基于半解析有限元法的钢轨导波适用模态研究

研究目的:为选择出适用于钢轨导波无损检测的优势模态,采用半解析有限元法并基于哈密顿原理建立钢轨导波传播的控制方程,求解0~100 k Hz频率范围内的钢轨导波频散特性曲线。通过建立有限元模型对钢轨低频范围内的振动模态进行分析,验证半解析有限元法的准确性。在此基础上,提出将有限元法与半解析有限元法相结合的方法,用以分类并追踪钢轨理想导波模态,并根据相应的振型对理想模态导波进行激励和验证。研究结论:(1)随着频率的增大,钢轨导波振动模态数目迅速增加,但频散效应呈减小趋势;(2)对于钢轨基本振动模态,其横截面变形由整体变形逐渐演化为局部变形,其中扭转振动模态适用于轨腰检测,横向弯曲振动模态及竖向弯曲振动模态适用于轨底缺陷的检测;(3)在理想导波模态最大变形位置处施加激励荷载可以成功地激励出理想的导波;(4)本研究结果可为导波传感器设计与优化以及检测试验提供理论参考。

Modal Applicability Analysis of Rail Guided Wave Based on Semi-analytical Finite Element Method

Research purposes:In order to select the dominant modes suitable for rail guided wave detection,the governing equation of rail guided wave propagation was established by semi-analytical finite element(SAFE)method and Hamilton principle.The dispersion characteristic curves of rail guided wave in the frequency range of 0-100 k Hz were subsequently calculated.Meanwhile,the finite element(FE)model was established to analyze the vibration mode of rail in the low frequency range,which has verified the accuracy of the SAFE method.By combining the FE and SAFE method,the ideal rail vibration modes were classified,and the ideal guided wave was excited and verified based on the corresponding deformation.Research conclusions:(1)With the increase of frequency,the number of vibration modes of waves increases rapidly while the dispersion effect decreases.(2)For the basic vibration modes of rail,the section deformation gradually concentrates on the local area,the torsional vibration mode is suitable for rail web detection,and both the transverse and vertical bending vibration modes are applicable to the inspection of rail bottom defects.(3)The ideal guided wave can be successfully excited by applying load at the maximum deformation position of the ideal mode.(4)The research results can provide theoretical reference for the design and optimization of the guided wave sensor and the detection experiment.