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在Rayleigh能量法和Southwell’s频率合成法的基础上,建立了一种计算基础受弹性约束,顶端带附加质量的变截面高耸结构基频的近似算法。高耸结构的基频可以表示成各惯性元和复原元所组成子系统的频率合成。同时还分析了不同变截面系数,顶端附加质量和基础约束刚度等因素对结构基频的影响。为了验证所提出的方法,最后将所得频率与有限元计算结果相比较,证明了建立的高耸工程结构基频计算公式具有较高的精度。提出的算法适用于各种基础类型的变截面高耸结构。
Based on the Rayleigh energy method and the Southwell’s frequency synthesis method, an approximate algorithm for calculating the fundamental frequency of high-rise structure with variable section based on the elastic constraint and the additional mass at the top is established. The fundamental frequency of the towering structure can be expressed as the frequency synthesis of the subsystems composed of the various elements of inertia and restoration. At the same time, the influence of different factors of variable cross-section, top additional mass and basic restraint stiffness on the fundamental frequency of the structure is also analyzed. In order to verify the proposed method, the final result is compared with the results of finite element analysis, which proves that the formula for calculating the fundamental frequency of high-rise engineering structure has high accuracy. The proposed algorithm is applicable to a variety of basic types of variable cross-section towering structure.