以能量变分原理为基础,综合考虑箱形梁满足应力自平衡的剪力滞、剪切变形和转动惯量等多重因素的影响,推导出箱梁的自由振动方程及自然边界条件。通过算例将本文解析计算结果与ANSYS有限元计算结果进行了比较。结果表明,两者计算结果吻合良好,论证了本文计算方法的正确。所得公式比以往箱形箱梁自振特性计算理论有一定发展,并得出了一些对工程设计有意义的结论;在剪力滞效应的作用下,箱形梁的固有频率减小幅度较大,不能忽略;剪力滞效应随频率阶次的升高而变大,随着跨宽比的减小而增大。
Based on energy variation principle,the differential equation of free vibration and the corresponding boundary conditions of box girder with consideration for the shear lag effect meeting self equilibrated stress,shear deformation as well as rotational inertia were induced.The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified.The obtained formulas developed the shear lag theory.Some meaningful conclusions for engineering design were obtained.The decrease extent of each order natural frequency of the box-girder beam is great under the shear lag effect.The shear lag effect of box girder increases when frequency order rises,and increases while span-width ratio decreases.