• 应用研究 •

### 功能梯度环形截面梁的横向自由振动

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
• 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

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