Surrogate models for seismic response analysis of flexible rocking structures

IF 4.3 2区 工程技术 Q1 ENGINEERING, CIVIL Earthquake Engineering & Structural Dynamics Pub Date : 2024-07-04 DOI:10.1002/eqe.4193
Andréia Horta Alvares da Silva, Božidar Stojadinović
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Abstract

Seismic design tools are based on surrogate models of the designed structure and the responses of those surrogates to earthquake ground motions. To design symmetric flexible rocking structures, a surrogate model that includes rocking and flexure is needed. In this paper, we derive the equation of motion of a flexible multi-degree-of-freedom (MDOF) structure rocking on its base in modal coordinates. Then, we introduce a set of two-degree-of-freedom (2DOF) surrogate models that accounts only for the first elastic vibration mode of the multimass structure and its rotation about the base pivot points. We investigate the surrogates' ability to represent the dynamics of an elastic MDOF structure that uplifts and rocks and the interaction between rocking and flexure. Therein, we detail the simplifications for the equations of motion of the 2DOF surrogate models and the adopted rocking impact model, and develop and check the sliding initiation condition. We show that the simplified 2DOF surrogate model responses compare well to experimental results. Then we assess the 2DOF surrogate model accuracy in representing the earthquake response of the MDOF model using Cloud Analysis and the coefficient of determination R 2 $R^2$ approach. We find that simplified 2DOF surrogate of the MDOF model is quite accurate ( R 2 = 0.99 $R^2\,=\,0.99$ ) in estimating its maximum relative top displacement and acceptably accurate ( R 2 = 0.90 $R^2\,=\,0.90$ ) in estimating its maximum base rotation based on a thousand randomly generated flexible rocking structure earthquake response analyses. Lastly, we discuss using the simplified 2DOF surrogate model of symmetric flexible rocking structures in preliminary seismic design, and give examples featuring a continuous elastic hollow semi-conical chimney and an inelastic flexible MDOF structure, both with a base that may uplift.

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用于柔性摇动结构地震响应分析的代用模型
抗震设计工具基于设计结构的代用模型以及这些代用模型对地震地面运动的响应。要设计对称柔性摇动结构,需要一个包括摇动和挠曲的代用模型。在本文中,我们以模态坐标推导了在基座上摇摆的柔性多自由度(MDOF)结构的运动方程。然后,我们引入了一组两自由度(2DOF)代用模型,该模型仅考虑多质量结构的第一弹性振动模式及其围绕基座支点的旋转。我们研究了这些代用模型在表示上浮和摇晃的弹性 MDOF 结构的动力学特性以及摇晃和挠曲之间的相互作用方面的能力。在此过程中,我们详细说明了对 2DOF 代用模型运动方程和所采用的摇摆冲击模型的简化,并开发和检验了滑动起始条件。结果表明,简化后的 2DOF 代用模型的响应与实验结果对比良好。然后,我们利用云分析和决定系数法评估了 2DOF 代理模型在表示 MDOF 模型地震响应方面的准确性。我们发现 MDOF 模型的简化 2DOF 代理在估计其最大相对顶部位移方面相当准确(),并且根据随机生成的一千个柔性摇动结构地震响应分析,在估计其最大底座旋转方面的准确性也可以接受()。最后,我们讨论了在初步抗震设计中使用对称柔性摇动结构的简化 2DOF 代理模型的问题,并举例说明了一个连续弹性空心半锥形烟囱和一个非弹性柔性 MDOF 结构,这两个结构的底座都可能发生上浮。
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来源期刊
Earthquake Engineering & Structural Dynamics
Earthquake Engineering & Structural Dynamics 工程技术-工程:地质
CiteScore
7.20
自引率
13.30%
发文量
180
审稿时长
4.8 months
期刊介绍: Earthquake Engineering and Structural Dynamics provides a forum for the publication of papers on several aspects of engineering related to earthquakes. The problems in this field, and their solutions, are international in character and require knowledge of several traditional disciplines; the Journal will reflect this. Papers that may be relevant but do not emphasize earthquake engineering and related structural dynamics are not suitable for the Journal. Relevant topics include the following: ground motions for analysis and design geotechnical earthquake engineering probabilistic and deterministic methods of dynamic analysis experimental behaviour of structures seismic protective systems system identification risk assessment seismic code requirements methods for earthquake-resistant design and retrofit of structures.
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