考虑各板面内剪切影响的箱梁竖向纯弯自振特性分析

Analysis of vertical pure bending natural vibration characteristics of box girder considering the influence of in-plane shear

为了方便研究考虑各板面内剪切影响的箱梁竖向纯弯曲自振频率,基于单位力法,结合箱梁弯曲剪应力的分布特点,推导出适用于箱梁各板面内的剪切影响系数表达式。以剪切影响系数为基础,利用哈密顿原理,导出考虑剪切及转动惯量影响的箱梁弯曲自振频率控制微分方程。采用分离变量法,结合边界条件给出了简支箱梁弯曲自振频率表达式。在该剪切影响系数的基础上,结合梁段单元刚度矩阵,编制了MATLAB程序用于分析考虑各板面内剪切影响的箱梁弯曲自振特性。数值算例表明:以本文程序计算的箱梁弯曲自振频率及振型与ANSYS空间有限元结果吻合较好;剪切变形对箱梁自振频率的影响随着频率阶数的增高而增大。参数分析表明,梁高对频率影响较大,当计入剪切影响时,转动惯量对箱梁弯曲自振频率的影响可忽略。

In order to facilitate the study of the vertical pure bending self-vibration frequency of the box girder considering the influence of the shear in each plane,the expression of shear influence coefficient applicable to the box girder is derived by unit force method combined with the distribution characteristics of the flexural shear stress.Based on the shear influence coefficient,the governing differential equation of the box girder considering the influence of shear and moment of inertia is obtained by using the Hamilton′s principle.Combined with the boundary conditions,the self-vibration frequency expression of the simply supported box girder is derived using the method of separation of variables.Based on the shear influence coefficient and the element stiffness matrix of beam segment,the MATLAB program is developed to analyze the bending vibration characteristics of the box girder considering the influence of shear in each plane.Numerical examples show that the natural vibration frequency and vibration mode of the box girder calculated by the program are in good agreement with the ANSYS space finite element results.The effect of shear deformation on the natural vibration frequency of the box girder increases with the increase of the frequency order.The parameter analysis shows that the height of box girder has a great influence on the frequency.While the shear effect is taken into account,the influence of rotational inertia on the bending natural frequency of the box girder is negligible.