于微分求积法的两端固结刚性吊杆拉力识别研究

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (2) : 94-103.

振动理论与交叉研究

于微分求积法的两端固结刚性吊杆拉力识别研究

彭涛1,2，稂其林2，陆小龙2，王涛2，田仲初*1,2

作者信息 +

Tension identification of rigid suspenders with two fixed ends based on the differential quadrature method

PENG Tao1,2，LANG Qilin2，LU Xiaolong2，WANG Tao2，TIAN Zhongchu*1,2

Author information +

文章历史 +

摘要

以修正Timoshenko梁理论为基础，提出了一种基于微分求积法的拱桥刚性吊杆拉力识别方法。基于修正Timoshenko梁理论建立刚性吊杆横向振动微分方程，通过选取切比雪夫多项式的根作为节点坐标，利用拉格朗日插值基函数近似表示位移函数；根据微分求积法基本原理计算各阶权重系数，引入边界条件后，将轴向力作用下的修正Timoshenko梁横向振动微分方程的求解转化为线性代数方程组广义代数特征值的计算问题，从而得到刚性吊杆实测基频与拉力之间的精确对应关系。通过数值算例和实桥应用对该方法进行了验证，结果表明，两端固结刚性吊杆的长细比小于222.23时，需要考虑抗弯刚度、剪切变形和转动惯量的影响才能保证拉力识别的精度。提出的基于微分求积法的吊杆拉力识别方法能够应用于各种工况和长细比下的刚性吊杆拉力识别，具有准确、实用和易编程的特点，能够满足实际工程应用要求。

Abstract

Based on the modified Timoshenko beam theory, a method for identifying the tension of rigid suspenders of arch bridges based on differential quadrature method was proposed. Based on the modified Timoshenko beam theory, the lateral vibration differential equation of the rigid suspender is established. By selecting the root of the Chebyshev polynomial as the node coordinate, the Lagrange interpolation basis function was used to approximately represent the displacement function. According to the basic principle of differential quadrature method, the weight coefficients of each order were calculated. After introducing the boundary conditions, the solution of the transverse vibration differential equation of the modified Timoshenko beam under the action of axial force was transformed into the calculation of the generalized algebraic eigenvalue of the linear algebraic equations, so as to obtain the accurate correspondence between the measured fundamental frequency and the tension of the rigid suspender. The method was verified by numerical examples and real bridge applications. The results showed that when the slenderness ratio of the rigid suspenders at both ends is less than 222.23, the influence of bending stiffness, shear deformation and moment of inertia should be considered to ensure the accuracy of tension identification. The proposed identification method of suspender tension based on differential quadrature method can be applied to the tension identification of rigid suspenders under various working conditions and slenderness ratios. It has the characteristics of accuracy, practicality and easy programming, and can meet the requirements of practical engineering applications.

导出引用

彭涛1, 2, 稂其林2, 陆小龙2, 王涛2, 田仲初1, 2. 于微分求积法的两端固结刚性吊杆拉力识别研究[J]. 振动与冲击, 2025, 44(2): 94-103

PENG Tao1, 2, LANG Qilin2, LU Xiaolong2, WANG Tao2, TIAN Zhongchu1, 2. Tension identification of rigid suspenders with two fixed ends based on the differential quadrature method[J]. Journal of Vibration and Shock, 2025, 44(2): 94-103

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