文献类型：期刊文献

英文题名：Boundary layer analysis for the eigenvalues of hanging rod

作者：Liao, Jie

机构：[1]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China

年份：2012

卷号：389

期号：1

起止页码：608

外文期刊名：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000302391400050)】；

基金：This paper is suggested by Professor Joseph B. Keller, who has devoted much-time and energy on this research. The author is grateful to his hospitality and generous help during my visit in Stanford University. The research was partially supported by NNSF of China 11126082 and 11171211.

语种：英文

外文关键词：Hanging rod; Eigenvalue problem; Singular perturbation; Boundary layer analysis

摘要：The motion of a naturally straight inextensible flexible elastic hanging rod is formulated and then linearized about the straight solution. To solve this equation by separation of variables, an eigenvalue problem is derived. When the stiffness of the rod is small, the eigenvalue equation is a singular perturbation problem. This paper is devoted to solving this eigenvalue problem by boundary layer analysis when the stiffness is suitably small, especially on the analytic approximate solutions of the first several eigenvalues and eigenfunctions. The first three eigenvalues are also compared with the numerical results computed by a finite difference method. The excellent agreement shows the efficiency of the boundary layer analysis. (C) 2011 Elsevier Inc. All rights reserved.