有限差分法在斜拉索张力振动测试识别中的应用

振动法测量斜拉索张力需要准确描述索力与自振频率的关系，考虑斜拉索边界条件、抗弯刚度和垂度的影响，使用有限差分法将斜拉索的静力平衡方程和自由振动方程离散，通过求解特征值问题建立了索力与振动频率的关系；然后将计算得到的模态频率与测试得到的模态频率比较，通过修正拉索张力计算值使计算频率与实测频率误差最小，最后修正的拉索张力则为斜拉索实际张力．通过对实际工程的测试结果分析表明，本文方法具有准确、实用的特点，可有效提高振动法测量斜拉索张力的精度。

Application of Finite Difference Method in Measurement of Cable Tension by Vibration Method

The relation between cable tension and natural vibration frequencies needs to be defined accurately for measurement of cable tension by vibration method. Taking the effects of boundary condition, flexural rigidity and sag of a cable into account, the governing equation of motion and the static equilibrium equation were discretized by finite difference method. The relation between cable tension and natural vibration frequencies was described by solving eigenvalue problem. The calculated value of cable tension was amended until the difference between the theoretical calculation results and the measurement results reached the minimum. The final calculated value of cable tension is regarded as the actual cable tension. The field measurement results are analyzed and it is indicated that the proposed method can effectively improve the measurement precision of cable tension.