Winkler弹性地基上矩形薄板随机振动响应的精确解

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• 英文论文题名：Exact solutions of random vibration responses for rectangular thin plate resting on Winkler elastic foundation
• 论文作者：陈国海 ; 杨迪雄
• 英文论文作者：Chen Guohai ; Yang Dixiong ; Department of Engineering Mechanics ; State Key Laboratory of Structural Analysis for Industrial Equipment ; Dalian University of Technology
• 年：2016
• 作者机构：大连理工大学工程力学系工业装备结构分析国家重点实验室;
• 论文关键词：Winkler弹性地基 ; 矩形薄板 ; 随机振动响应 ; 虚拟激励法 ; 精确解
• 英文论文关键词：Winkler elastic foundation ; rectangular thin plate ; random vibration ; pseudo excitation method ; exact solution
• 会议召开时间：2016-10-27
• 会议录名称：第九届全国防震减灾工程学术研讨会论文集
• 语种：中文
• 分类号：TU311.3
• 学会代码：OGTY
• 会议名称：第九届全国防震减灾工程学术研讨会
• 会议地点：中国安徽合肥
• 主办单位：中国土木工程学会、中国工程院土木、水利与建筑工程学部、中国土木工程学会防震减灾工程技术推广委员会、合肥工业大学、安徽省住房和城乡建设厅
• 学会名称：中国土木工程学会
• 页数：11
• 文件大小：405k
• 原文格式：O
• 会议级别：全国

摘要

弹性地基上薄板结构的随机振动分析对于工程设计具有重要的参考价值,本文求得了平稳随机激励作用下Winkler弹性地基上矩形薄板随机振动响应的精确解。首先,通过引入Winkler弹性地基上6类存在一组对边简支边界条件的矩形薄板结构的自由振动精确解,应用虚拟激励法解析推导并获得了位移、速度、加速度响应以及各应力分量的功率谱密度函数的显式表达式。其次,为提高计算效率,将自由振动分析获得的精确振型函数和频率响应函数分别在空间域和频域进行离散化处理,同时将功率谱密度显式表达式由解析运算转化为矩阵运算。然后,通过将功率谱密度在频域内积分并开方获得了各响应的均方根。最后,矩形薄板随机振动响应精确解与有限元解比较后表明,本文离散解析法获得的精确解具有高精度和高效率。
Random vibration analysis of thin plate on elastic foundation is of significance for engineering design.This paper obtains the exact solutions of random vibration responses for rectangular thin plate under stationary excitation resting on the Winkler elastic foundation.Firstly,based on pseudo excitation method(PEM),the explicit power spectral density(PSD)functions of the deflection,velocity,acceleration responses and stress components are analytically derived by introducing the exact closedform solution of free vibration for rectangular thin plate with 6 different boundaries on Winkler elastic foundation.To enhance the efficient computing,secondly,the exact modal shape functions and frequency response functions of thin plate from free vibration analysis are discretized in space domain and frequency domain,respectively.Then,root mean squares of various responses are achieved by integrating the corresponding response PSD over the domain.Finally,comparison between exact solutions of vibration dynamic responses for rectangular thin plate and finite element solutions indicates that,the exact solutions by using discrete analytic method have the high accuracy and efficiency.

引文

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