基于修正Winkler模型的有限深度地基支承梁振动抑制  

Vibration suppression of beams supported by finite-depth foundation based on modified Winkler model

作　　者：马建军[1,2] 刘宗通 王超圣 刘丰军 李达[1,2] 高笑娟 MA Jianjun;LIU Zongtong;WANG Chaosheng;LIU Fengjun;LI Da;GAO Xiaojuan(School of Civil Engineering and Architecture,Henan University of Science and Technology,Luoyang 471023,China;Engineering Technology Research Center of Safety and Protection of Buildings of Henan Province,Luoyang 471023,China)

机构地区：[1]河南科技大学土木建筑学院,河南洛阳471023 [2]河南省建筑安全与防护工程技术研究中心,河南洛阳471023

出　　处：《地震工程与工程振动》2024年第6期138-149,共12页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(11502072);河南省重点研发与推广专项-科技攻关项目(222102320462)。

摘　　要：弹性地基对其支承结构的振动通常具有抑制作用,其中的土-结构相互作用效应对结构物动力学特性的影响具有非线性能量汇的典型特征。基于修正Winkler模型将有限深度弹性地基等效为非线性能量汇系统的附加质量,开展了简谐激励下弹性地基对其支承有限长梁的振动抑制效果分析和参数优化研究。采用Galerkin方法离散控制方程,应用增量谐波平衡法和弧长延拓法分析了弹性地基上简支梁的非线性动力响应。利用数值方法验证理论结果正确性,进而通过参数分析和多参数优化,揭示了有限范围地基对其支承梁动力响应的抑制效果,探明了弹性地基非线性刚度和阻尼的最佳参数范围。结果表明,通过工程技术手段将土体参数调整到最佳范围后,可实现有限长梁振幅衰减率达96%以上,且具有较宽的减振频带。The elastic foundation typically exerts a suppressive effect on the vibration response of the supported structure,and the influence of the soil-structure interaction effect on the dynamic characteristics of the structure exhibits typical nonlinear energy sink characteristics.At present,more and more attention has been paid to the dynamic research of elastic foundation beams considering soil motion.Based on the modified Winkler model,the finite-depth elastic foundation is equivalent to the additional mass of the nonlinear energy sink system,and the vibration suppression effect and parameter optimization of the elastic foundation on the finite-length beam supported by it under simple harmonic excitation is conducted.The nonlinear dynamic response of a simply supported beam on an elastic foundation is analyzed using the Galerkin method,the incremental harmonic balance method,and the arc-length continuation method.Furthermore,on the basis of verifying the correctness of the theoretical results by numerical methods,through multi-parameter optimization and analysis,the suppression effect of limited range soil on the dynamic response of its supporting beam is revealed,and the optimal parameter range of nonlinear stiffness and damping of the elastic foundation is proved.The results show that by adjusting the elastic soil parameters to the optimal range by technical means,the amplitude reduction percentage of the finite-length beam can reach more than 96%,and it has a wide vibration suppression frequency band.

关 键 词：修正Winkler模型 有限长梁 非线性能量汇 多参数优化 振动抑制 

分 类 号：O328[理学—一般力学与力学基础] TU348[理学—力学]