Abstract A proportional viscous damping model based on a bell-shaped basis function parameterized by the frequency and damping ratio at its peak has recently been proposed. The basis function in the frequency domain has a fixed frequency bandwidth and could not match a damping ratio curve that changes precipitously over a short frequency interval. This study proposes new parameters to control the bandwidth, while maintaining the sparsity of damping coefficient matrix and the order of computational efficiency. Three types of modification are introduced. Types 1 and 3 control the bandwidth while maintaining the symmetry of the bell shape on the logarithmic scale, and Type 2 allows the left and right bandwidths to be adjusted independently. Type 3 controls the bandwidth while maintaining the same number of nonzeros in the expanded damping matrix, but the other two have the number of nonzeros increased for a smaller bandwidth. These modifications make the model versatile in matching any smooth damping ratio curve, particularly for a curve that has damping ratios changing drastically over a short frequency interval. Several examples are given to showcase their matching performance and the sparsity of their expanded damping coefficient matrices.

中文翻译：

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频率带宽可调的钟形比例粘性阻尼模型

摘要 最近提出了一种基于钟形基函数的比例粘性阻尼模型，该基函数由其峰值处的频率和阻尼比参数化。频域中的基函数具有固定的频率带宽，无法匹配在短频率间隔内急剧变化的阻尼比曲线。本研究提出了新的参数来控制带宽，同时保持阻尼系数矩阵的稀疏性和计算效率的顺序。介绍了三种类型的修改。类型 1 和 3 控制带宽，同时保持对数刻度上的钟形对称，类型 2 允许独立调整左右带宽。类型 3 控制带宽，同时在扩展阻尼矩阵中保持相同数量的非零值，但其他两个的非零数增加了较小的带宽。这些修改使模型在匹配任何平滑的阻尼比曲线方面具有通用性，特别是对于阻尼比在短频率间隔内急剧变化的曲线。给出了几个例子来展示它们的匹配性能和它们的扩展阻尼系数矩阵的稀疏性。