Frequency equations for the in-plane vibration of orthotropic circular annular plate

被引：21
|
作者：
Ravari, M. R. Karamooz [1 ]
Forouzan, M. R. [1 ]
机构：
[1] Isfahan Univ Technol, Dept Mech Engn, Esfahan 8415683111, Iran
来源：
ARCHIVE OF APPLIED MECHANICS | 2011年 / 81卷 / 09期
关键词：
In-plane; Vibration; Orthotropic material; Frequency equation; General boundary condition;
D O I：
10.1007/s00419-010-0488-6
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency equation, first the equation of motion for the circular annular plate in the cylindrical coordinate is derived by using the stress-strain- displacement expressions. Helmholtz decomposition is used to uncouple the equations of motion. The wave equation is obtained by assumption a harmonic solution for the uncoupled equations. Using the separation of the variables leads to the general wave equation solution and the in-plane displacements in the r and theta directions. Finally, boundary conditions are exerted and the natural frequency is derived for general boundary conditions. The obtained results are validated by comparing with the previously reported and those from finite element analysis.
引用
收藏
页码：1307 / 1322
页数：16
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