单层双向偏心结构振型影响参数推导分析

发布时间：2018-11-11 17:31

【摘要】：为了深入分析单层双向偏心结构平扭耦联参数的影响规律,建立单层双向偏心结构(3自由度)的动力方程,并采用数学领域中三次方程求解的盛金公式,推导出单层双向偏心结构的动力特性显式解析解。根据所得显式解的形式及其对应的判定条件,在合理范围内提取出不同于单向偏心体系的影响参数,分别为:相对偏心距、偏心角、主扭平频率比以及次扭平频率比。根据盛金公式推导所得的显式解析解,总结出结构的主要动力特性指标(频率和振型),进而分析了每个参数对双向偏心结构的平扭耦联特性的影响。结果表明,双向偏心结构平扭耦联参数与单向偏心结构有相似之处,但更为复杂,会涉及到主扭平频率比与次扭平频率比,且两者影响程度也有明显区别。
[Abstract]:In order to deeply analyze the influence of horizontal and torsional coupling parameters on single-layer bidirectional eccentric structure, the dynamic equation of single-layer bidirectional eccentric structure (3 degrees of freedom) is established, and the Sheng Jingong equation is used to solve the cubic equation in the field of mathematics. An explicit analytical solution for the dynamic characteristics of a single layer biaxial eccentric structure is derived. According to the form of the explicit solution and the corresponding judgment conditions, the influence parameters which are different from the unidirectional eccentricity system are extracted within a reasonable range, which are: relative eccentricity, eccentric angle, principal torsional frequency ratio and secondary torsional frequency ratio. Based on the explicit analytical solution derived from Shengjin's formula, the main dynamic characteristics (frequency and mode type) of the structure are summarized, and the influence of each parameter on the coupling characteristics of the bidirectional eccentric structure is analyzed. The results show that the horizontal and torsional coupling parameters of bidirectional eccentric structures are similar to those of unidirectional eccentric structures, but they are more complex and involve the main torsional frequency ratio and the secondary torsional frequency ratio, and there are obvious differences between the two factors.
【作者单位】：天津大学建筑工程学院滨海土木工程结构与安全教育部重点实验室;
【基金】：国家自然科学基金资助项目(51278335)
【分类号】：TU311.3

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