检索结果-南通市图书馆

Closed form solutions for free vibrations of rectangular Mindlin plates

Acta Mechanica Sinica 2009年第5期25卷 689-698页

作者： Yufeng Xing Bo Liu The Solid Mechanics Research Center, Beihang University,100191 Beijing, China The Solid Mechanics Research Center Beihang University 100191 Beijing China

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate.

关键词： Mindlin plate Free vibration Closed form solution separation of variable

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

SYMPLECTIC SOLUTION SYSTEM FOR REISSNER PLATE BENDING

引用

Applied Mathematics and Mechanics(English Edition) 2004年第2期25卷 178-185页

作者：姚伟岸隋永枫 State Key Laboratory of Structural Analysis of Industrial Equipment Dalian University of Technology

Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were *** Hamiltonian solution system can also be applied to Reissner plate bending problem,and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamiltonian system was *** in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction_vector *** the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed *** adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are *** is showed that the all eigensolutions for zero eigenvalue are basic solutions of the Saint_Venant problem and they form a perfect symplectic subspace for zero *** the eigensolutions for nonzero eigenvalue are covered by the Saint_Venant *** symplectic solution method is not the same as the classical semi_inverse method and breaks through the limit of the traditional semi_inverse *** symplectic solution method will have vast application.

关键词： Reissner plate Hamiltonian system symplectic geometry separation of variable

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：