Analysis of Bending Natural Vibration Characteristics of Box Girder Based on Additional Deflection for Shear Lag
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.
box girderspatial effectadditional deflectionnatural vibration frequencydifference ratio parameter
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