两类典型边界下桥梁吊杆频率估计公式化研究

Formulation Study on Frequency Estimate of Bridge Derricks under Two Typical Boundary Conditions

固支-固支和固支-铰支2类典型边界条件下桥梁承重吊杆频率表达式无类似于铰支-铰支边界条件下的显式表达式,这是由于这2类边界条件下短吊杆的频率方程是含有三角函数和双曲线函数的超越方程,需要进行非线性迭代,迭代过程可能造成数据溢出等数值病态。推导2类典型边界条件下承重短吊杆频率的统一表达式,并借助非线性迭代和参数拟合等手段,给出显式拟合公式。数值对比研究表明:在2类典型边界条件下频率拟合公式的相对误差在±2%以内。这些拟合公式是吊杆频率快速估计的简洁方法。

The frequency expression of bearing derricks of bridges under 2 typical boundary conditions,i.e. fixed- fixed support and fixed- hinge support is not similar to the explicit expression under the hinge support- hinge support boundary conditions because the frequency equation of short derricks under such 2boundary conditions is a transcendental equation containing trigonometric function and hyperbolic function and shall be subject to nonlinear iteration,and the iteration process may cause numerical ill- conditions such as data overflow,etc. This paper derives a unified expression of frequency of short bearing derricks under 2 typical boundary conditions and presents the explicit fitting formulae with the help of means such as nonlinear iteration and parameter fitting,etc. The numerical comparative study shows that the relative error of frequency fitting formulae under 2 typical boundary conditions is within ± 2%. These fitting formulae provide a succinct method for quick estimate of derrick frequency.