Calculation of Rayleigh Damping Coefficients for a Transient Structural Analysis

Abstract

Direct numerical integration of differential equations of motion is widely used by engineers to describe the behavior of structures under dynamic loading. The method entails directly integrating the motion equations over time. In the direct method, the damping matrix is formed as a linear combination of mass and stiffness matrices multiplied by the Rayleigh damping coefficients α and β, respectively. The Rayleigh damping coefficients have a significant effect on the response of building structures under dynamic loading. Therefore, the design values of the damping coefficients α and β have crucial importance to ensure accurate and reliable results in a dynamic analysis. The paper presents a time domain analysis for a building subjected to seismic excitations using the modal superposition and direct integration methods. The direct method considers the damping properties of building structures by Rayleigh damping coefficients obtained using various approaches. The building's response to seismic load is compared by response spectra. The authors proposed the least conservative approach for calculating the Rayleigh damping coefficients for analyzing a building in the time domain.