Abstract This paper proposes a proportional viscous damping model that is computationally very efficient for response history analysis of a large-scale structure with a large number of degrees of freedom. The proposed model is based on a bell-shaped basis function parameterized by the frequency and damping ratio at its peak. Any damping ratio curve in the frequency domain can be easily matched by adding several bell-shaped basis functions. Three methods based on least-squares curve-fitting are used to determine the model parameter values. This model allows for solving structural dynamic response using a sparse block matrix without approximation nor iterative refinement. The block matrix maintains the positive definiteness of the traditional effective stiffness matrix, allowing efficient solution methods such as Cholesky factorization and the conjugate gradient method for solutions. It also allows assigning different damping ratio curves to different structural zones, suitable for soil-structure interaction analysis. Its performance compared against existing damping models is particularly remarkable for large-scale structures with a large number of degrees of freedom in the order of thousands or even millions. The larger the number of degrees of freedom, the better the relative efficiency compared to existing damping models. Several examples are given to demonstrate this remarkable performance.

中文翻译：

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大自由度结构的稀疏比例粘性阻尼模型

摘要 本文提出了一种比例粘性阻尼模型，该模型对于具有大量自由度的大型结构的响应历史分析在计算上非常有效。所提出的模型基于钟形基函数，该函数由其峰值处的频率和阻尼比参数化。通过添加几个钟形基函数，可以轻松匹配频域中的任何阻尼比曲线。三种基于最小二乘曲线拟合的方法用于确定模型参数值。该模型允许使用稀疏块矩阵求解结构动态响应，无需近似或迭代细化。块矩阵保持了传统有效刚度矩阵的正定性，允许有效的求解方法，例如 Cholesky 分解和求解的共轭梯度法。它还允许为不同的结构区域分配不同的阻尼比曲线，适用于土-结构相互作用分析。与现有阻尼模型相比，它的性能对于具有数千甚至数百万数量级的大量自由度的大型结构尤其显着。与现有阻尼模型相比，自由度数越大，相对效率就越好。给出了几个例子来证明这种卓越的性能。与现有阻尼模型相比，它的性能对于具有数千甚至数百万数量级的大量自由度的大型结构尤其显着。与现有阻尼模型相比，自由度数越大，相对效率就越好。给出了几个例子来证明这种卓越的性能。与现有阻尼模型相比，它的性能对于具有数千甚至数百万数量级的大量自由度的大型结构尤其显着。与现有阻尼模型相比，自由度数越大，相对效率就越好。给出了几个例子来证明这种卓越的性能。