全部

力学与实践 ›› 2015, Vol. 37 ›› Issue (1): 95-99.doi: 10.6052/1000-0879-14-144

• 应用研究 • 上一篇    下一篇

功能梯度环形截面梁的横向自由振动

刘艳庄, 王忠民, 曹升虎   

  1. 西安理工大学土木建筑工程学院, 西安 710048
  • 收稿日期:2014-05-19 修回日期:2014-06-26 出版日期:2015-02-15 发布日期:2015-02-14
  • 通讯作者: 刘艳庄, 硕士, 主要从事结构动力学等方面的工作. E-mail:360097964@qq.com E-mail:360097964@qq.com
  • 基金资助:

    国家自然科学基金(11272254)和陕西省教育厅科学研究计划(11JK0850)资助项目.

THE TRANSVERSE FREE VIBRATION OF A BEAM OF ANNULAR CROSS-SECTION MADE OF FUNCTIONALLY GRADED MATERIALS

LIU Yanzhuang, WANG Zhongmin, CAO Shenghu   

  1. School of Civil Engineering and Architecture, Xi'an University of Technology, Xi'an 710048, China
  • Received:2014-05-19 Revised:2014-06-26 Online:2015-02-15 Published:2015-02-14

摘要:

对功能梯度材料制成的环形截面梁,假设材料的物性参数沿壁厚方向按幂率变化,基于Lagrange函数和Hamilton 原理,建立了该梁横向自由振动的Hamilton 对偶方程组. 采用辛方法求解了Hamilton 矩阵的辛本征问题,得到了简支、两端固定、悬臂和左端固定右端铰支4 种约束的FGM(functionally gradedmaterials)环形截面梁的固有频率和振型函数. 算例给出了这4 种约束的FGM 环形截面梁前8 阶无量纲固有频率随材料体积分数的变化规律,分析了材料体积分数对FGM 环形截面梁固有频率的影响.

关键词:

横向振动|功能梯度材料|环形截面梁|辛方法

Abstract:

For a beam of annular cross-section made of functionally graded materials (FGM), we assume that the physical parameters of the materials along the direction of the wall thickness varying in a simple power law. Based on the Lagrange's function and the Hamilton's principle, the Hamilton's canonical equations for the transverse free vibration of the beam are established. A symplectic eigenvalue problem of the Hamilton matrix is solved by using the symplectic method. Then, the natural frequencies and the vibration mode functions of the beam are obtained, with conditions on the two ends as the simply supported, the fixed, the cantilever and the fixed-simply supported. Numerical examples are given for the first eight order dimensionless natural frequencies against the material volume fraction, and the effect of the material volume fraction on the natural frequency is analyzed.

Key words:

transverse vibration|functionally graded materials|an annular cross-section beam|symplectic method

中图分类号: 

  • O326