简支薄壁箱梁自由振动的摄动法解析解

发布时间：2018-05-29 11:32

本文选题：箱梁 + 剪力滞　；参考：《哈尔滨工业大学学报》2016年12期

【摘要】：为研究简支薄壁箱梁中剪力滞效应对结构动力特性的影响,基于模态摄动法提出了一种求解薄壁箱梁自由振动的新方法.该方法以相同跨度等截面欧拉梁的频率和模态为Ritz基函数,将箱梁自由振动的微分方程组转化为一组非线性代数方程进行求解.对于简支箱梁,可进一步将代数方程组简化为一元二次方程,从而得到精确的特征值和特征向量.在此基础上,利用所得箱梁振动模态的解析表达式,提出了模态剪力滞系数的概念,从而建立了箱梁固有频率和剪力滞效应之间的关系.随后研究了模态剪力滞系数随跨宽比、翼板抗弯刚度和截面抗弯刚度之比的变化规律.计算结果表明:简支梁腹板处剪力滞系数最大且大于1,为正剪力滞效应;随着模态阶数的增加、跨宽比的减小和翼板抗弯刚度和截面抗弯刚度之比的增大,剪力滞效应呈现增大的趋势.
[Abstract]:In order to study the influence of shear lag effect on the dynamic characteristics of thin-walled box girder, a new method for solving the free vibration of thin-walled box girder is proposed based on the modal perturbation method. In this method, the frequency and mode of Euler beam with the same span and equal section are Ritz basis functions, and the differential equations of free vibration of box girder are transformed into a set of nonlinear algebraic equations to be solved. For simply supported box girders, the algebraic equations can be further simplified to quadratic equations, and the exact eigenvalues and Eigenvectors can be obtained. On this basis, the concept of modal shear lag coefficient is proposed by using the analytical expression of vibration modes of box girder, and the relationship between natural frequency and shear lag effect of box girder is established. Then the variation of modal shear lag coefficient with the ratio of span to width bending stiffness of wing plate and section bending stiffness is studied. The results show that the shear lag coefficient at the web of simply supported beam is the largest and greater than 1, which is a positive shear lag effect, and with the increase of modal order, the ratio of span to width decreases and the ratio of bending stiffness to section stiffness increases. The shear lag effect shows an increasing trend.
【作者单位】：北京科技大学土木工程系;中电建路桥集团有限公司;
【基金】：北京市自然科学基金(8143037)
【分类号】：U441.3

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