Winkler地基梁动力学系统的无量纲化与参数识别  

Dimensionless and Parameter Identification of Dynamic System of Beam on Winkler Foundation

作　　者：郑罡[1,2] 曹和生 杜宗松 蔡汶秀 陈鹏 Zheng Gang;Cao Hesheng;Du Zongsong;Cai Wenxiu;Chen Peng(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：《动力学与控制学报》2024年第1期60-68,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金项目(51978112,51478072)。

摘　　要：为简化Winkler地基梁动力学系统的双参数识别计算,提出一种新无量纲方法,通过对系统时间、空间坐标进行线性变换,实现动力学方程系数的彻底归一化,得到与系统参数解耦的广义频率方程,发现频率、频率比仅由无量纲梁长决定的本质.提出基于频率比互等关系的双参数识别算法,该算法通过对广义频率方程进行一次求解即可在相应边界条件下得到频率、频率比关于无量纲梁长的预解集,在得到该系统任意两阶实测频率后,即可依托于时间、空间还原系数所建立的线性转换关系实现对双系统参数的定解.较之于传统双参数识别算法,该算法具有两个特点:(1)识别计算仅涉及单变量超越方程的求解与线性转换,避免了双参数超越方程组的非线性迭代问题,可使识别计算得到有效简化.(2)任意系统参数值的变化仅影响时空、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改变而导致重复迭代的情况,实现了解的一般化.In order to simplify the dual parameter identification calculation of the dynamic system of the beam on Winkler Foundation,a new dimensionless method is proposed.The time and space coordinates of the system are linearly transformed to realize the complete normalization of the coefficients of the dynamic equation.The generalized frequency equation decoupled from the system parameters is obtained.It is found that the frequency and frequency ratio are only determined by the dimensionless span.Based on this discovery,a dual parameter identification algorithm based on the reciprocal relationship of frequency ratios is proposed.This algorithm can obtain the resolvent set of frequency and frequency ratio with respect to the dimensionless span under the corresponding boundary conditions by solving the generalized frequency equation once.After obtaining any two order measured frequencies of the system,the dual system parameters can be determined by relying on the linear transformation relationship established by the time and space reduction coefficients.Compared with the traditional two parameter identification algorithm,this algorithm has two characteristics:(1)The identification calculation only involves the solution and linear transformation of the univariate transcendental equation,which avoids the nonlinear iteration problem of the two parameter transcendental equation set in the traditional method,and can effectively simplify the identification calculation.(2)The change of any system parameter value only affects the size of the time and space reduction coefficients.Therefore,the resolvent set has generality applicable to any change of system parameter value,which can effectively avoid the repeated iterative solution caused by the change of system parameter value in traditional methods,and realize the generalization of the solution.

关 键 词：WINKLER地基梁 动力学系统 无量纲化 归一化 参数识别 

分 类 号：O321[理学—一般力学与力学基础]