Winkler梁地基中心空腔宽度识别算法  

An Algorithm for Identifying the Cavity Width at the Center of Winkler Beam Foundations

作　　者：郑罡[1,2] 黎浩 蔡汶秀 曹和生 ZHENG Gang;LI Hao;CAI Wenxiu;CAO Hesheng(State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China;College of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆400074 [2]重庆交通大学土木工程学院,重庆400074

出　　处：《佳木斯大学学报(自然科学版)》2025年第2期79-83,149,共6页Journal of Jiamusi University:Natural Science Edition

基　　金：国家自然科学基金项目(51978112,51478072)。

摘　　要：为了更准确高效地识别机场路面,铁路轨道,路基路面等工程构件下地基脱空的真实情况,将其简化为含地基中心矩形空腔的Winkler地基梁模型,引入时、空还原坐标对动力学方程进行无量纲化,得到系数归一的标准化动力学方程;利用分离变量法求解得到了两端固支,两端简支,两端自由三种经典边界条件下的频率方程,计算得到了无量纲下空腔特征的预解集;讨论了梁体各阶频率随空腔特征变化的一般规律,并提出利用预解集进行空腔宽度识别的算法,建立有限元模型进行算法验证,结果表明,在三种经典边界条件下通过频率预解集进行空腔宽度识别误差均小于4%;该算法具有两个特点:(1)系统参数值的变化仅影响时间、空间还原系数的大小,预解集具有适用于系统参数值任意变化的一般性,可有效避免因系统参数值变化而产生的重复迭代计算,实现了解的一般化;(2)仅需时、空还原系数的线性变化即可完成空腔宽度识别计算,有效简化了识别计算过程。In order to more accurately and efficiently identify the real situation of foundation dehollowing under airport pavement,railroad track,roadbed pavement and other engineering components,it is simplified into the Winkler foundation beam model containing a rectangular cavity in the center of the foundation,and the time and space reduction coefficients are introduced to dimensionless the dynamic equations,and the normalized dynamic equations with the coefficients normalized to unity are obtained.The frequency equations under three classical boundary conditions of solidly supported both ends,simply supported both ends and using the separated variable method to solve the frequency equations under the three classical boundary conditions of both ends solidly supported,both ends simply supported and both ends free,the pre-solution set of the cavity characteristics under dimensionless is obtained.The general law of the change of the frequency of each order of the beam with the change of the cavity characteristics is discussed and the algorithm of using the pre-solution set for the identification of the width of the cavity is proposed and the algorithm is verified by establishing a finite element model,and the results show that the error of the identification of the width of the cavity by the frequency pre-solution set is less than 4%.The algorithm has two features:(1)The change of any system parameter value only affects the size of time and space reduction coefficients,the pre-solution set has the generality applicable to any change of system parameter value,which can effectively avoid the repeated iterative calculations due to the change of system parameter value,and realize the generalization of the understanding.(2)The recognition calculation involves only linear transformations,and effectively simplifies the process of recognition calculation.

关 键 词：Winkler梁 无量纲化 频率方程 空腔识别 识别算法 

分 类 号：O321[理学—一般力学与力学基础]