Analysis of Bending Natural Vibration Characteristics of Box Girder Based on Additional Deflection for Shear Lag
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摘要:
为揭示弯曲空间效应对自振频率削弱的影响规律，选取剪力滞效应引起的附加挠度为广义位移，将箱梁翘曲附加变形纳入体系总动能中，运用Hamilton原理，建立考虑剪切、剪力滞及双重效应影响的箱梁弯曲自振频率变分解析解，引入空间效应对自振频率削弱影响的差值比参数，详细分析截面尺寸及边中跨径比对差值比参数的影响. 算例分析表明：考虑剪切和双重效应影响的箱梁自振频率解析解与有限元数值解吻合较好；频率阶数越大，各效应对自振频率的削弱程度越大，其中，双重效应影响最为显著，对一阶频率，双重效应对简支和连续箱梁自振频率分别削弱了4.72%和4.80%；跨宽比、宽高比和边中跨径比越大，自振频率差值比越小；板宽比越大，剪力滞、双重效应自振频率差值比越小，剪切自振频率差值比越大；同一跨宽比时，剪力滞和剪切效应对自振频率的削弱程度相当；不同宽高比下，剪力滞效应对自振频率的削弱程度近乎相同，剪切效应影响较为显著；低阶自振频率计算时可按不带悬臂板的箱梁进行计算.
Abstract:In order to reveal the influence of the bending space effect on natural vibration frequency weakening, the additional deflection caused by the shear lag effect was selected as the generalized displacement, and the warping additional deformation of box girder was incorporated into the total kinetic energy of the system. The bending variational solution of the natural vibration frequency of box girder considering the influence of shear deformation, shear lag, and their double effects was established by using the Hamilton principle. The difference ratio parameter of spatial effect on natural vibration frequency weakening was introduced, and the influence of the section size and the side-to-middle span on the difference ratio parameter was analyzed in detail. The example analysis shows that the analytical solution of the natural vibration frequency of the box girder considering shear derformation and double effects is in good agreement with the finite element numerical solution. A larger frequency order indicates a greater weakening degree of each effect to the natural vibration frequency. The double effect is the most significant, which reduces the natural vibration frequency of simply supported and continuous box girders by 4.72% and 4.80% respectively for the first-order frequency. The larger span width ratio, width-to-height ratio, and side-to-middle span ratio indicate a smaller difference ratio of natural vibration frequency. A larger plate width ratio is accompanied by a smaller difference ratio of natural vibration frequency considering shear lag and double effect and a larger difference ratio of natural vibration frequency considering shear derformation . At the same span width ratio, shear lag and shear derformation effects weaken the natural vibration frequency to the same extent. At the different width-to-height ratio ratios, the shear lag effect weakens the natural vibration frequency to almost the same extent, and the shear derformation effect has a more significant impact. Low-order natural vibration frequency can be calculated using a box girder without a cantilever plate.
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图 3 跨宽比对箱梁弯曲自振频率差值比的影响
Figure 3. Influence of span width ratio on difference ratio of bending natural vibration frequency of box girder
图 4 宽高比对箱梁自振频率差值比的影响
Figure 4. Influence of width-to-height ratio on natural vibration frequency difference ratio of box girder
图 5 板宽比对箱梁弯曲自振频率差值比的影响
Figure 5. Influence of plate width ratio on difference ratio of bending natural vibration frequency of box girder
图 6 边中跨径比对连续箱梁自振频率差值比的影响
Figure 6. Influence of side-to-middle span ratio on natural vibration frequency difference ratio of continuous box girder
表 1 不等跨连续梁自振频率参数影响因子
Table 1. Influence factors of natural vibration frequency parameters of continuous girders with unequal span
lb/l n 1 2 3 4 5 6 0.5 1.250 2.000 2.250 2.500 3.250 4.000 0.6 1.215 1.777 1.926 2.340 3.137 3.503 0.7 1.174 1.565 1.699 2.264 2.908 3.060 0.8 1.125 1.390 1.542 2.200 2.613 2.728 0.9 1.066 1.248 1.437 2.118 2.351 2.500 1.0 1.000 1.132 1.368 2.000 2.135 2.365 
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表 2 简支箱梁弯曲自振频率对比
Table 2. Comparison of bending natural vibration frequency of simply supported box girder
Hz n f0 fsl fsd fss ANSYS 结果 Midas 结果 1 3.243 3.160 3.167 3.090 3.108 3.121 2 12.973 11.663 11.871 10.874 10.783 11.124 3 29.188 23.250 24.349 20.851 22.957 23.385 4 51.890 36.511 38.927 31.891 33.325 33.891 5 81.079 51.398 54.491 43.838 44.681 45.332 6 116.753 68.215 70.429 56.690 59.690 60.449
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表 3 连续箱梁弯曲自振频率对比
Table 3. Comparison of bending natural vibration frequency of continuous box girder
Hz n f0 fsl fsd fss ANSYS 结果 Midas 结果 1 3.246 3.160 3.170 3.090 3.192 3.221 2 4.157 4.019 4.033 3.908 4.036 4.242 3 6.073 5.778 5.815 5.556 5.356 5.667 4 12.978 11.663 11.875 10.874 10.048 10.524 5 14.794 13.097 13.385 12.135 11.877 12.487 6 18.150 15.648 16.093 14.356 12.366 13.191
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