基于振动频率法的两端固支拉索索力计算实用公式

Practical Formulas for Vibration Based Method of Tension Estimation for Cables with Fixed Boundaries

从拉索横向振动方程的通解出发,通过在弦理论公式的基础上引入刚度修正系数,提出了可用于两端固支拉索索力测试的统一实用公式。误差分析结果表明,该统一实用公式具有足够的精度,其采用无量纲参数η来表征拉索的抗弯刚度大小,当η≤0.88时,采用各阶频率计算的拉索索力误差不超过3%,当η≤0.55时,误差不超过1%。在实际工程中,若实测得到了多阶频率,则可以通过求解一元二次方程的方法对拉索的抗弯刚度进行识别,同时得到准确的拉索索力。大量数值算例和实际工程案例表明,该实用公式能准确的对拉索索力和抗弯刚度进行识别,具有广阔的应用前景。

According to the general solution of the vibration equation,this paper proposed a unified practical fomiula to estimate cable tension for vibrations under fixed-fixed boundary condition by introducing a correction coefficient multiplied to the taut string fomiula.Error analysis results show that the error in the estimated cable tensions for various frequencies is less than3%when n≤0.88,and less than1%when n≤0.55.Moreover the proposed fomiulas can be used to i-dentify the cable tension and bending stiffness simultaneously by solving a quadratic equation based on the tested multi-frequencies.Finally the proposed fomiulas have been validated against several numerical examples as well as practical test cases.