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基于H∞理论,提出一种定量评价结构鲁棒性的新方法。采用状态空间模型描述结构系统,基于H∞最优,采用系统传递函数的H∞范数作为结构鲁棒性的定量评价指标。对线性系统,分离刚度矩阵的不确定性,给出了H∞结构鲁棒性指标的计算方法;对非线性系统,引入L2性能准则表达鲁棒性。通过单自由度体系和桁架结构,明确了鲁棒性指标的物理意义,分析影响结构鲁棒性的因素。结果表明:基于H∞理论的结构鲁棒性指标代表了结构稳态振动反应的最大振幅与干扰幅值之比,可以反映外部干扰和结构内部的不确定性与结构的响应是否成比例;提高结构整体承载力储备、耗能能力以及关键构件的冗余度可以增强结构的鲁棒性;且H∞鲁棒性指标对结构参数变化较为敏感。
Based on H∞ theory, a new method for quantitatively evaluating structural robustness is proposed. The state space model is used to describe the structural system. Based on the optimal H∞, the H∞ norm of the system transfer function is used as the quantitative evaluation index of structural robustness. For the linear system, the uncertainty of the stiffness matrix is separated and the calculation method of the robustness index of H∞ structure is given. For the nonlinear system, L2 performance criterion is introduced to express the robustness. Through the single degree of freedom system and the truss structure, the physical meaning of the robustness index is clarified, and the factors affecting the structural robustness are analyzed. The results show that the structural robustness index based on the H∞ theory represents the ratio of the maximum amplitude to the disturbance amplitude of the steady-state vibration response of the structure, which can reflect whether the external disturbance and the structure’s internal uncertainty are proportional to the structure’s response; Structural overall capacity reserve, energy dissipation capacity and redundancy of key components can enhance the structural robustness; and H∞ robustness index is more sensitive to structural parameter changes.