore, optimization of friction dampers can be performed in a reasonable time. Accuracy and validation of the presented method is demonstrated on a single-story shear building model equipped with a single friction damper by comparing the frequency domain solution with time marching results. A multi-story building is considered as a case study where the slip force of each dry friction damper is optimized in order to minimize the relative displacement between the stories.