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重力失真和质量失真对缩尺试验误差的理论分析

Theoretical analysis of gravity distortion and mass distortion to scale test error
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摘要 为了定量分析重力失真和质量失真对缩尺试验误差的影响,确定重力失真和质量失真的动力相似关系,根据原型和缩尺模型的动力运动方程引出误差的定义。将简单的无阻尼竖向和水平SDOF体系作为研究对象,通过完全相似模型和部分相似模型的动力运动方程进行公式推导,分别得到在谐波作用下,原型与重力失真和质量失真模型之间相对位移的误差公式。对比误差公式的计算结果和数值试验的计算结果,论证误差公式推导的正确性,并结合参数分析,讨论谐波作用幅值和频率比对重力失真和质量失真模型误差的影响规律。研究结果表明:已知无阻尼竖向或水平SDOF体系的原型参数、谐波作用幅值和频率以及重力失真或质量失真动力相似关系,就可以利用误差公式直接计算得到原型与缩尺模型受谐波作用时相对位移的误差大小;重力失真对竖向SDOF体系的误差影响要大于对水平SDOF体系的误差影响,且质量失真对水平SDOF体系误差影响十分显著;竖向SDOF体系在重力失真或质量失真条件下误差随谐波作用幅值的增大而减小,水平SDOF体系在重力失真或质量失真条件下误差不随谐波作用幅值的变化而变化。通过误差公式计算出重力失真和质量失真所引起的误差大小,可以用于修正缩尺模型反推原型的位移响应,从而消除重力失真和质量失真对试验的影响。 In order to analyze the influence of gravity distortion and mass distortion on the error of scaled test,determine the dynamic similarity relationship between gravity distortion and mass distortion,and derive the definition of error according to the dynamic equation of motion of prototype and scaled model.Taking simple undamped vertical and horizontal SDOF systems as the research object,the formula of relative displacement between the prototype and the gravity distortion and mass distortion models under harmonic action was derived through the dynamic motion equations of completely similar models and partially similar models.Comparing the calculation results of the error formula with the calculation results of the numerical tests,the correctness of the deduction of the error formula was demonstrated.Combined with the parameter analysis,the influence of harmonic action amplitude and frequency ratio on the gravity distortion and the mass distortion was discussed.The research results are drawn as follows.Given the prototype parameters of the undamped vertical or horizontal SDOF system,the amplitude and frequency of harmonic action,and the dynamic similarity of gravity distortion or mass distortion,the error size of the relative displacement of the prototype and the scaled model under harmonic action can be directly calculated by using the error formula.The influence of gravity distortion on the error of the vertical SDOF system is greater than that of the horizontal SDOF system,and the mass distortion has a very significant effect on the error of the horizontal SDOF system.Under the condition of gravity distortion or mass distortion,the error of vertical SDOF system decreases with the increase of harmonic action amplitude,while the error of horizontal SDOF system does not change with the change of harmonic action amplitude under the condition of gravity distortion or mass distortion.The error caused by gravity distortion and mass distortion can be calculated through the error formula,which can be used to correct the d
作者 李常青 刘吉龙 蒋丽忠 LI Changqing;LIU Jilong;JIANG Lizhong(School of Civil Engineering,Central South University,Changsha 410075,China;National Engineering Research Center for High-speed Railway Construction Technology,Changsha 410075,China)
出处 《铁道科学与工程学报》 EI CAS CSCD 北大核心 2023年第9期3616-3624,共9页 Journal of Railway Science and Engineering
基金 国家自然科学基金资助项目(U1934207) 湖南省创新型省份建设专项资金资助项目(2019RS3009) 中国中铁股份有限公司科技研究开发计划项目(2020-重点-02)。
关键词 重力失真 质量失真 缩尺试验 SDOF体系 误差公式 gravity distortion mass distortion scale test SDOF system error formula
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