Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes

被引：9
作者：
Ram, YM [1 ]
Elishakoff, I
机构：
[1] Louisiana State Univ, Dept Mech Engn, Baton Rouge, LA 70803 USA
[2] Florida Atlantic Univ, Dept Mech Engn, Boca Raton, FL 33431 USA
来源：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2004年 / 460卷 / 2046期
关键词：
inverse problems; physical parameter identification; vibrating rods; mode shapes;
D O I：
10.1098/rspa.2003.1214
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
It is shown that the cross-sectional area of a non-uniform axially vibrating rod can be reconstructed from one of its mode shapes, and that the solution, up to a scale factor, is unique. The conditions, which allow construction of a physical rod with positive smooth cross-sectional area, are given. The problem is addressed for the discrete and the continuous models of the rod. Examples demonstrate the various results.
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页码：1583 / 1596
页数：14
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