The paper deals with the seismic response analysis of nonlinear secondary oscillators. Bilinear, sliding and rocking single-degree-of-freedom dynamic systems are analysed as representative of a wide spectrum of secondary structures and non-structural components. In a first stage, the equations governing their full dynamic interaction with linear multi-degree-of-freedom primary structures are formulated, and then conveniently simplified using primary-secondary two-degree-of-freedom systems and dimensionless coefficients. In a second stage, the cascade approximation is applied, whereby the feedback action of the secondary oscillator on the primary structure is neglected. Owing to the piecewise linearity of the secondary systems being considered, efficient semi-analytical and step-by-step numerical solutions are presented. The semi-analytical solutions allow the direct evaluation of the seismic response under pulse-type ground excitations and are also used to validate step-by-step numerical schemes, which in turn can be used for general-type seismic excitations. In a third stage, a set of decoupling criteria are proposed for the pulse-type base excitations, identifying the conditions under which a cascade analysis is admissible from an engineering standpoint. Finally, the influence and relative dependencies between the input parameters of the ground motion and the primary-secondary assembly are quantified on the response of the secondary systems through nonlinear floor response spectra, and general trends are identified and discussed.

中文翻译：

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非线性次振子对理想化地震脉冲的动态响应分析

该论文涉及非线性次振子的地震响应分析。双线性、滑动和摇摆单自由度动态系统被分析为代表广泛的二级结构和非结构组件。在第一阶段，制定控制其与线性多自由度初级结构的完全动态相互作用的方程，然后使用初级-次级双自由度系统和无量纲系数方便地简化。在第二阶段，应用级联近似，从而忽略次级振荡器对初级结构的反馈作用。由于考虑了二次系统的分段线性，因此提出了有效的半解析和逐步数值解。半解析解允许直接评估脉冲型地面激励下的地震响应，也可用于验证逐步数值方案，进而可用于一般类型的地震激励。在第三阶段，为脉冲型基础激励提出了一组解耦标准，确定了从工程角度允许级联分析的条件。最后，通过非线性地板响应谱量化地震动输入参数与主次组件之间的影响和相对依赖性对次系统响应的影响，并确定和讨论总体趋势。