弦理论与刚性索理论频率误差曲线在工程中的应用

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (9) : 147-152.

振动理论与交叉研究

弦理论与刚性索理论频率误差曲线在工程中的应用

蔡汶秀1,郑罡*1,孙测世2,唐宇1

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Application of frequency error curve of string theory and rigid cable theory in engineering

CAI Wenxiu1, ZHENG Gang*1, SUN Ceshi2, TANG Yu1

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文章历史 +

摘要

弦理论方法有效识别索力对拉索的评估具有重要意义。为解决拉索的弦理论在工程应用问题，本文通过拉索系统动力学方程的无量纲化，使得决定系统的唯一参数为名义长细比。绘制无量纲名义长细比-频率曲线，利用弦理论和刚性索理论的频率差异性，给出弦理论索力计算公式满足特定索力误差需求的适用范围。对于超出适用界限的部分，以频率误差上限为例，通过幂次函数推导出三参数频率修正公式和索力修正公式，在此基础上，提出一种无量纲体系下的索力识别算法。由文献算例，验证了索力修正公式的可行性，并应用于实桥测试中，索力识别误差均满足工程需求。结果表明：①不同精度的频率误差曲线可满足弦理论特定的工程应用，为解决实际工程问题提供理论支撑。②该修正公式简洁直观、形式统一，且理论误差在2%以内，可覆盖工程拉索名义长细比的适用范围。

Abstract

String theory play a crucial role in effectively identifying cable forces for the assessment of cables. In order to solve the problem of cable string theory applied in engineering, this paper non-dimensionalizes the dynamics equation of the cable system, making the only parameter determining the system the nominal slenderness ratio. By plotting the non-dimensional nominal slenderness ratio-frequency curve and utilizing the frequency differences between string theory and rigid cable theory, the paper provides the applicable range for the string theory cable force calculation formula to meet specific cable force error requirements. For parts beyond the applicable limits, taking the frequency error upper limit as an example, a three-parameter frequency correction and cable force correction formula is proposed through a power function. On this basis, an algorithm for the identification of the cable force in the dimensionless system is proposed. The feasibility of the cable force correction formula is verified by literature examples and applied in actual bridge testing. The cable force identification errors all meet the engineering requirements. The results show: ① Frequency error curves of different accuracies can meet the specific engineering applications of string theory, providing theoretical support for solving practical engineering problems. ② The correction formula is concise , intuitive, unified in form, and its theoretical error is within 2%. The applicability of the nominal slenderness ratios covers all engineering cables.

导出引用

蔡汶秀1, 郑罡1, 孙测世2, 唐宇1. 弦理论与刚性索理论频率误差曲线在工程中的应用[J]. 振动与冲击, 2025, 44(9): 147-152

CAI Wenxiu1, ZHENG Gang1, SUN Ceshi2, TANG Yu1. Application of frequency error curve of string theory and rigid cable theory in engineering[J]. Journal of Vibration and Shock, 2025, 44(9): 147-152

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