Frequency-independent damping models for a high-rise building with simultaneous horizontal and vertical seismic motions

Recent seismic analyses indicate that the structural damping ratio should be considered frequency-independent, for safe and accurate estimations. In response, damping models like the Wilson–Penzien (WP) damping model, that is one of the modal damping, provide frequency independence across all modes; however, these models require considerable computational resources, especially for large-scale models. While Rayleigh damping is computationally efficient, it maintains a nearly constant damping ratio only within a limited frequency range. To address these limitations, several alternative damping models have been introduced, such as uniform (UN), causal hysteretic (CH), and extended Rayleigh (ER). We use the factor W ξ to represent the frequency range where the damping ratio remains approximately constant, defined as the ratio of maximum to minimum frequencies ( f max / f min ), within a specified tolerance of the target damping ratio. For Rayleigh damping, W ξ = 3.7, while the CH and ER models achieve W ξ values greater than 20. Although the UN model achieves a high W ξ , it demands large computational resources in the implicit analyses, commonly used for seismic response studies. In this study, we address the simultaneously inputting horizontal and vertical seismic motion into a large-scale dynamic analysis model of a high-rise building. In this analysis, horizontal, vertical, and local beam vibration modes spanning a wide frequency range appeared. Considering that these modes require the same damping ratio, damping models with W ξ values of 50 or higher are desirable. However, this threshold considerably exceeds W ξ values achievable with the existing models, rendering these models unsuitable for the intended application. Therefore, we propose and validate the efficiency of two new damping models (ER-W and CH19) that meet this requirement by improving existing models. Using these damping models, it is possible to analyze the horizontal and vertical modes and local vibration modes of the beam, assuming a simultaneous horizontal and vertical input to a high-rise building.