Modeling method of element Rayleigh damping for the seismic analysis of a 3D FEM model with multiple damping properties

Abstract

Damping modeling is important for the accurate evaluation of the seismic response of structures. Our group previously reported a damping modeling method using element Rayleigh damping and evaluated the effectiveness using a simple lumped-mass model with multiple damping properties; however, the effectiveness of the method was not evaluated for three-dimensional (3D) finite element method (FEM) models with multiple damping properties. Moreover, further studies showed that the method needed to be improved to be applied to 3D FEM models. Therefore, the method has been improved to enable application to the seismic analysis of 3D FEM models, and the effectiveness of the method has been evaluated. The proposed method uses a weighted least-squares method to automatically determine the coefficients of element Rayleigh damping. The weighted least-squares method minimizes the differences between the modal damping ratios to be modeled and those given by element Rayleigh damping. Although all modal damping ratios in a simple lumped-mass model were used for damping modeling in our previous study, obtaining them for 3D FEM models is impractical because these models have more natural modes than simple lumped-mass models. Therefore, we used modal damping ratios below a cut-off frequency. The effectiveness of the proposed method was evaluated by comparing it with conventional methods in terms of the modeling errors related to the modal damping ratios and the maximum absolute acceleration. The proposed method tended to have lower errors than the conventional methods and is concluded to be more effective for the seismic analysis of 3D FEM models with multiple damping properties. The proposed method can automatically determine the coefficients of element Rayleigh damping and can more accurately model the damping properties of analysis models, indicating that the proposed method is a powerful tool for the seismic analysis of 3D FEM models with multiple damping properties.