考虑剪力滞效应的薄壁曲线箱梁自由振动的有限段法

Finite segment method for analyzing the free vibration of thin-walled curved box girder considered the shear lag effect

基于有限元法和薄壁曲杆理论,提出了考虑剪力滞效应影响的薄壁曲线箱梁自由振动分析的有限段法。取曲线箱梁剪力滞微分方程齐次解为位移模式中的峰值函数,通过Hamilton原理,推导出梁段单元的自由振动方程,得到了单元刚度矩阵和单元质量矩阵。通过矩阵组合,将曲线箱梁自振频率问题转化为广义特征值问题进行求解。文中给出了算例,并与有限元解法作了比较,证明了方法的正确性和可靠性。研究表明:剪力滞效应能够降低曲梁的刚度和自振频率,并且随着曲率半径和宽跨比的增大,剪力滞效应对于曲梁自振频率的影响也更加显著。

Based on the finite element method and the thin-walled curved bar theory, a finite segment method was presented for analyzing the free vibration of the thin-walled curved box girder considered the influence of shear lag effect. The homogeneous solutions derived from the shear lag differential equations of curved box girder was used as the peak function of the displacement patterns, the mass matrix and stiffness matrix of finite segment were derived by means of Hamilton principle. By composing those matrices, the problem of the free vibration frequency of curved box girder was transformed into solving the generalized eigenvalue problem. In this paper, an example was given and compared with the Ansys solution; the correctness of this method was proved. This shows:the free vibration frequency and stiffness of continuous curved box girder was discussed because of the shear lag effect. And with the increase of the curvature radius and the width to span the influence of shear lag effect on the curved box girder will be more obvious.