A Calculation Method for Determining the Number of Truncated Modes Based on Hysteretic Damping Model

Purpose This study aims to propose a method to determine the number of truncated modes for the mode superposition method based on the hysteretic damping model. Methods Based on the quasi-static method, indexes such as the cumulative modal contribution coefficient of foundation shear force, the norm of cumulative displacement contribution coefficient and the norm of cumulative static load contribution coefficient can be obtained. Considering these indexes, this paper proposes a computational method to determine the number of truncated modes. Results When the computational accuracy of the working condition is not high, the 1-norm of the cumulative modal static load contribution coefficient vector can be used as the index to determine the number of truncated modes. When the computational accuracy of the working condition is high, it is recommended to select the 2-norm and the infinite norm of the cumulative modal static load contribution coefficient as indexes. Furthermore, the indexes of non-classically damped systems based on different modes are not monotonically increasing or decreasing. Conclusion The proposed method for determining the number of truncated modes can be applied to both classically damped systems and non-classically damped systems based on hysteretic damping model.