基于动力刚度矩阵的波形钢腹板PC 连续箱梁桥自振频率分析

In order to reasonably analyze the influence of the shear deformation of the corrugated steel web on the natural vibration frequency of the PC continuous box girder bridge with corrugated steel webs, firstly, the element stiffness matrix of the PC box girder bridge with corrugated steel webs is derived by using the principle of energy variation. Secondly, according to the derived element stiffness matrix, a solution program for calculating the natural vibration frequency of the multi-span constant-section PC continuous box girder bridge with corrugated steel webs considering the influence of the shear effect of the steel web is compiled by using MATLAB software. The correctness of the natural vibration frequency values calculated by this program has been verified by the measured frequency values of the built actual bridge and the calculated values of the ANSYS three-dimensional finite element. Finally, the influence parameters of the flexural vibration frequency of the multi-span constant-section PC continuous box girder bridge with corrugated steel webs are analyzed. The results show that: the natural vibration frequency values calculated by the research program in this study are in good agreement with the measured values and finite element values of the built actual bridge, and this solution program has a high accuracy, and the differences of the first 5 natural vibration frequencies are within 6.01% and 7.32%; the shear deformation effect of the corrugated steel web has a relatively large influence on the natural vibration frequency of the PC continuous box girder bridge with corrugated steel webs, while whether the shear modulus of the corrugated steel web is corrected and the model of the corrugated steel web have a relatively small influence on the flexural vibration frequency of this bridge type, and the differences of the first 5 flexural vibration frequencies are within 1.07% and 0.55% and can be ignored; the dynamic analysis problem of the PC continuous girder bridge with corrugated steel webs considering the shear deformation effect can be conveniently incorporated into the matrix displacement system of the ordinary bar system structure, avoiding the complexity of the establishment and solution of the ANSYS finite element model, and can provide a certain reference basis for the calculation and analysis of the flexural vibration frequency of this bridge type.

为合理分析波形钢腹板的剪切变形对波形钢腹板PC连续箱梁桥自振频率的影响,首先,运用能量变分原理推导出波形钢腹板PC箱梁桥的单元刚度矩阵。其次,根据推导所得的单元刚度矩阵,采用MATLAB软件编制了考虑钢腹板剪切效应影响的多跨等截面波形钢腹板PC连续箱梁桥自振频率计算的求解程序。该程序计算所得自振频率值的正确性,得到了已建实桥频率实测值和ANSYS三维有限元计算值的验证。最后,对多跨等截面波形钢腹板PC连续箱梁桥弯曲振动频率的影响参数进行了分析。结果表明:本研究程序计算的自振频率值与已建实桥的实测值及有限元值吻合较好,该求解程序具有较高的精度,前5阶自振频率的差值在6. 01%和7. 32%以内;波形钢腹板的剪切变形效应对波形钢腹板PC连续箱梁桥的自振频率影响较大,而波形钢腹板的剪切模量是否进行修正及波形钢腹板的型号对该桥型的弯曲振动频率的影响较小,前5阶弯曲振动频率的差值在1. 07%和0. 55%以内,可以将其忽略不计;可将考虑剪切变形效应下波形钢腹板PC连续梁桥的动力分析问题,方便地纳入到普通杆系结构矩阵位移体系中,避免了ANSYS有限元模型建立和求解的复杂性,可为该桥型弯曲振动频率的计算与分析提供一定的参考依据。