基于Galerkin法的新型波形钢腹板箱梁桥动力特性研究

为科学合理地分析波形腹板钢箱-混凝土组合梁的自振特性，综合考虑剪切效应和剪力滞效应，运用Galerkin法和Hamilton原理推导了该桥型的自由振动控制微分方程和自然边界条件。根据自然边界条件，求解出剪切变形效应和剪力滞效应影响下波形腹板钢箱-混凝土组合梁竖向弯曲振动频率的计算公式，将其计算结果与实桥的实测结果、模型试验结果及ANSYS三维有限元结果进行了对比，并对竖向弯曲振动频率的影响因素和基频进行了分析。结果表明：竖向弯曲振动频率计算公式的结果与实桥的实测结果、模型试验的实测结果、ANSYS有限元结果吻合良好，验证了所推导的频率计算公式的正确性；竖向弯曲振动频率随高跨比的增大而增大，当高跨比小于0.05时，竖向弯曲振动频率的增幅较为平缓，当高跨比大于0.05时，竖向弯曲振动频率的增幅较为显著；竖向弯曲振动频率随宽跨比的增大而增大，但整体增幅不明显；竖向弯曲振动频率随波形钢腹板厚度的增加而不断增大，阶数越高，增幅越显著；箱梁剪力滞对竖向弯曲振动频率影响很小，前5阶最大误差仅为6.73%，波形钢腹板剪切变形对竖向弯曲振动频率影响较大，前5阶最大误差已高达51.18%。

Dynamic Characteristics of New Type Composite Box Girder Bridge with Corrugated Steel Webs Based on Galerkin Method

In order to analyze the free vibration characteristics of steel box-concrete composite girder with corrugated webs, considering the shear deformation and the shear lag effect, the governing differential equations and natural boundary conditions of steel box-concrete composite girder with corrugated webs were derived by using Galerkin and Hamilton principle. According to the natural boundary conditions, a formula for calculating the natural frequencies of vertical bending vibration of the steel box-concrete composite girder with corrugated webs was obtained. The proposed method results were compared with the modal test results, the model test results and the FE results, and the influence factors and fundamental frequency were analyzed. The results show that the proposed method results are in good agreement with the modal test results of the field bridge, the model test results and the FE results, which verifies the correctness of the derived frequency calculation formula. The natural frequencies of vertical bending vibration increase with the increase of height-span ratios. When the height-span ratios are less than 0.05, the increase of the natural frequencies of vertical bending vibration is relatively gentle. When the height-span ratios are greater than 0.05, the increase of the natural frequencies of vertical bending vibration is relatively significant. The natural frequencies of vertical bending vibration increase with the increase of width-span ratios, but the overall increase is not obvious. The natural frequencies of vertical bending vibration increase continuously with the increase of the thickness of corrugated steel webs, and the higher the order, the more significant the increase. The shear lag effect of box girder has little influence on the natural frequencies of vertical bending vibration, and the maximum error of the first five orders is only 6.73%. The shear deformation of corrugated steel webs has great influence on the natural frequencies of vertical bending vibration, and the maximum error of the first five orders is as high as 51.18%.