基于频率计算系杆拱桥吊杆张拉力的实用公式

Practical Formulas to Calculate Suspender Tension Based on Frequency

为了分析频率对吊杆张拉力的影响,根据吊杆的振动力学特性,考虑到吊杆在振动过程中处于动平衡状态,建立吊杆的运动偏微分方程,推导出考虑抗弯刚度、转动惯量、剪切变形、转动惯量和剪切变形耦合影响下频率与索力的计算公式.通过不同吊杆长度及各自不同阶频率进行对比及频率差拟合分析,分析认为通过高阶频率差求基频会造成基频值识别变大,从而导致索力识别值偏大,得出基于一阶频率的频率修正值,同时得出了索力计算实用公式.通过算例,分析对比了弦振动公式、考虑抗弯刚度公式和本文公式.计算表明:采用实用公式确定的索力与实际张拉力相比,误差可控制在5%以内.证明了实用公式的正确性和实用性.

In order to analyze the influence of frequency on suspender tension,a partial differential equation of motion is established for the suspender according to its vibration mechanical properties and dynamic equilibrium. Then,a computational formula for the frequency and suspender force is built taking into account the influence of flexural rigidity,rotational inertia,shear deformation,and the coupling of rotational inertia and shear deformation. Comparing frequencies of different orders and fitting frequency difference for various lengths of suspenders leads to the finding that the fundamental frequency worked out using high-order differential frequency will contain a positive error and thus causes a positive deviation in the cable force. On this basis,the modified value for the first-order frequency is then obtained and practical formulas for calculating the cable force are proposed. In a case study,the proposed formulas are compared with the string vibration formula and the formula that takes the bending stiffness into consideration. The result show that using the practical formulas,the error between the calculated suspender tension and the measured value is no more than 5%,which validates the practical formulas.