用非均匀轴向振动杆的某一振型重构其横截面积

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-06-08 DOI:10.1098/rspa.2003.1214

Y. Ram, I. Elishakoff

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引用次数: 12

摘要

结果表明，非均匀轴向振动杆的横截面积可以由其模态振型之一重构，且解在一定比例因子范围内是唯一的。给出了允许构造具有正光滑横截面积的物理棒的条件。该问题针对杆的离散模型和连续模型进行了讨论。示例演示了各种结果。

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

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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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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