Winkler地基板动力学系统的广义化与简化求解  

Generalized and simplified solution of Winkler foundation plate dynamic system

作　　者：郑罡[1] 杜宗松 曹和生 黎浩 ZHENG Gang;DU Zongsong;CAO Hesheng;LI Hao(State Key Lab 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：《西安建筑科技大学学报(自然科学版)》2024年第6期791-796,共6页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金(51978112)。

摘　　要：为简化Winkler地基板动力学系统的求解,对该系统时间、空间坐标进行缩放变换,建立了与系统参数解耦的广义动力学方程与频率方程,得到无量纲频率关于板长的预解集,即:频率-板长曲面.分析此曲面特性,并基于此曲面提出预解-定解简化算法,通过与文献算例比对,验证了该算法的正确性与准确性.研究表明:任意系统参数值的变化,仅影响时间、空间还原系数的大小,因此,频率-板长曲面具有适用于系统参数值任意变化的一般性,可作为该系统的一般解;依托于频率-板长曲面,仅通过线性转换即可实现对系统频率的定解,不仅避免了传统方法所涉及的多参数超越方程组的非线性迭代求解问题,同时也避免了因系统参数变化而导致的重复求解,实现了该系统求解的简化.In order to simplify the solution of the Winkler foundation plate dynamic system,the time and space coordinates of the system are scaled and transformed,and the generalized dynamic equation and frequency equation that are decoupled from the system parameters are established.The pre-solution set of dimensionless frequency on plate length is obtained,namely:frequency-plate length surface.The characteristics of this surface are analyzed,a pre-solution-definite solution simplification algorithm is proposed based on this surface,and the correctness and accuracy of the algorithm are verified by comparing it with the literature example.The results show that:the change of any system parameter value only affects the size of the time and space reduction coefficient,so the frequency-plate length surface has a generality suitable for arbitrary changes in the system parameter value,which can be used as the general solution of the system;relying on the frequency-plate length surface,the fixed solution of the system frequency can be realized only through linear conversion,which not only avoids the nonlinear iterative solution of the multi-parameter transcendental equation system involved in the traditional method,but also avoids the repeated solution caused by the change of system parameters,and realizes the simplification of the system solution.

关 键 词：Winkler地基板 动力学系统 预解集 简化求解 

分 类 号：TU470.1[建筑科学—结构工程]