一种薄壁箱梁自振频率分析的多参数翘曲位移函数法

以能量变分原理为基础,设置3个不同的剪滞纵向位移差函数以准确反映薄壁箱梁不同宽度翼板的剪滞变化幅度,在综合考虑剪力滞后、剪切变形及转动惯量效应的基础上,提出一种能对工程中常用的梯形薄壁箱梁自振特性进行分析的方法。本文利用最小势能原理建立了梯形薄壁箱梁的控制微分方程和自然边界条件,据此推导几种常用边界条件的固有频率方程(简支、悬臂、连续、两端固支)。在算例中,本文将解析解与板壳有限元结果进行比较,证明本文方法的有效性,明确剪力滞后效应对几种不同边界条件梯形箱梁自振特性影响的规律,为箱梁动力特性的进一步研究奠定基础。本文所得公式对目前的剪滞分析理论有所进展,具有一定的理论意义和实用价值,因此更具一般性。

An Approach of Multi-parameter Warping Displacement Function for Natural Frequency Analysis of Thin-walled Box Girders

Based on the energy variation principle,this paper proposes an approach to analysis of shear lag effect,shear deformation and rotational inertia on the dynamic characteristic of trapezoidal thin-walled box girders generally used in engineering.Consideration has made to three different longitudinal displacement difference functions to accurately reflect the amplitude of shear lag changes in the thin-walled box girders with various widths of wing slabs.The minimum potential principle is applied to establish the governing differential equation of motion and the corresponding natural boundary condition,which is used to obtain the natural frequency equation for the trapezoidal section box girder of different boundary types,such as simple support,cantilever,continuous beam and fixed ends.The calculation examples compare the finite shell element solutions with the analytical solutions and verify the validity of the proposed approach.The formulas obtained in this study develop the shear lag theory. They have a theroritical significance and value general application.