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A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions

机译:一种消除弹性边界条件下复杂边界条件效应的新型张力估计方法

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摘要

To establish a rigorous mathematical foundation for a recently developed tension determination method incorporating the mode shape functions, the frequency equations and mode shape functions for the vibrating cables with various types of boundary conditions are first derived in this research. According to these analytical expressions in terms of dimensionless parameters, it is confirmed that the mode shape functions associated with complicated boundary conditions are all dominantly contributed by the sinusoidal components to suggest a more convenient option than the intertwined frequency equations. Based on this discovery, the cable tension can be generally decided with an explicit formula similar to that for the case with hinged boundary constraints at both ends. The effective vibration length for each selected mode in the formula, however, needs to be pre-determined by fitting the corresponding sinusoidal function with the mode shape ratios identified from multiple synchronized measurements. Parametric study Is also conducted on the derived mode shapes to systematically investigate the interference effect of the hyperbolic component near the boundaries and provide valuable guidelines for the sensor deployment in engineering applications. Finally, the performance of the developed methodology in the cases with more involved boundary constraints is certified with demonstrative numerical examples and laboratory experiments.
机译:为了为结合模态形状函数的最新开发的张力确定方法建立严格的数学基础,本研究首先导出了具有各种边界条件的振动电缆的频率方程和模态形状函数。根据这些关于无量纲参数的分析表达式,可以确认与复杂边界条件相关的模态形状函数都是正弦分量的主要贡献,从而提出了比交错频率方程更方便的选择。基于此发现,通常可以使用与两端都有铰接边界约束的情况类似的显式公式来确定电缆张力。但是,公式中每个选定模式的有效振动长度需要通过将相应的正弦函数与从多个同步测量中确定的模式形状比进行拟合来预先确定。还对派生的模式形状进行参数研究,以系统地研究双曲线分量在边界附近的干扰效果,并为工程应用中的传感器部署提供有价值的指导。最后,在具有更多涉及边界约束的情况下,已开发的方法的性能已通过演示性的数值示例和实验室实验得到了验证。

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