Reissner 能量方程视角下的改进 Timoshenko 梁 动力学方程及其在轴力识别中的应用
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O327

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内蒙古大学科研启动基金资助项目(10000-22311201/056);国家自然科学基金资助项目(52078284,52268032, 51778103);广东省自然科学基金资助项目(2021A1515011770,2022A0505020006,2022A1515010812);汕头大 学科研启动基金资助项目(NTF18012);桥梁结构健康与安全国家重点实验室开放课题(BHSKL20-10-KF)


An enhanced dynamic equation for Timoshenko beams based on the Reissner energy function and its application to axial force identification
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    摘要:

    在轴力识别中,动力测试法建立在杆件振动理论的基础上,因此杆件的振动方程决定了轴力识别的结果。为 提高杆件轴力识别的精度,从能量角度出发,推导出轴力作用下 Timoshenko 梁的自由振动方程。引入缩聚假设,建 立了 Timoshenko 梁关于位移、应力和轴力的 Ressiner 能量方程;使用极值定理,求得平面梁的运动和应力的平衡方 程,化简上述平衡方程得到轴力作用下 Timoshenko 梁自由振动的方程,发现与经典结构动力学方程相比,所提出的 方程多出与轴力和剪切效应有关的两项。使用本文推导的方程分别从数值模拟和试验研究两个方面对杆件进行轴 力识别,发现与传统的识别方法相比精度有较大的提高,验证了其正确性和适用性。

    Abstract:

    The dynamic method for identifying axial force is grounded in vibration theory, making the vibration equation of a bar member crucial for accurate axial force estimation. Traditionally, the Timoshenko beam is derived from the equilibrium of trans? verse forces and moments. In this paper, an energy-based approach is applied to derive a new vibration equation for the Timoshen? ko beam under axial loading. The Ressiner energy equation for a Timoshenko beam, incorporating displacement, stress and axial force, is established using a condensation hypothesis from an energy perspective. The motion equation and stress equilibrium are calculated using the extremum principle, leading to a new free vibration equation for the Timoshenko beam under axial force. Com? pared to classical textbooks, the proposed dynamics equation includes two additional terms related to axial forces and shear effects. The new equation is validated through numerical simulations and laboratory experiments to identify the axial force in bar members. The results demonstrate that the proposed equation significantly improves the accuracy of axial force identification, confirming its correctness and applicability.

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郭 鑫,魏 达,姚亚东,李东升. Reissner 能量方程视角下的改进 Timoshenko 梁 动力学方程及其在轴力识别中的应用[J].振动工程学报,2024,37(10):1723~1730.[GUO Xin, WEI Da, YAO Ya-dong, LI Dong-sheng. An enhanced dynamic equation for Timoshenko beams based on the Reissner energy function and its application to axial force identification[J]. Journal of Vibration Engineering,2024,37(10):1723~1730.]

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  • 在线发布日期: 2024-10-25
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