以结构动力响应微分求积（DQ）分析方法的基本数值格式为基础，探讨了时步内时间点分别为均匀分布、Chebyshev分布和Chebyshev-Gauss-Lobatto（CGL）分布时该方法的数值稳定性与数值耗散性，并通过等效一阶模型严格推导出方法的代数精度阶数。研究表明，该方法的数值稳定性与时步内时间点分布情况密切相关，不均匀分布格式明显优于均匀分布格式，但体系阻尼比对方法的稳定性具有重大影响；代数精度由离散时间点数决定，一般情况下都能实现比较高的数值精度；两种不均匀时间点分布格式，即Chebyshev格式和CGL格式的DQ分析方法，均具有极佳的数值耗散特性。
Abstract
Based on basic numerical mode of the differential quadrature (DQ) method for dynamic response of structures, the numerical stability and numerical dissipation of DQ method were investigated when time point distributions were uniform distribution, Chebyshev one and Chebyshev-Gauss-Lobatto (CGL) one, respectively within a time step.The algebraic accuracy order number of DQ method was strictly deduced with the equivalent first-order model.The study showed that the method’s numerical stability is closely related to time point distributions within a time step, non-uniform modes are obviously better than uniform ones, but the system damping ratio has large influence on the method’s stability; the method’s algebraic accuracy depends on number of discrete time points, higher numerical accuracy can be realized generally; DQ methods with time points’ two non-uniform distribution modes of Chebyshev distribution and CGL one, respectively have excellent numerical dissipation.
关键词
结构动力响应 /
微分求积 /
数值稳定性 /
代数精度 /
数值耗散性
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Key words
dynamic response of structures /
differential quadrature (DQ) /
numerical stability /
algebraic accuracy /
numerical dissipation
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