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基频是连续梁的重要参数之一,在结构动力响应、抗震设计、冲击系数及共振分析等方面具有重要的理论意义。针对《公路桥梁设计通用规范》(JTG D60—2015)中连续梁基频公式近似计算结果与实际偏差较大的问题,研究常规等截面及大跨径变截面连续梁基频的近似计算问题,依托结构动力学基本特征方程推导出连续梁基频的近似计算公式,将结构参数的常见变化范围进行整理并各自均匀提取若干数值作为参数样本,计算中不考虑剪切变形及横隔板、齿板等细部构造的影响,将所有参数样本全排列得到10万余座不同参数的桥梁样本,实现常见参数连续梁“全覆盖”。利用APDL编程语言对ANSYS进行二次开发,结合工作站的强大计算能力,批量计算10万余座桥梁样本的理论基频,最终对连续梁基频近似计算公式的形式进行理论分析,结合1stopt与MATLAB软件对各种可能的计算公式进行非线性拟合,直至得出形式简明、计算精度高的最佳基频近似计算公式。研究结果表明:连续梁基频的近似计算公式和有限元计算值最大误差为2.1%,平均绝对值误差为0.3%,判定系数R2均大于0.999 9,近似程度良好。经实际工程验证,可快速准确地对连续梁基频进行估算、验算。
The fundamental frequency is one of the important parameters of continuous beam, which has important theoretical significance in the aspects of dynamic response, seismic design, impact coefficient and resonance analysis. Aiming at the problem of approximate calculation result and actual deviation of the continuous beam fundamental frequency formula in “General Specification for Design of Highway Bridges and Bridge” (JTG D60-2015), the approximate calculation of the fundamental frequency of conventional constant cross section and continuous beam with variable cross section is studied. Based on the basic characteristic equation of structural dynamics, the approximate formula of the fundamental frequency of continuous beam is deduced. The common range of structural parameters is sorted out and several numerical values are taken as parameters respectively. The shear deformation, diaphragm, Plate and other detailed structure of the impact of all the parameters of the sample were all arranged more than 100,000 different parameters of the bridge samples to achieve common parameters of continuous beams “full coverage ”. Based on APDL programming language, ANSYS was developed for the second time. Based on the powerful calculation ability of workstations, the theoretic fundamental frequency of more than 100,000 bridge samples was calculated in batches. Finally, the theoretical form of the fundamental frequency approximation formula of continuous beam was analyzed. The software performs a non-linear fit on all possible calculation formulas until the best approximation of the fundamental frequency is obtained with a simple form and a high calculation accuracy. The results show that the maximum error of the approximate formula of the fundamental frequency of continuous beam and the calculated value of finite element is 2.1% and the average absolute value error is 0.3%. The coefficient of determination R2 is greater than 0.999 9 and the approximate degree is good. The actual engineering verification, can quickly and accurately estimate the continuous beam fundamental frequency, checking.